Spacecraft Dynamics

Model dynamics of one or more spacecraft

Since R2021b

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Libraries:
Aerospace Blockset / Spacecraft / Spacecraft Dynamics

Description

The Spacecraft Dynamics block models translational and rotational dynamics of spacecraft using numerical integration. It computes the position, velocity, attitude, and angular velocity of one or more spacecraft over time. For the most accurate results, use a variable step solver with low tolerance settings (less than 1e-8). To trade off accuracy for speed, use larger tolerances, depending on your mission requirements.

You can define initial orbital states as

• A set of orbital elements.

• Position and velocity state vectors.

To propagate orbital states, the block uses the gravity model selected for the current central body. It also includes external accelerations and forces that you provide as inputs to the block. To define initial attitude states, use quaternions, direction cosine matrices (DCMs), or Euler angles.

To propagate attitude states, the block uses moments provided as inputs to the block and mass properties defined on the block.

Aerospace Blockset™ uses quaternions that are defined using the scalar-first convention.

The Spacecraft Dynamics block supports scalar and vector expansion. The block parameter and input port dimensions determine the number of the output signals and the number of spacecraft. After scalar and vector expansion, all parameters in the Orbit, Mass, and Attitude tabs and all input ports except for φθψ (Moon libration angles) and αδW (right ascension, declination, and rotation angle) input ports are defined for each spacecraft.

The size of the provided initial conditions determines the number of spacecraft being modeled. If you supply more than one value for a parameter in the Orbit, Attitude, or Mass tabs, the block outputs a constellation of satellites. Any parameter with a single provided value is expanded and applied to all the satellites in the constellation. For example, if you provide a single value for all the parameters on the block except True anomaly, which contains six values, the block creates a constellation of six satellites, varying true anomaly only.

The block applies the same expansion behavior to the block input ports. All input ports support expansion except Moon libration angles (when Central body is Moon) and Spin axis right ascension (RA) at J2000, Spin axis declination (Dec) at J2000, and Initial rotation angle at J2000 (when Central body is Custom). All other ports accept either a single value expanded to all spacecraft being modeled, or individual values applied to each spacecraft.

For more information on the coordinate systems and rotational and translational dynamics the Spacecraft Dynamics block uses, see Algorithms.

To help model the drag on spacecraft for high precision orbit propagation, the Orbit Propagator block supports atmospheric drag. Atmospheric drag affects spacecraft flying at low Earth orbit (LEO); it is less relevant further away from Earth. For the atmospheric drag equation, see Atmospheric Drag.

Examples

Getting Started with the Spacecraft Dynamics Block

Model six degree-of-freedom rigid-body dynamics of a spacecraft or constellation of spacecraft with the Spacecraft Dynamics block from the Aerospace Blockset.

Open Live Script

Developing the Apollo Lunar Module Digital Autopilot

Develop Apollo Lunar Module digital autopilot using Simulink^® and Aerospace Blockset.

Open Live Script

Analyzing Spacecraft Attitude Profiles with Satellite Scenario

Propagate orbit and attitude states in Simulink and visualize computed trajectory and attitude profile in a satellite scenario.

Open Live Script

Hohmann Transfer with the Spacecraft Dynamics Block

Model a Hohmann transfer of a spacecraft between two circular coplanar orbits.

Open Live Script

Ports

Input

F_b — Applied forces

3-element vector | numSat-by-3 array

Force applied to the spacecraft center of mass in the body frame, specified as a 3-element vector or numSat-by-3 array at the current time step. numSat is the number of spacecraft.

Dependencies

To enable this port, select the Input body forces check box.

Data Types: double

M_b — Applied moments

3-element vector | numSat-by-3 array

Moment applied to the spacecraft with respect to mass in the body frame, specified as a 3-element vector or numSat-by-3 array at the current time step. numSat is the number of spacecraft.

Dependencies

To enable this port, select the Input body moments check box.

Data Types: double

A — External acceleration

3-element vector | m-by-3 array

External acceleration to apply to the spacecraft with respect to the ICRF or fixed-frame at the current timestep, specified as a 3-element vector or m-by-3 array.

Dependencies

To enable this port, select the Input external accelerations check box.

To specify the acceleration coordinate frame, set the External acceleration coordinate frame parameter.

Data Types: double

φθψ — Moon libration angles

3-element vector

Moon libration angles for transformation between the ICRF and Moon-centric fixed-frame using the Moon-centric Principal Axis (PA) system, specified as a 3-element vector. To get these values, use the Moon Libration block.

Note

The fixed-frame used by this block when Central body is set to Moon is the Mean Earth/pole axis (ME) system. For more information, see Algorithms.

Dependencies

To enable this port:

• Set Central body to Moon.

• Select the Input Moon libration angles check box.

Data Types: double

αδW — Right ascension, declination, and rotation angle

3-element vector

Central body spin axis instantaneous right ascension, declination, and rotation angle, specified as a 3-element vector. This port is available only for custom central bodies.

Dependencies

To enable this port:

• Set Central body to Custom.

• Set Central body spin axis source to Port.

Data Types: double

m — Spacecraft mass

scalar | 1D array of size numSat

Spacecraft mass at the current timestep. numSat is the number of spacecraft.

Dependencies

To enable this port, set Mass type to Custom Variable.

Data Types: double

dm/dt — Rate of change of mass

scalar | 1D array of size numSat

Rate of change of mass (positive if accreted, negative if ablated) at the current timestep, specified as a scalar or 1D array of size numSat. numSat is the number of spacecraft.

Dependencies

To enable this port, set Mass type to Simple Variable.

Data Types: double

I — Spacecraft inertia tensor

3-by-3 array | 3-by-3-by-numSat array

Spacecraft inertia tensor, specified as a 3-by-3 array or 3-by-3-by-numSat array at the current timestep. numSat is the number of spacecraft.

Dependencies

To enable this port, set Mass type to Custom Variable.

Data Types: double

dI/dt — Rate of change of inertia tensor matrix

3-by-3 array | 3-by-3-by-numSat array

Rate of change of inertia tensor matrix, specified as a 3-by-3 array or 3-by-3-by-numSat array at the current time step. numSat is the number of spacecraft.

Dependencies

To enable this port, set Mass type to Custom Variable.

Data Types: double

V_re — Relative velocity

3-element vector | numSat-by-3 array

Relative velocity at which the mass is accreted to or ablated from the body in body-fixed axes, specified as a 3-element vector or numSat-by-3 array. numSat is the number of spacecraft.

Dependencies

To enable this port:

• Set Mass type to Custom Variable or Simple Variable.

• Select the Include mass flow relative velocity check box.

Data Types: double

ρ — Atmospheric density

scalar

Atmospheric density to calculate acceleration due to atmospheric drag.

Dependencies

To enable this port:

• Set the Propagation method parameter to Numerical (high precision).

• Set the Central Body parameter to Earth.

• Select the Include atmospheric drag check box.

• Set the Atmospheric density source parameter to Port.

Data Types: double

F107a — 81-day average Ottawa F10.7 cm solar flux

scalar

81-day average Ottawa F10.7 cm solar flux, centered on the current day specified in Start date/time. These F107 Average values correspond to the 10.7 cm radio flux at the actual distance of the Earth from the Sun. This site provides both classes of values:

https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-radio/noontime-flux/penticton/

Dependencies

To enable this port:

• Set the Propagation method parameter to Numerical (high precision).

• Set the Central Body parameter to Earth.

• Select the Include atmospheric drag check box.

• Set the Atmospheric density source parameter to Dialog.

Data Types: double

F107 — Daily Ottawa F10.7 cm solar flux

scalar

Daily Ottawa F10.7 cm solar flux, centered on the current day specified in Start date/time. The f107Daily values do not correspond to the radio flux at 1 AU. This site provides both classes of values:

https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-radio/noontime-flux/penticton/

Dependencies

To enable this port:

• Set the Propagation method parameter to Numerical (high precision).

• Set the Central Body parameter to Earth.

• Select the Include atmospheric drag check box.

• Set the Atmospheric density source parameter to Dialog.

Data Types: double

aph — Daily magnetic index information

N-by-7 array

Daily magnetic index information (aph), specified as an N-by-7 array. The magnetic index information consists of:

Daily magnetic index (AP)

3 hour AP for current time

3 hour AP for 3 hours before current time

3 hour AP for 6 hours before current time

3 hour AP for 9 hours before current time

Average of eight 3 hour AP indices from 12 to 33 hours before current time

Average of eight 3 hour AP indices from 36 to 57 hours before current time

The effects of daily magnetic index are not large or established below 80,000 m. For more information, see Limitations on NRLMSISE-00 Atmosphere Model.

Dependencies

To enable this port:

• Set the Propagation method parameter to Numerical (high precision).

• Set the Central Body parameter to Earth.

• Select the Include atmospheric drag check box.

• Set the Atmospheric density source parameter to Dialog.

Data Types: double

Flags — Variation flags

array of 23

Variation flags, specified as an array of 23, to enable or disable particular variations for the outputs. You can specify one of the following values for a field. The default value for each field is 1.

• 0.0

  Removes the value effect on the output.

• 1.0

  Applies the main and the cross-term effects of that value on the output.

• 2.0

  Applies only the cross-term effect of that value on the output.

Field	Description
Flags(1)	F10.7 effect on mean
Flags(2)	Independent of time
Flags(3)	Symmetrical annual
Flags(4)	Symmetrical semiannual
Flags(5)	Asymmetrical annual
Flags(6)	Asymmetrical semiannual
Flags(7)	Diurnal
Flags(8)	Semidiurnal
Flags(9)	Daily AP. If you set this field to -1, the block uses the entire matrix of magnetic index information (APH) instead of APH(:,1)
Flags(10)	All UT, longitudinal effects
Flags(11)	Longitudinal
Flags(12)	UT and mixed UT, longitudinal
Flags(13)	Mixed AP, UT, longitudinal
Flags(14)	Terdiurnal
Flags(15)	Departures from diffusive equilibrium
Flags(16)	All exospheric temperature variations
Flags(17)	All variations from 120,000 meter temperature (TLB)
Flags(18)	All lower thermosphere (TN1) temperature variations
Flags(19)	All 120,000 meter gradient (S) variations
Flags(20)	All upper stratosphere (TN2) temperature variations
Flags(21)	All variations from 120,000 meter values (ZLB)
Flags(22)	All lower mesosphere temperature (TN3) variations
Flags(23)	Turbopause scale height variations

Dependencies

To enable this port:

• Set the Propagation method parameter to Numerical (high precision).

• Set the Central Body parameter to Earth.

• Select the Include atmospheric drag check box.

• Set the Atmospheric density source parameter to Dialog.

• Set the Flags source parameter to Port.

Data Types: double

C_d — Atmospheric drag coefficient

scalar | vector of size numSat

Atmospheric drag coefficient, specified as a scalar or vector of size numSat.

Dependencies

To enable this port:

• Set the Propagation method parameter to Numerical (high precision).

• Set the Central Body parameter to Earth.

• Select the Include atmospheric drag check box.

• Set the Drag coefficient source parameter to Port.

Data Types: double

A_d — Atmospheric drag area

scalar | vector of size numSat

Atmospheric drag area, specified as a scalar or vector of size numSat.

Dependencies

To enable this port:

• Set the Propagation method parameter to Numerical (high precision).

• Set the Central Body parameter to Earth.

• Select the Include atmospheric drag check box.

• Set the Drag area source parameter to Port.

Data Types: double

Output

X — Position of spacecraft

3-element vector | numSat-by-3 array

Position of the spacecraft with respect to the ICRF or fixed-frame outport coordinate frame, returned as a 3-element vector or numSat-by-3 array at the current time step. numSat is the number of spacecraft.

Dependencies

• To change the output coordinate frame for this port, set the State vector output coordinate frame parameter.

• The size of the initial conditions provided in the Mass, Orbit, or Attitude tab control the port dimension.

Data Types: double

V — Velocity

3-element vector | numSat-by-3 array

Velocity of the spacecraft with respect to the ICRF or fixed-frame outport coordinate frame, returned as a 3-element vector or numSat-by-3 array at the current time step. numSat is the number of spacecraft.

Dependencies

• To change the output coordinate frame for this port, set the State vector output coordinate frame parameter.

• The size of the initial conditions provided in the Mass, Orbit, or Attitude tab control the port dimension.

Data Types: double

A — Total inertial acceleration

3-element vector | numSat-by-3 array

Total inertial acceleration of the spacecraft with respect to the ICRF, returned as a 3-element vector or numSat-by-3 array at the current timestep. numSat is the number of spacecraft.

Dependencies

• To enable this port, select the Output total inertial acceleration check box

• The size of the initial conditions provided in the Orbit tab control the port dimension.

Data Types: double

q_body2icrf — Spacecraft attitude quaternion

4-element quaternion | numSat-by-4 array

Spacecraft attitude quaternion, returned as a (scalar first) quaternion rotation from the body axis to the outport frame, as a 4-element quaternion, or numSat-by-4 array (scalar first) at the current time step. numSat is the number of spacecraft.

Dependencies

The coordinate frame and attitude format of this port depends on these settings:

• To specify the attitude reference coordinate frame, set the Attitude reference coordinate frame parameter.

• Set Attitude representation to Quaternion.

Data Types: double

DCM — Spacecraft attitude direction cosine matrix

3-by-3 array | numSat-by-3-by-3 array

Spacecraft attitude direction cosine matrix (DCM), returned as a3-by-3 array or numSat-by-3-by-3 array. numSat is the number of spacecraft.

Dependencies

The coordinate frame and attitude format of this port depends on these settings:

• To specify the attitude reference coordinate frame, set the Attitude reference coordinate frame parameter.

• Set Attitude representation to DCM.

Data Types: double

R1,R2,R3 — Spacecraft attitude Euler angles

3-element vector | numSat-by-3 array

Spacecraft attitude Euler angles, returned as a 3-element vector or numSat-by-3 array. numSat is the number of spacecraft.

Dependencies

The coordinate frame and attitude format of this port depend on these settings:

• To specify the attitude reference coordinate frame, set the Attitude reference coordinate frame parameter.

• Set Attitude representation to Euler angles.

Data Types: double

ω — Angular rate of spacecraft

3-element vector | numSat-by-3 array

Angular rate of the spacecraft relative to the attitude reference coordinate frame, returned as a 3-element vector or numSat-by-3 array, expressed as body axis angular rates PQR. numSat is the number of spacecraft.

Dependencies

The attitude reference coordinate frame depends on the Attitude reference coordinate frame parameter.

Data Types: double

dω/dt — Body angular acceleration

3-element array | numSat-by-3 array

Body angular acceleration relative to the ICRF frame, returned as a 3-element array or numSat-by-3 array. numSat is the number of spacecraft.

Dependencies

To enable this port, select the Output total inertial angular acceleration check box.

The attitude reference coordinate frame depends on the Attitude reference coordinate frame parameter.

Data Types: double

q_icrf2ff — Coordinate system transformation

4-element array

Coordinate system transformation between the ICRF and fixed-frame coordinate system at the current timestep, returned as a 4-element array.

Dependencies

To enable this port, select the Output quaternion (ICRF to Fixed-frame) check box.

Data Types: double

t_utc — Time at current time step

scalar | 6-element array

Time at current time step, returned as a:

• scalar — If you specify the Start data/time parameter as a Julian date.

• 6-element array — If you specify the Start data/time parameter as a Gregorian date with six elements (year, month, day, hours, minutes, seconds).

This value equals the Start date/time parameter value plus the elapsed simulation time.

Dependencies

To enable this parameter, select the Output current date/time (UTC Julian date) check box.

Data Types: double

Fuel Status — Fuel status

scalar | numSat-element array

Fuel tank status at the current timestep, returned as a scalar or numSat-element array, returned as:

• 1 — Tank is full.

• 0 — Tank is not full or empty.

• -1 — Tank is empty.

numSat is the number of spacecraft.

Dependencies

To enable this port:,

• Set Mass type to Simple Variable.

• Select the Output fuel tank status check box.

Data Types: double

Parameters

Main

Input body forces — Option to enable external forces

on (default) | off

To enable external forces to be included in the integration of the spacecraft equations of motion in the body frame, select this check box. Otherwise, clear this check box.

Programmatic Use

Block Parameter: forcesin

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Input body moments — Option to enable external moments

on (default) | off

To enable external moments to be included in the integration of the spacecraft equations of motion in the body frame, select this check box. Otherwise, clear this check box.

Programmatic Use

Block Parameter: momentsIn

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Input external accelerations — Option to input additional force accelerations

off (default) | on

To enable additional external accelerations to be included in the integration of the spacecraft equations of motion, select this check box. Otherwise, clear this check box.

Programmatic Use

Block Parameter: accelIn

Type: character vector

Values: 'off' | 'on'

Default: 'off'

External acceleration coordinate frame — Frame for acceleration input port

ICRF (default) | Fixed-frame

Frame for acceleration input port A, specified as ICRF or Fixed-frame.

Dependencies

To enable this parameter, select the Input external accelerations check box.

Programmatic Use

Block Parameter: accelFrame

Type: character vector

Values: 'ICRF' | 'Fixed-frame'

Default: 'ICRF'

State vector output coordinate frame — Position and velocity state output port coordinate frame

ICRF (default) | Fixed-frame

Position and velocity state output port coordinate frame setup, specified as ICRF or Fixed-frame.

Programmatic Use

Block Parameter: outportFrame

Type: character vector

Values: 'ICRF' | 'Fixed-frame'

Default: 'ICRF'

Data Types: string

Output total inertial acceleration — Option to enable total acceleration port

off (default) | on

Enable the total acceleration output computed by the block with respect to the ICRF or fixed-frame outport coordinate frame. This acceleration includes all external accelerations, forces, and internal environmental accelerations that act on the spacecraft.

Note

Do not use this port as part of a simulation loop (in other words, do not feed this output back into the block).

Tunable: Yes

Dependencies

To change the output coordinate frame for this port, set the State vector output coordinate frame parameter.

Programmatic Use

Block Parameter: AccelOut

Type: character vector

Values: 'on' | 'off'

Default: 'off'

Data Types: string

Start date/time (UTC Julian date) — Initial start time for simulation

juliandate (2020, 1, 1, 12, 0, 0) (default) | valid scalar Julian date | valid Gregorian date including year, month, day, hours, minutes, seconds as 1D or 6-element array for Gregorian dates

Initial start date and time of simulation, specified as a Julian or Gregorian date. The block defines initial conditions using this value.

Tip

To calculate the Julian date, use the juliandate function.

Tunable: Yes

Dependencies

The data format for this parameter is controlled by the Time format parameter.

Programmatic Use

Block Parameter: startDate

Type: character vector

Values: 'juliandate(2020, 1, 1, 12, 0, 0)' | valid scalar Julian date | valid Gregorian date including year, month, day, hours, minutes, seconds as 1D or 6-element array

Default: 'juliandate(2020, 1, 1, 12, 0, 0)'

Output current date/time (UTC Julian date) — Option to add output port t_utc

on (default) | off

To output the current date or time, select this check box. Otherwise, clear this check box.

Dependencies

The data format for this parameter is controlled by the Time format parameter.

Programmatic Use

Block Parameter: dateOut

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Action for out-of-range input — Out-of-range block behavior

Warning (default) | Error | None

Out-of-range block behavior action. Specify one of these options.

Action	Description
None	No action.
Warning	Warning displays in the MATLAB® Command Window. Model simulation continues.
Error (default)	MATLAB returns an exception. Model simulation stops.

Programmatic Use

Block Parameter: action

Type: character vector

Values: 'None' | 'Warning' | 'Error'

Default: 'Warning'

Mass

Mass type — Spacecraft mass type

Fixed (default) | Simple Variable | Custom Variable

Spacecraft mass type, specified as:

• Fixed — Mass and inertia are constant throughout the simulation.

• Simple Variable — Mass and inertia vary linearly as a function of mass rate.

• Custom Variable — Instantaneous mass, inertia, and inertia rate are inputs to the block.

Programmatic Use

Block Parameter: massType

Type: character vector

Values: 'Fixed' | 'Simple Variable' | 'Custom Variable'

Default: 'Fixed'

Data Types: double

Mass — Initial mass of rigid body spacecraft

4.0 (default) | scalar | vector of size numSat

Initial mass of rigid body spacecraft, specified as scalar or vector of size numSat. numSat is the number of spacecraft.

Tunable: Yes

Dependencies

To enable this parameter, set the Mass type parameter to either Fixed or Simple variable.

Programmatic Use

Block Parameter: mass

Type: character vector

Values: scalar | vector of size numSat

Default: '4.0'

Empty mass — Spacecraft empty mass

3.5 (default) | scalar | vector of size numSat

Spacecraft empty (dry) mass, specified as a scalar or vector of size numSat. numSat is the number of spacecraft.

Tunable: Yes

Dependencies

To enable this parameter, set Mass type to Simple variable.

Programmatic Use

Block Parameter: emptyMass

Type: character vector

Values: 1D array of size numSat | 1D array of size numSat

Default: '3.5'

Data Types: double

Full mass — Spacecraft full mass

4.0 (default) | scalar | vector of size numSat

Spacecraft full (wet) mass, specified as a scalar or vector of size numSat. numSat is the number of spacecraft.

Tunable: Yes

Dependencies

To enable this parameter, set Mass type to Simple variable.

Programmatic Use

Block Parameter: fullMass

Type: character vector

Values: scalar | vector of size numSat

Default: '4.0'

Data Types: double

Inertia tensor — Inertia tensor matrix

[0.2273, 0, 0; 0 0.2273 0; 0 0 .0040] (default) | 3-by-3 array | 3-by-3-by-numSat array

Initial inertia tensor matrix of the spacecraft, specified, as a 3-by-3 array for a single spacecraft or a 3-by-3-by-numSat array for multiple spacecraft.

Tunable: Yes

Dependencies

To enable this parameter, set Mass type to Fixed.

Programmatic Use

Block Parameter: inertia

Type: character vector

Values: '[0.2273, 0, 0; 0 0.2273 0; 0 0 .0040]' | 3-by-3 array | 3-by-3-by-numSat array

Default: '[0.2273, 0, 0; 0 0.2273 0; 0 0 .0040]'

Empty inertia tensor — Empty inertia tensor matrix

[0.1989, 0, 0; 0 0.1989 0; 0 0 .0035] (default) | 3-by-3 array | 3-by-3-by-numSat array

Empty (dry) inertia tensor matrix, specified as a 3-by-3 array for a single spacecraft or a 3-by-3-by-numSat array for multiple spacecraft.

Tunable: Yes

Dependencies

To enable this parameter, set Mass type to Simple variable.

Programmatic Use

Block Parameter: emptyInertia

Type: character vector

Values: 3-by-3 array | 3-by-3-by-numSat array

Default: [0.1989, 0, 0; 0 0.1989 0; 0 0 .0035]

Full inertia tensor — Full inertia tensor matrix

[0.2273, 0, 0; 0, 0.2273, 0; 0, 0, .0040] (default) | 3-by-3 array | 3-by-3-by-numSat array

Full (wet) inertia tensor matrix, specified as a 3-by-3 array for a single spacecraft or a 3-by-3-by-numSat array for multiple spacecraft.

Tunable: Yes

Dependencies

To enable this parameter, set Mass type to Simple variable.

Programmatic Use

Block Parameter: fullInertia

Type: character vector

Values: 3-by-3 array | 3-by-3-by-numSat array

Default: [0.2273, 0, 0; 0, 0.2273, 0; 0, 0, .0040]

Include mass flow relative velocity — Option to enable mass flow velocity

off (default) | on

To enable mass flow velocity to the block, select this check box. The mass flow velocity is the relative velocity in the body frame at which the mass is accreted or ablated. To disable mass flow velocity to the block, clear this check box.

Dependencies

To enable this parameter, set Mass type to Simple variable or Custom variable.

Programmatic Use

Block Parameter: useMassFlowRelativeVelocity

Type: character vector

Values: 'on' | 'off'

Default: 'off'

Data Types: double

Limit mass flow when mass is empty or full — Option to limit mass flow

on (default) | off

To limit the mass flow when the spacecraft mass is full or empty, select this check box. Otherwise, clear this check box.

Dependencies

To enable this parameter, set Mass type to Simple variable.

Programmatic Use

Block Parameter: limitMassFlow

Type: character vector

Values: 'on' | 'off'

Default: 'on'

Data Types: double

Output fuel tank status — Option to enable fuel tank status

on (default) | off

To enable fuel tank status, select this check box. Otherwise, clear this check box.

Dependencies

To enable this parameter, set Mass type to Simple variable.

Programmatic Use

Block Parameter: outputFuelStatus

Type: character vector

Values: 'on' | 'off'

Default: 'on'

Data Types: double

Orbit

Define the initial states of the spacecraft.

Initial state format — Input method for initial states of orbit

Orbital elements (default) | ICRF state vector | Fixed-frame state vector

Input method for initial states of orbit, specified as Orbital elements, ICRF state vector, or Fixed-frame state vector.

Programmatic Use

Block Parameter stateFormatNum when propagator is set to High precision (numerical)

Type: character vector

Values: 'Orbital elements' | 'Orbital elements' | 'ICRF state vector' | 'Fixed-frame state' when propagator is set to 'High precision (numerical)'

Default: 'Orbital elements'

Orbit type — Orbit classification

Keplerian (default) | Elliptical equatorial | Circular | Circular equatorial

Orbit classification, specified as:

• Keplerian — Model elliptical, parabolic, and hyperbolic orbits using six standard Keplerian orbital elements.

• Elliptical equatorial — Fully define an equatorial orbit, where inclination is 0 or 180 degrees and the right ascension of the ascending node is undefined.

• Circular — Define a circular orbit, where eccentricity is 0 and the argument of periapsis is undefined. To fully define a circular orbit, select Circular equatorial.

• Circular equatorial — Fully define a circular orbit, where eccentricity is 0 and the argument of periapsis is undefined.

Dependencies

To enable this parameter, set Initial state format to Orbital elements.

Programmatic Use

Block Parameter: orbitType

Type: character vector

Values: 'Keplerian' | 'Elliptical equatorial' | 'Circular inclined' | 'Circular equatorial'

Default: 'Keplerian'

Semi-major axis — Half of major axis of ellipse

6786000 (default) | scalar | 1D array of size numSat

Half of ellipse major axis, specified as a 1D array of size numSat. numSat is the number of spacecraft.

• For parabolic orbits, this block interprets this parameter as the periapsis radius (distance from periapsis to the focus point of orbit).

• For hyperbolic orbits, this block interprets this parameter as the distance from periapsis to the hyperbola center.

Tunable: Yes

Dependencies

To enable this parameter, set Initial state format to Orbital elements.

Programmatic Use

Block Parameter: semiMajorAxis

Type: character vector

Values: scalar | 1D array of size numSat

Default: '6786000'

Eccentricity — Deviation of orbit

0.01 (default) | scalar | value between 0 and 1, or greater than 1 for Keplerian orbit type | 1D array of size numSat

Deviation of the orbit from a perfect circle, specified as a scalar or 1D array of size numSat. numSat is the number of spacecraft.

If Orbit type is set to Keplerian, this value can be:

• 1 for parabolic orbit

• Greater than 1 for hyperbolic orbit

Tunable: Yes

Dependencies

To enable this parameter:

• Set Initial state format to Orbital elements.

• Set Orbit type to Keplerian or Elliptical equatorial.

Programmatic Use

Block Parameter: eccentricity

Type: character vector

Values: 0.01 | scalar | value between 0 and 1, or greater than 1 for Keplerian orbit type | 1D array of size numSat

Default: '0.01'

Inclination — Tilt angle of orbital plane

50 (default) | scalar | 1D array of size numSat | degrees between 0 and 180 | radians between 0 and pi

Vertical tilt of the ellipse with respect to the reference plane measured at the ascending node, specified as a scalar or 1D array of size numSat, in specified units. numSat is the number of spacecraft.

Tunable: Yes

Dependencies

To enable this parameter:

• Set Initial state format to Orbital elements

• Set Orbit type to Keplerian or Circular inclined

Programmatic Use

Block Parameter: inclination

Type: character vector

Values: 50 | scalar | 1D array of size numSat | degrees between 0 and 180 | radians between 0 and pi

Default: '50'

RAAN — Angular distance in equatorial plane

95 (default) | scalar value between 0 and 360 | 1D array of size numSat

Right ascension of ascending node (RAAN), specified as a value between 0 and 360, specified as a scalar or 1D array of size numSat, in specified units. numSat is the number of spacecraft. RAAN is the angular distance along the reference plane from the International Celestial Reference Frame (ICRF) x-axis to the location of the ascending node — the point at which the spacecraft crosses the reference plane from south to north.

Tunable: Yes

Dependencies

To enable this parameter:

• Set Initial state format to Orbital elements.

• Set Orbit type to Keplerian or Circular inclined.

Programmatic Use

Block Parameter: raan

Type: character vector

Values: '95' | scalar value between 0 and 360 | 1D array of size numSat

Default: '95'

Argument of periapsis — Angle from spacecraft ascending node to periapsis

93 (default) | value between 0 and 360 | 1D array of size numSat

Angle from the spacecraft ascending node to periapsis (closest point of orbit to the central body), specified as a 1D array of size numSat, in specified units. numSat is the number of spacecraft.

Tunable: Yes

Dependencies

To enable this parameter:

• Set Initial state format to Orbital elements

• Set Orbit type to Keplerian

Programmatic Use

Block Parameter: argPeriapsis

Type: character vector

Values: 93 | scalar value between 0 and 360 | 1D array of size numSat

Default: '93'

True anomaly — Angle between periapsis and initial position of spacecraft

203 (default) | scalar value between 0 and 360 | 1D array of size numSat

Angle between periapsis (closest point of orbit to the central body) and the initial position of spacecraft along its orbit at Start date/time, specified as a scalar or 1D array of size numSat, in specified units. numSat is the number of spacecraft.

Tunable: Yes

Dependencies

To enable this parameter:

• Set Initial state format to Orbital elements.

• Set Orbit type to Keplerian or Elliptical inclined.

Programmatic Use

Block Parameter: trueAnomaly

Type: character vector

Values: '203' | scalar value between 0 and 360 | 1D array of size numSat

Default: '203'

Argument of latitude — Angle between ascending node and initial position of spacecraft

200 (default) | scalar | value between 0 and 360 | 1D array of size numSat

Angle between the ascending node and the initial position of spacecraft along its orbit at Start date/time, specified as a scalar or 3-element vector or 1D array of size numSat, in specified units. numSat is number of spacecraft.

Tunable: Yes

Dependencies

To enable this parameter:

• Set Initial state format to Orbital elements.

• Set Orbit Type to Circular inclined.

Programmatic Use

Block Parameter: argLat

Type: character vector

Values: '200' | scalar value between 0 and 360 | 1D array of size numSat

Default: '200'

Longitude of periapsis — Angle between ICRF x-axis and eccentricity vector

100 (default) | scalar | value between 0 and 360 | 1D array of size numSat

Angle between the ICRF x-axis and the eccentricity vector, specified as a scalar or 3-element vector or 1D array of size numSat, in specified units. numSat is the number of spacecraft

Tunable: Yes

Dependencies

To enable this parameter:

• Set Initial state format to Orbital elements.

• Set Orbit type to Elliptical equatorial.

Programmatic Use

Block Parameter: lonPeriapsis

Type: character vector

Values: 100 | scalar value between 0 and 360 | 1D array of size numSat

Default: '100'

True longitude — Angle between ICRF x-axis and initial position of spacecraft

150 (default) | scalar | value between 0 and 360 | 1D array of size numSat | numSat-by-3 vector

Angle between the ICRF x-axis and the initial position of spacecraft along its orbit at Start date/time, specified as a scalar or 1D array of size numSat or a numSat-by-3 vector, in specified units. numSat is the number of spacecraft.

Tunable: Yes

Dependencies

To enable this parameter:

• Set Initial state format to Orbital elements.

• Set Orbit type to Circular equatorial.

Programmatic Use

Block Parameter: trueLon

Type: character vector

Values: '150' | scalar value between 0 and 360 | 1D array of size numSat | numSat-by-3 vector

Default: '150'

ICRF position — Cartesian position vector of spacecraft

[3649700.0 3308200.0 -4676600.0] (default) | 3-element vector | | numSat-by-3 array

Cartesian position vector of spacecraft in ICRF coordinate system at Start date/time, specified as a 3-element vector for single spacecraft or a numSat-by-3 array for multiple spacecraft. numSat is the number of spacecraft.

Tunable: Yes

Dependencies

To enable this parameter, set Initial state format to ICRF state vector.

Programmatic Use

Block Parameter: inertialPosition

Type: character vector

Values: [3649700.0 3308200.0 -4676600.0] | 3-element vector | numSat-by-3 array

Default: '[3649700.0 3308200.0 -4676600.0]'

ICRF velocity — Cartesian velocity vector of spacecraft

[-2750.8 6666.4 2573.4] (default) | 3-element vector | numSat-by-3 array

Cartesian velocity vector of spacecraft in ICRF coordinate system at Start date/time, specified as a 3-element vector for single spacecraft or a numSat-by-3 array for multiple spacecraft. numSat is the number of spacecraft.

Tunable: Yes

Dependencies

To enable this parameter, set Initial state format to ICRF state vector.

Programmatic Use

Block Parameter: inertialVelocity

Type: character vector

Values: [-2750.8 6666.4 2573.4] | 3-element vector | 2-D array of size numSat-by-3 array

Default: '[-2750.8 6666.4 2573.4]'

Fixed-frame position — Position vector of spacecraft

[-4142689.0 -2676864.7 -4669861.6] (default) | 3-element vector | numSat-by-3 array

Cartesian position vector of spacecraft in fixed-frame coordinate system at Start date/time, specified as a 3-element vector for single spacecraft or a numSat-by-3 array for multiple spacecraft. numSat is the number of spacecraft.

Tunable: Yes

Dependencies

To enable this parameter, set Initial state format to Fixed-frame state vector.

Programmatic Use

Block Parameter: fixedPosition

Type: character vector

Values: '[-4142689.0 -2676864.7 -4669861.6]' | 3-element vector for single spacecraft | numSat-by-3 array

Default: '[-2750.8 6666.4 2573.4]'

Fixed-frame velocity — Velocity vector of spacecraft

[1452.7 -6720.7 2568.1] (default) | 3-element vector | numSat-by-3 array

Cartesian velocity vector of spacecraft in fixed-frame coordinate system at Start date/time, specified as a 3-element vector for single spacecraft or a numSat-by-3 array for multiple spacecraft. numSat is the number of spacecraft.

Tunable: Yes

Dependencies

To enable this parameter, set Initial state format to Fixed-frame state vector.

Programmatic Use

Block Parameter: fixedVelocity

Type: character vector

Values: '[1452.7 -6720.7 2568.1]' | 3-element vector | numSat-by-3 array

Default: '[1452.7 -6720.7 2568.1]'

Attitude

Attitude reference coordinate frame — Attitude and angular rate coordinate frame

ICRF (default) | Fixed-frame | NED | LVLH

Attitude and angular rate coordinate frame with respect to the attitude and angular rate initial conditions, specified as:

• ICRF

• Fixed-frame

• NED

• LVLH

Programmatic Use

Block Parameter: attitudeFrame

Type: character vector

Values: 'ICRF' | 'Fixed-frame' | 'NED' | 'LVLH'

Default: 'ICRF'

Data Types: string

Attitude representation — Orientation format

Quaternion (default) | DCM | Euler angles

Orientation format for spacecraft attitude (initial condition and output port), specified as Quaternion, DCM, or Euler angles.

Programmatic Use

Block Parameter: attitudeFrame

Type: character vector

Values: 'Quaternion' | 'DCM' | 'Euler angles'

Default: 'Quaternion'

Data Types: double

Initial body attitude — Spacecraft initial attitude

[1, 0, 0, 0] (default) | 4-element vector | numSat-by-4 array | 3-by-3 array | numSat-by-3-by-3 array

Spacecraft initial attitude (orientation) of the spacecraft provided as either a quaternion, DCM, or Euler angle set with respect to Attitude representation.

Tunable: Yes

Dependencies

This parameter name and value format changes depending on the Attitude representation parameter.

Parameter Name	Attitude Representation Setting	Value Format
Initial quaternion	Quaternion	4-element vector numSat-by-4 array
Initial DCM	DCM	3-by-3 array numSat-by-3-by-3 array
Initial Euler angles	Euler angles	3-element vector numSat-by-3 array

Programmatic Use

Block Parameter: attitude

Type: character vector

Values: 4-element vector | numSat-by-4 array | 3-by-3 array | numSat-by-3-by-3 array | 3-element array | numSat-by-3 array

Default: '[1, 0, 0, 0]'

Data Types: double

Angle rotation order — Angle rotation order

ZYX (default) | ZYX | ZYZ | ZXY | ZXZ | YXZ | YXY | YZX | YZY | XYZ | XYX | XZY | XZX

Rotation angle sequence for Euler angle attitude representation.

Tunable: Yes

Dependencies

To enable this parameter, set Attitude representation to Euler angles.

Programmatic Use

Block Parameter: rotationOrder

Type: character vector

Values: 'ZYX' | 'ZYZ' |'ZXY' | 'ZXZ' | 'YXZ' | 'YXY' | 'YZX' | 'YZY' | 'XYZ' | 'XYX' | 'XZY' | 'XZX'

Default: 'ZYX'

Data Types: double

Initial body angular rates PQR — Initial body-fixed angular rates

[0, 0, 0] (default) | 3-element vector | numSat-by-3 array

Initial body-fixed angular rates (PQR) with respect to Attitude reference coordinate frame.

Tunable: Yes

Programmatic Use

Block Parameter: attitudeRate

Type: character vector

Values: | 3-element vector | numSat-by-3 array

Default: [0, 0, 0]

Data Types: double

Output total inertial angular acceleration — Option to enable total vehicle acceleration

off (default) | on

Enable output total vehicle acceleration computed by the block with respect to the ICRF attitude reference coordinate frame. This acceleration includes all moments that act on the spacecraft.

Tunable: Yes

Programmatic Use

Block Parameter: angAccelOut

Type: character vector

Values: 'on' | 'off'

Default: 'off'

Data Types: string

Include gravity gradient torque — Option to enable gravity gradient torque

on (default) | off

Select this check box to enable the use of the gravity gradient torque in the block rotational dynamics equations. Otherwise, clear this check box.

Tunable: Yes

Programmatic Use

Block Parameter: angAccelOut

Type: character vector

Values: 'on' | 'off'

Default: 'on'

Data Types: double

Central Body

Central body — Celestial body around which spacecraft orbits

Earth (default) | Moon | Mercury | Venus | Mars | Jupiter | Saturn | Uranus | Neptune | Custom

Celestial body, specified as Earth, Moon, Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune, or Custom, around which the spacecraft defined in the Orbit tab orbits.

Programmatic Use

Block Parameter: centralBody

Type: character vector

Values: 'Earth' | 'Moon' |'Mercury' | 'Venus' | 'Mars' | 'Jupiter' | 'Saturn' | 'Uranus' | 'Neptune' | 'Custom' |

Default: 'Earth'

Gravitational potential model — Gravity model for central body

Spherical harmonics when Central body set to Earth, Moon, Mars, or Custom, Oblate ellipsoid when Central body set to Mercury, Venus, Jupiter, Saturn, Uranus, or Neptune (default) | Point-mass | Oblate ellipsoid (J2)

Control the gravity model for the central body by specifying as Spherical harmonics, Point-mass, or Oblate ellipsoid (J2).

Dependencies

Available options are based on Central body settings.

Earth, Moon, Mars, or Custom	Mercury, Venus, Jupiter, Saturn, Uranus, or Neptune
Spherical harmonics	Oblate ellipsoid (J2)
Point-mass	Point-mass
Oblate ellipsoid (J2)	—

Programmatic Use

Block Parameter: gravityModel when centralBody set to 'Earth', 'Moon', 'Mars', or 'Custom' | gravityModelnoSH when centralBody set to Mercury, Venus, Jupiter, Saturn, Uranus, or Neptune

Type: character vector

Values: 'Spherical harmonics' | 'Point-mass' | 'Oblate ellipsoid (J2)' when centralBody set to 'Earth', 'Moon', 'Mars', or 'Custom'; 'Point-mass' | 'Oblate ellipsoid (J2)' when centralBody set to Mercury, Venus, Jupiter, Saturn, Uranus, or Neptune

Default: 'Spherical harmonics' when centralBody set to 'Earth', 'Moon', 'Mars', or 'Custom'; 'Oblate ellipsoid (J2)' when centralBody set to Mercury, Venus, Jupiter, Saturn, Uranus, or Neptune

Spherical harmonic model — Spherical harmonic model

EGM2008 for Central body set to Earth, LP-100K for Central body set to Moon, GMM2B for Central body set to Mars, (default) | EGM96 | EIGEN-GL04C | LP-165P

Spherical harmonic gravitational potential model, specified according to the specified Central body.

Dependencies

Available options are based on Central body settings:

Central body	Spherical Harmonic Model Option
Earth	EGM2008, EGM96, or EIGEN-GL04C
Moon	LP-100K or LP-165P
Mars	GMM2B

Programmatic Use

Block Parameter: 'earthSH' when centralBody set to 'Earth' | 'moonSH' when centralBody set to 'Moon' | 'marsSH' when centralBody set to 'Mars'

Type: character vector

Values: 'EGM2008' | 'EGM96' | 'EIGEN-GL04C' when centralBody set to 'earthSH'; 'LP-100K' | 'LP-165P' when centralBody set to 'moonSH'; 'GMM2B' when centralBody set to 'marsSH'

Default: 'Spherical harmonics'

Rotational rate — Rotational rate

4.06124975e-3 (default) | scalar

Rotational rate of a custom central body, specified as a scalar.

Dependencies

To enable this parameter, set Central body to Custom.

Programmatic Use

Block Parameter: 'customOmega'

Type: character vector

Values: '4.06124975e-3' | scalar

Default: '4.06124975e-3'

Data Types: double

Spherical harmonic coefficient file — Harmonic coefficient MAT-file

aerogmm2b.mat (default) | harmonic coefficient MAT-file

Harmonic coefficient MAT-file that contains definitions for a custom planetary model, specified as a character vector or string.

This file must contain these variables:

Variable	Description
Re	Scalar of planet equatorial radius in meters (m).
GM	Scalar of planetary gravitational parameter in meters cubed per second squared (m3/s2) .
degree	Scalar of maximum degree.
C	(degree+1)-by-(degree+1) matrix containing normalized spherical harmonic coefficients matrix, C.
S	(degree+1)-by-(degree+1) matrix containing normalized spherical harmonic coefficients matrix, S.

Dependencies

To enable this parameter:

• SetCentral body to Custom.

• Set Gravitational potential model to Spherical harmonics.

Programmatic Use

Block Parameter: shFile

Type: character vector

Values: 'aerogmm2b.mat' | harmonic coefficient MAT-file

Default: 'aerogmm2b.mat'

Degree — Degree of harmonic model

120 (default) | scalar | maximum of 2159

Degree of harmonic model, specified as a scalar.

Planet Model	Recommended Degree	Maximum Degree
EGM2008	120	2159
EGM96	70	360
LP100K	60	100
LP165P	60	165
GMM2B	60	80
EIGENGL04C	70	360

Dependencies

To enable this parameter:

• Set Central body to Earth, Moon, Mars, or Custom.

• Set Gravitational potential model to Spherical harmonics.

Programmatic Use

Block Parameter: shDegree

Type: character vector

Values: '80' | scalar

Default: '80'

Use Earth orientation parameters (EOPs) — Option to use Earth orientation parameters

on (default) | off

Select this check box to use Earth orientation parameters for the transformation between the ICRF and fixed-frame coordinate systems. Otherwise, clear this check box.

Dependencies

To enable this parameter, set Central body to Earth.

Programmatic Use

Block Parameter: useEOPs

Type: character vector

Values: 'on' | 'off'

Default: 'on'

IERS EOP data file — Earth orientation data

aeroiersdata.mat (default) | MAT-file

Custom list of Earth orientation data, specified in a MAT-file.

Dependencies

To enable this parameter:

• Select the Use Earth orientation parameters (EOPs) check box.

• Set Central body to Earth.

Programmatic Use

Block Parameter: eopFile

Type: character vector

Values: 'aeroiersdata.mat' | MAT-file

Default: 'aeroiersdata.mat'

Input Moon libration angles — Moon libration Euler angle rate

off (default) | on

To specify Euler libration angles (φ θ ψ) for Moon orientation, select this check box.

Dependencies

To enable this parameter, set Central body to Moon.

Programmatic Use

Block Parameter: useMoonLib

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Output quaternion (ICRF to Fixed-frame) — Option to add output transformation quaternion port

off (default) | on

To add output transformation quaternion port for the quaternion transformation from the ICRF to the fixed-frame coordinate system, select this check box. Otherwise, clear this check box.

Programmatic Use

Block Parameter: outputTransform

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Central body spin axis source — Central body spin source

Port (default) | Dialog

Central body spin axis source, specified as Port or Dialog. The block uses the spin axis to calculate the transformation from the ICRF to the fixed-frame coordinate system for the custom central body.

Dependencies

To enable this parameter, set Central body to Custom.

Programmatic Use

Block Parameter: cbPoleSrc

Type: character vector

Values: 'Port' | 'Dialog'

Default: 'Port'

Spin axis right ascension (RA) at J2000 — Right ascension of central body spin axis at J2000

317.68143 (default) | double scalar

Right ascension of central body spin axis at J2000 (2451545.0 JD, 2000 Jan 1 12:00:00 TT), specified as a double scalar.

Tunable: Yes

Dependencies

To enable this parameter:

• Set Central body to Custom.

• Set Central body spin axis source to Dialog.

Programmatic Use

Block Parameter: cbRA

Type: character vector

Values: '317.68143' | double scalar

Default: '317.68143'

Spin axis RA rate (deg/century) — Right ascension rate of central body spin axis

-0.1061 (default) | double scalar

Right ascension rate of the central body spin axis, specified as a double scalar, in specified angle units/century.

Tunable: Yes

Dependencies

To enable this parameter:

• Set Central body to Custom.

• Set Central body spin axis source to Dialog.

Programmatic Use

Block Parameter: cbRARate

Type: character vector

Values: '-0.1061' | double scalar

Default: '-0.1061'

Spin axis declination (Dec) at J2000 — Declination of central body spin axis at J2000

52.88650 (default) | double scalar

Declination of the central body spin axis at J2000 (2451545.0 JD, 2000 Jan 1 12:00:00 TT), specified as a double scalar.

Tunable: Yes

Dependencies

To enable this parameter:

• Set Central body to Custom.

• Set Central body spin axis source to Dialog.

Programmatic Use

Block Parameter: cbDec

Type: character vector

Values: '52.88650' | double scalar

Default: '52.88650'

Spin axis Dec rate (deg/century) — Declination rate of central body spin axis

-0.0609 (default) | double scalar

Declination rate of the central body spin axis, specified as a double scalar, in specified angle units/century.

Tunable: Yes

Dependencies

To enable this parameter:

• Set Central body to Custom.

• Set Central body spin axis source to Dialog.

Programmatic Use

Block Parameter: cbDecRate

Type: character vector

Values: '-0.0609' | double scalar

Default: '-0.0609'

Initial rotation angle at J2000 — Rotation angle of central body x-axis

176.630 (default) | double scalar

Rotation angle of the central body x axis with respect to the ICRF x-axis at J2000 (2451545.0 JD, 2000 Jan 1 12:00:00 TT), specified as a double scalar, in specified angle units.

Tunable: Yes

Dependencies

To enable this parameter:

• Set Central body to Custom.

• Set Central body spin axis source to Dialog.

Programmatic Use

Block Parameter: cbRotAngle

Type: character vector

Values: '176.630' | double scalar

Default: '176.630'

Rotation rate (deg/day) — Rotation rate of central body x-axis

350.89198226 (default) | double scalar

Rotation rate of the central body x axis with respect to the ICRF x-axis (2451545.0 JD, 2000 Jan 1 12:00:00 UTC), specified as a double scalar, in angle units/day.

Tunable: Yes

Dependencies

To enable this parameter:

• Set Central body to Custom.

• Set Central body spin axis source to Dialog.

Programmatic Use

Block Parameter: cbRotRate

Type: character vector

Values: '350.89198226' | double scalar

Default: '350.89198226'

Equatorial radius — Equatorial radius

3396200 (default) | double scalar

Equatorial radius for a custom central body, specified as a double scalar.

Tunable: Yes

Dependencies

To enable this parameter, set Gravitational potential model to None, Point-mass, or Oblate ellipsoid (J2).

Programmatic Use

Block Parameter: customR

Type: character vector

Values: '3396200' | double scalar

Default: '3396200'

Flattening — Flattening ratio

0.00589 (default) | double scalar

Flattening ratio for custom central body, specified as a double scalar.

Tunable: Yes

Dependencies

To enable this parameter:

• Set Central body to Custom.

• Set Gravitational potential model to Point-mass, Oblate ellipsoid (J2), or Spherical harmonics.

Programmatic Use

Block Parameter: customF

Type: character vector

Values: '0.00589' | double scalar

Default: '0.00589'

Gravitational parameter — Gravitational parameter

4.305e13 (default) | double scalar

Gravitational parameter for a custom central body, specified as a double scalar.

Tunable: Yes

Dependencies

To enable this parameter:

• Set Central body to Custom.

• Set Gravitational potential model to None, Point-mass, or Oblate ellipsoid (J2).

Programmatic Use

Block Parameter: customMu

Type: character vector

Values: '4.305e13' | double scalar

Default: '4.305e13'

Second degree zonal harmonic (J2) — Most significant or largest spherical harmonic term

1.0826269e-03 (default) | double scalar

Most significant or largest spherical harmonic term, which accounts for oblateness of a celestial body, specified as a double scalar.

Tunable: Yes

Dependencies

To enable this parameter:

• Set Central body to Custom.

• Set Gravitational potential model to Oblate ellipsoid (J2).

Programmatic Use

Block Parameter: customJ2

Type: character vector

Values: '1.0826269e-03' | double scalar

Default: '1.0826269e-03'

Drag

Include atmospheric drag — Option to include atmospheric drag

off (default) | on

To include atmospheric drag, select this check box.

Dependencies

To enable this parameter:

• Set the Propagation method parameter to Numerical (high precision).

• Set the Central Body parameter to Earth.

Programmatic Use

Block Parameter: useDrag

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Atmospheric density source — Source of atmospheric density value

Dialog (default) | Port

Source of atmospheric density value, specified as Dialog or Port.

Dependencies

To enable this parameter:

• Set the Propagation method parameter to Numerical (high precision).

• Set the Central Body parameter to Earth.

• Select the Include atmospheric drag check box.

Programmatic Use

Block Parameter: atmosSrc

Type: character vector

Values: 'Dialog' | 'Port'

Default: 'Dialog'

Atmospheric model — Atmospheric model

NRLMSISE-00 (default)

Atmospheric model for atmospheric drag calculation, specified as NRLMSISE-00.

Dependencies

To enable this parameter:

• Set the Propagation method parameter to Numerical (high precision).

• Set the Central Body parameter to Earth.

• Select the Include atmospheric drag check box.

• Set the Atmospheric density source parameter to Dialog.

Programmatic Use

Block Parameter: atmosModel

Type: character vector

Values: 'NRLMSISE-00'

Default: 'NRLMSISE-00'

Flags source — Variation flag source

Dialog (default) | Port

Variation flag source, specified as Dialog or Port.

Dependencies

To enable this parameter:

• Set the Propagation method parameter to Numerical (high precision).

• Set the Central Body parameter to Earth.

• Select the Include atmospheric drag check box.

Programmatic Use

Block Parameter: fluxFlagsSrc

Type: character vector

Values: 'Dialog' | 'Port'

Default: 'Dialog'

Flags — Variation flags

ones(1,23) (default)

Variation flags, specified as an array of 23 (ones(1,23)). You can specify one of the following values for a field. The default value for each field is 1.

• 0.0 — Removes the effect on the output.

• 1.0 — Applies the main and the cross-term effects of that value on the output.

• 2.0 — Applies only the cross-term effect of that value on the output.

The array has these fields.

Field	Description
Flags(1)	F10.7 effect on mean
Flags(2)	Independent of time
Flags(3)	Symmetrical annual
Flags(4)	Symmetrical semiannual
Flags(5)	Asymmetrical annual
Flags(6)	Asymmetrical semiannual
Flags(7)	Diurnal
Flags(8)	Semidiurnal
Flags(9)	Daily AP. If you set this field to -1, the block uses the entire matrix of magnetic index information (APH) instead of APH(:,1).
Flags(10)	All UT, longitudinal effects
Flags(11)	Longitudinal
Flags(12)	UT and mixed UT, longitudinal
Flags(13)	Mixed AP, UT, longitudinal
Flags(14)	Terdiurnal
Flags(15)	Departures from diffusive equilibrium
Flags(16)	All exospheric temperature variations
Flags(17)	All variations from 120,000 meter temperature (TLB)
Flags(18)	All lower thermosphere (TN1) temperature variations
Flags(19)	All 120,000 meter gradient (S) variations
Flags(20)	All upper stratosphere (TN2) temperature variations
Flags(21)	All variations from 120,000 meter values (ZLB)
Flags(22)	All lower mesosphere temperature (TN3) variations
Flags(23)	Turbopause scale height variations

Dependencies

To enable this parameter:

• Set the Propagation method parameter to Numerical (high precision).

• Set the Central Body parameter to Earth.

• Select the Include atmospheric drag check box.

• Set the Flags source to Dialog.

Programmatic Use

Block Parameter: fluxFlags

Type: character vector

Values: 'ones(1,23)'

Default: 'ones(1,23)'

Include anomalous oxygen in density calculation — Option to include anomalous oxygen in density calculation

off (default) | on

To include anomalous oxygen in density calculations, select this check box.

Dependencies

To enable this parameter:

• Set the Propagation method parameter to Numerical (high precision).

• Set the Central Body parameter to Earth.

• Select the Include atmospheric drag check box.

Programmatic Use

Block Parameter: useOxygen

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Drag coefficient source — Source of drag coefficient

Dialog (default) | Port

Source of drag coefficient, specified as Dialog or Port.

Dependencies

To enable this parameter:

• Set the Propagation method parameter to Numerical (high precision).

• Set the Central Body parameter to Earth.

• Select the Include atmospheric drag check box.

Programmatic Use

Block Parameter: dragCoeffSrc

Type: character vector

Values: 'Dialog' | 'Source'

Default: 'Dialog'

Drag coefficient — Spacecraft coefficient of drag

2.179 (default) | scalar | vector of size numSat

Spacecraft coefficient of drag used by atmospheric drag calculation, specified as a scalar or as a vector of size numSat.

Dependencies

To enable this parameter:

• Set the Propagation method parameter to Numerical (high precision).

• Set the Central Body parameter to Earth.

• Select the Include atmospheric drag check box.

• Set the Drag coefficient source parameter to Dialog.

Programmatic Use

Block Parameter: dragCoeff

Type: character vector

Values: scalar | vector of size numSat

Default: '2.179'

Drag area source — Source of drag area

Dialog (default) | Port

Source of drag area, specified as Dialog or Port.

Dependencies

To enable this parameter:

• Set the Propagation method parameter to Numerical (high precision).

• Set the Central Body parameter to Earth.

• Select the Include atmospheric drag check box.

• Set the Drag coefficient source parameter to Dialog.

Programmatic Use

Block Parameter: dragAreaSrc

Type: character vector

Values: 'Dialog' | 'Source'

Default: 'Dialog'

Drag area — Area to compute acceleration due to atmospheric drag

1.0 (default) | scalar | vector of size numSat

Area to compute acceleration due to atmospheric drag, specified as a scalar or as a vector of size numSat. This area of the spacecraft is perpendicular to the spacecraft relative velocity.

Dependencies

To enable this parameter:

• Set the Propagation method parameter to Numerical (high precision).

• Set the Central Body parameter to Earth.

• Select the Include atmospheric drag check box.

• Set the Drag coefficient source parameter to Dialog.

Programmatic Use

Block Parameter: dragArea

Type: character vector

Values: scalar | vector of size numSat

Default: '1.0'

Units

Units — Parameter and port units

Metric (m/s) (default) | Metric (km/s) | Metric (km/h) | English (ft/s) | English (kts)

Parameter and port units, specified as shown here.

Units	Forces	Moment	Mass	Inertia	Distance	Velocity	Acceleration	Area	Density
Metric (m/s)	Newton	Newton-meter	Kilograms	Kilogram m2	meters	meters/sec	meters/sec2	m2	kg/m3, some density outputs 1/m3
Metric (km/s)	Newton	Newton-meter	Kilograms	Kilogram m2	kilometers	kilometers/sec	kilometers/sec2	m2	kg/m3, some density outputs 1/m3
Metric (km/h)	Newton	Newton-meter	Kilograms	Kilogram m2	kilometers	kilometers/hour	kilometers/hour2	m2	kg/m3, some density outputs 1/m3
English (ft/s)	Pound-force	Foot-pound	Slugs	Slug ft2	feet	feet/sec	feet/sec2	feet2	lbm/ft3, some density outputs 1/ft3
English (kts)	Pound-force	Foot-pound	Slugs	Slug ft2	nautical mile	knots	knots/sec	feet2	lbm/ft3, some density outputs 1/ft3

Programmatic Use

Block Parameter: units

Type: character vector

Values: 'Metric (m/s)' | 'Metric (km/s)' | 'Metric (km/h)' | 'English (ft/s)' | 'English (kts)'

Default: 'Metric (m/s)'

Angle units — Angle units

Degrees (default) | Radians

Parameter and port units for angles, specified as Degrees or Radians.

Programmatic Use

Block Parameter: angleUnits

Type: character vector

Values: 'Degrees' | 'Radians'

Default: 'Degrees'

Time format — Time format for start date and time output

Julian date (default) | Gregorian

Time format for Start date/time (UTC Julian date) and output port t_utc, specified as Julian date or Gregorian.

Programmatic Use

Block Parameter: timeFormat

Type: character vector

Values: 'Julian date' | 'Gregorian'

Default: 'Julian date'

Algorithms

Coordinate Systems

The Spacecraft Dynamics block works in the ICRF and fixed-frame coordinate systems.

• ICRF — International Celestial Reference Frame. This frame can be treated as equal to the ECI coordinate system realized at J2000 (Jan 1 2000 12:00:00 TT). For more information, see ECI Coordinates.

• Fixed-frame — Fixed-frame is a generic term for the coordinate system that is fixed to the central body. The axes of the system rotate with the central body and are not fixed in inertial space. If the Use Earth orientation parameters (EOPs) check box is not selected, the block still uses the IAU2000/2005 reduction, but with Earth orientation parameters set to 0.

  • When Central Body is Earth and the Use Earth orientation parameters (EOPs) check box is selected, the fixed-frame coordinate system for the Moon is the Mean Earth/pole axis frame (ME). This frame is realized by two transformations. First, the values in the ICRF frame are transformed into the Principal Axis system (PA), which is the axis defined by the libration angles provided as inputs to the block (for more information, see Moon Libration). The states are then transformed into the ME system using a fixed rotation from the "Report of the IAU/IAG Working Group on cartographic coordinates and rotational elements: 2006" [7].

  • When Central Body is Moon and the Input Moon libration angles check box is selected, the fixed-frame coordinate system for the Moon is the coordinate system defined by the libration angles provided as inputs to the block (for more information, see Moon Libration).

  • When Central Body is Custom, the fixed-frame coordinate system is defined by the poles of rotation and prime meridian defined by the block input α, δ, W, or the spin axis properties. In all other cases, the fixed frame for each central body is defined by the directions of the poles of rotation and prime meridians defined in the "Report of the IAU/IAG Working Group on cartographic coordinates and rotational elements: 2006" [7].

Translational Dynamics

The Spacecraft Dynamics block uses the Simulink solver to solve translational and rotational equations of motion of one or more spacecraft. The block translational dynamics are governed by these equations:

$$\overrightarrow{a_{icrf}}={\stackrel{\rightharpoonup }{a}}_{centralbodygravity}+body2inertial\left(\frac{{\stackrel{\rightharpoonup }{F}}_b}{m}\right)\overrightarrow{a_{applied}}$$

$$\overrightarrow{a_{icrf}}\underset{\text{integrate}}{\Rightarrow }\overrightarrow{r_{icrf}},\overrightarrow{v_{icrf}}$$

where:

• $${\overrightarrow{a}}_{applied}$$ are the custom acceleration components from the A (applied acceleration) port.

• $${\overrightarrow{F}}_b$$ are the input body force components.

• m is the spacecraft mass.

The method for computing central body acceleration depends on the current setting for the Gravitational potential model parameter. For gravity models that include nonspherical acceleration terms, the block computes nonspherical gravity in a fixed-frame coordinated system (for example, ITRF, in the case of Earth). However, the block always performs numerical integration in the inertial ICRF coordinate system. Therefore, at each timestep, the block:

1. Transforms position and velocity states into the fixed-frame.

2. Calculates nonspherical gravity in the fixed-frame.

3. Transforms the resulting acceleration into the inertial frame.

4. Sums the resulting acceleration with the other acceleration terms.

5. Integrates the summed acceleration terms.

Point-Mass

This option treats the central body as a point-mass, including only the effects of spherical gravity using Newton's law of universal gravitation.

$${\overrightarrow{a}}_{\text{centralBodyGravity}}=-\frac{\mu }{r^2}\frac{\overrightarrow{r_{icrf}}}{r}$$

where μ is the standard gravitation parameter of the central body.

Oblate Ellipsoid

In addition to spherical gravity, this option includes the perturbing effects of the second-degree, zonal harmonic gravity coefficient J₂, accounting for the oblateness of the central body. J₂ accounts for the vast majority of the central bodies gravitational departure from a perfect sphere.

$${\overrightarrow{a}}_{\text{centralBodyGravity}}=-\frac{\mu }{r^2}\frac{\overrightarrow{r_{icrf}}}{r}+fixed2inertial\left({\overrightarrow{a}}_{nonspherical}\right),$$

where:

$$\begin{array}{l}{\overrightarrow{a}}_{nonspherical}=\left\{\left[\frac{1}{r}\frac{\partial }{\partial r}U-\frac{r_{f{f}_k}}{r^2\sqrt{r_{f{f}_i}{}^2}+r_{f{f}_j}{}^2}\frac{\partial }{\partial \varphi }U\right]r_{f{f}_i}\right\}i\\ \text{ +}\left\{\left[\frac{1}{r}\frac{\partial }{\partial r}U+\frac{r_{f{f}_k}}{r^2\sqrt{r_{f{f}_i}{}^2}+r_{f{f}_j}{}^2}\frac{\partial }{\partial \varphi }U\right]r_{f{f}_j}\right\}j\\ \text{ +}\left\{\frac{1}{r}\left(\frac{\partial }{\partial r}U\right)r_k+\sqrt{\frac{r_{f{f}_i}{}^2+r_{f{f}_j}{}^2}{{}^{r^2}}}\frac{\partial }{\partial \varphi }U\right\}k\end{array}$$

given the partial derivatives in spherical coordinates:

$$\frac{\partial }{\partial r}U=\frac{3\mu }{r^2}{\left(\frac{R_{cb}}{r}\right)}^2{P}_{2,0}\left[\sin \left(\varphi \right)\right]J_2$$

$$\frac{\partial }{\partial \varphi }U=-\frac{u}{r}{\left(\frac{R_{cb}}{r}\right)}^2{P}_{2,1}\left[\sin \left(\varphi \right)\right]J_2$$

where:

• ϕ and λ are the satellite geocentric latitude and longitude.

• P_2,0 and P_2,1 associated Legendre functions.

• μ is the standard gravitation parameter of the central body.

• R_cb is the central body equatorial radius.

The transformation fixed2inertial converts fixed-frame position, velocity, and acceleration into the ICRF coordinate system with origin at the center of the central body, accounting for centrifugal and coriolis acceleration. For more information about the fixed and intertial coordinate systems used for each central body, see Coordinate Systems.

Spherical Harmonics

This option adds increased fidelity by including higher-order perturbation effects accounting for zonal, sectoral, and tesseral harmonics. For reference, the second-degree, zeroth order zonal harmonic J₂ is -C_2,0. The Spherical Harmonics model accounts for harmonics up to max degree l=l_max, which varies by central body and geopotential model.

$${\overrightarrow{a}}_{\text{centralBodyGravity}}=-\frac{\mu }{r^2}\frac{\overrightarrow{r_{icrf}}}{r}+fixed2inertial\left({\overrightarrow{a}}_{nonspherical}\right),$$

where

$$\begin{array}{l}{\overrightarrow{a}}_{nonspherical}=\left\{\left[\frac{1}{r}\frac{\partial }{\partial r}U-\frac{r_{f{f}_k}}{r^2\sqrt{r_{f{f}_i}{}^2}+r_{f{f}_j}{}^2}\frac{\partial }{\partial \varphi }U\right]r_{f{f}_i}\right\}i\\ \text{ +}\left\{\left[\frac{1}{r}\frac{\partial }{\partial r}U+\frac{r_{f{f}_k}}{r^2\sqrt{r_{f{f}_i}{}^2}+r_{f{f}_j}{}^2}\frac{\partial }{\partial \varphi }U\right]r_{f{f}_j}\right\}j\\ \text{ +}\left\{\frac{1}{r}\left(\frac{\partial }{\partial r}U\right)r_k+\sqrt{\frac{r_{f{f}_i}{}^2+r_{f{f}_j}{}^2}{{}^{r^2}}}\frac{\partial }{\partial \varphi }U\right\}k\end{array}$$

given the partial derivatives

$$\frac{\partial }{\partial r}U=-\frac{u}{r^2}{{\displaystyle \sum _{l=2}^{l_{\max }}{\displaystyle \sum _{m=0}^l\left(\frac{R_{cb}}{r}\right)}}}^l\left(l+1\right)P_{l,m}\left[\sin \left(\varphi \right)\right]\left\{C_{l,m}\cos (m\lambda )+S_{l,m}\sin \left(m\lambda \right)\right\}$$

$$\frac{\partial }{\partial \varphi }U=\frac{u}{r}{{\displaystyle \sum _{l=2}^{l_{\max }}{\displaystyle \sum _{m=0}^l\left(\frac{R_{cb}}{r}\right)}}}^l\left\{P_{l,m+1}\left[\sin \left(\varphi \right)\right]-\left(m\right)\tan \left(\varphi \right)P_{l,m}\left[\sin \left(\varphi \right)\right]\right\}\left\{C_{l,m}\cos (m\lambda )+S_{l,m}\sin \left(m\lambda \right)\right\}$$

$$\frac{\partial }{\partial \lambda }U=\frac{u}{r}{{\displaystyle \sum _{l=2}^{l_{\max }}{\displaystyle \sum _{m=0}^l\left(\frac{R_{cb}}{r}\right)}}}^l\left(m\right)P_{l,m}\left[\sin \left(\varphi \right)\right]\left\{S_{l,m}\cos (m\lambda )-C_{l,m}\sin (m\lambda )\right\},$$

where:

• ϕ and λ are the satellite geocentric latitude and longitude.

• P_l,m are associated Legendre functions.

• μ is the standard gravitation parameter of the central body.

• R_cb is the central body equatorial radius.

• C_l,m and S_l,m are the unnormalized harmonic coefficients.

The transformation fixed2inertial converts fixed-frame position, velocity, and acceleration into the ICRF coordinate system with origin at the center of the central body, accounting for centrifugal and coriolis acceleration. For more information about the fixed and intertial coordinate systems used for each central body, see Coordinate Systems.

Rotational Dynamics

Rotational dynamics are governed by:

$${\dot{\overrightarrow{\omega }}}_{b_{icrf}}=\left[\overrightarrow{M_b}-{\overrightarrow{\omega }}_{b_{icrf}}\times \left(I_{mom}{\overrightarrow{\omega }}_{b_{icrf}}\right)-{\dot{I}}_{mom}{\overrightarrow{\omega }}_{b_{icrf}}\right]\text{inv}\left(I_{mom}\right)$$

$${\dot{\overrightarrow{\omega }}}_{b_{icrf}}\underset{\text{integrate}}{\Rightarrow }{\overrightarrow{q}}_{b_{icrf}},{\overrightarrow{\omega }}_{b_{icrf}},$$

where:

• $${\overrightarrow{M}}_b$$ are the body moment components.

• $$I_{mom}$$ is the spacecraft inertia tensor matrix.

When Mass type is Fixed, $${\dot{I}}_{mom}$$ equals 0.

When Mass type is Simple Variable, this equation estimates the rate of change of the inertia tensor:

$${\dot{I}}_{mom}=\frac{I_{full}-I_{empty}}{m_{full}-m_{empty}}\dot{m}$$

This equation gives the rate of change of the quaternion vector:

$$\left[\begin{array}{c}{\dot{q}}_0\\ {\dot{q}}_1\\ {\dot{q}}_2\\ {\dot{q}}_3\end{array}\right]=\left[\begin{array}{cccc}0& {\omega }_b\left(1\right)& {\omega }_b\left(2\right)& {\omega }_b\left(3\right)\\ -{\omega }_b\left(1\right)& 0& -{\omega }_b\left(3\right)& {\omega }_b\left(2\right)\\ -{\omega }_b\left(2\right)& {\omega }_b\left(3\right)& 0& -{\omega }_b\left(1\right)\\ -{\omega }_b\left(3\right)& -{\omega }_b\left(2\right)& {\omega }_b\left(1\right)& 0\end{array}\right]\left[\begin{array}{c}{q}_0\\ q_1\\ q_2\\ q_3\end{array}\right]$$

Atmospheric Drag

The Orbit Propagator block uses this atmospheric drag equation:

$$a_{drag}=-\frac{1}{2}\rho \left(\frac{C_{D}A}{m}\right)v_{rel}^2$$

where:

• m — Spacecraft mass used by atmospheric drag calculation.

• C_D — Coefficient of drag assuming that it is dimensionless at approximately 2.179.

• ρ — Atmospheric density.

• A — Area normal to v_rel, where

  $${\overrightarrow{v}}_{rel}={\overrightarrow{v}}_{sat}+{\overrightarrow{v}}_{atmos}$$

• v_rel — Velocity relative to atmosphere.

References

[1] Vallado, David. Fundamentals of Astrodynamics and Applications. 4th ed. Hawthorne, CA: Microcosm Press, 2013.

[2] Vepa, Ranjan. Dynamics and Control of Autonomous Space Vehicles and Robotics. New York: Cambridge University Press, 2019.

[3] Stevens, Frank L., and Brian L. Stevens. Aircraft Control and Simulation. 2nd ed. Hoboken, NJ: John Wiley & Sons, 2003.

[4] Gottlieb, R. G. Fast Gravity, Gravity Partials, Normalized Gravity, Gravity Gradient Torque and Magnetic Field: Derivation, Code and Data. NASA Contractor Report 188243. Houston: NASA, February 1993.

[5] Konopliv, A. S., S. W. Asmar, E. Carranza, W. L. Sjogen, D. N. Yuan. "Recent Gravity Models as a Result of the Lunar Prospector Mission." Icarus 150, no. 1 (2001): 1–18.

[6] Lemoine, F. G. et al. "An Improved Solution of the Gravity Field of Mars (GMM-2B) from Mars Global Surveyor." Journal of Geophysical Research 106, no. E10 (2001): 23359–23376.

[7] Seidelmann, P. Kenneth et al. "Report of the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements: 2006." Celestial Mech Dyn Astr 98 (20017): 155–180 (2007).

[8] Standish, E. M. "JPL Planetary and Lunar Ephemerides." DE405/LE405. Interoffice memorandum. JPL IOM 312.F-98-048. August 26, 1998.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2021b