Gravitational Field

Model gravitational field

Libraries:
Simscape / Multibody / Forces and Torques

Description

The Gravitational Field block models a gravitational field centered at the base frame of the block. The field applies a gravitational force at the center of mass (COM) of each rigid body in the connected mechanism. The block applies force to each rigid body COM, even when bodies connect through a Weld Joint block.

Model the gravitational field with either the point mass gravity model or the spherical harmonic gravity model.

Point Mass Model

Set Gravity Type to Point Mass to model gravity from a single point source. The gravitational force follows Newton’s law of universal gravitation

$F_{g} = - G \frac{M m}{R_{B F}^{2}},$

where:

F_g is the gravitational force on the rigid body.
G is the universal gravitational constant, 6.67384 × 10^-11 m³kg^-1s^-2.
M is the mass of the point source that generates the gravitational field.
m is the mass of the rigid body, which can be either positive or negative.
R_BF is the distance between the source mass and the COM of the rigid body.

The figure below shows these variables and the inverse-square relationship between force and distance.

The plot shows the inverse square dependence between the gravitational force and distance.

Spherical Harmonic Model

Set Gravity Type to Spherical Harmonic to model spherical harmonic gravitational fields. The Spherical Harmonic model requires an Aerospace Toolbox license.

Limitations

The block does not apply gravitational forces to flexible bodies within the connected mechanism.

Ports

Frame

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B — Base frame
frame

Base frame in which the gravitational field is centered.

Parameters

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To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Gravity Type — gravitational field to model
`Point Mass` (default) | `Spherical Harmonic`

gravitational field to model. Use Point Mass to model gravity from a single point source. Use Spherical Harmonic to model gravitational fields using spherical harmonic expansion. To use the Spherical Harmonic parameter setting, you must have an Aerospace Toolbox license.

Mass — Point-source mass
1 `kg` (default) | scalar

Mass of the point source that generates the gravitational field. This value can be positive or negative.

Dependencies

To enable this parameter, set Gravity Type to Point Mass.

Gravitational Parameter — Product of gravitational constant and mass
1 `m^3/s^2` (default) | positive scalar

The product of the universal gravitational constant and the mass that generates the gravitational field.