How to solve second-degree algebraic equation containing elements of struct arrays?

Hi guys,

in my script I have two struct arrays and I want to solve a second-degree algebraic equations that involves some their fields.

I tried to use the symbolic toolbox but it seems not working with struct arrays.

Here is my script:

clc; clear all; close all

% Definition of data structures for two ellipses (attempt with numbers, at the end )
% Under planar approximation the so-called Keplerian elements set just
% consists of a, e, ω, and θ. Instead of a, e, we can also give in input
% r_p and r_a

% First ellipse
ell1.a     = 30000;               % (km)
ell1.e     = 0.6;              
ell1.r_p   = 12000;               % (km)
ell1.r_a   = 2*ell1.a - ell1.r_p;
ell1.omega = deg2rad(0);          % (rad)
ell1.theta = deg2rad(10);         % (rad)
ell1.p = ell1.a*(1-ell1.e^2);     % (km)

% Second ellipse
ell2.a     = 24000;               % (km)
ell2.e     = 0.4;
ell2.r_p   = 9000 ;               % (km)
ell2.r_a   = 2*ell2.a - ell2.r_p;
ell2.omega = deg2rad(10);          % (rad)
ell2.theta = deg2rad(45);         % (rad)
ell2.p = ell2.a*(1-ell2.e^2);      % (km)  

% Necessary condition to find intersections: e1 =/ e2

% Relative geometry for confocal ellipses
Delta_omega = ell2.omega - ell1.omega % relative orientation between two ellipses

Delta_omega = 0.1745

Delta_theta = -Delta_omega

Delta_theta = -0.1745

% Equation to obtain the intersections between two ellipses represented 
% by the Keplerian elements sets (a1, e1,ω1) and (a2, e2, ω2)

% Auxiliary parameters
a = ell1.p - ell2.p;
b = ell1.p * ell2.e * cos(Delta_omega) - ell2.p * ell1.e;
c = -ell1.p * ell2.e * sin(Delta_omega)

c = -1.3336e+03

k1 = b^2 + c^2;
k2 = a*b;
k3 = a^2 - c^2;

lambda = k2^2 - k1*k3

lambda = 3.8064e+13

%Solve the second-degree algebraic equation, where cosθ_1 is the unknown, 
% by using the "Symbolic Math Toolbox" 
syms k1 k2 k3 

eqn = k1 * cos(ell1.theta)^2 + 2*k2 * cos(ell1.theta)^2 + k3 == 0;
S = solve(eqn,cos(ell1.theta))     % cos(ell1.theta) is the unknown!

S = struct with fields:
    k1: [0×1 sym]
    k2: [0×1 sym]

% Old not working part
% syms k1 k2 k3 ell1.theta 
% 
% eqn = k1 * cos(ell1.theta)^2 + 2*k2 * cos(ell1.theta)^2 + k3
% S = solve(eqn)

Can you help me, please?

Edit: code corrected!

Answer 1

[KSSV]

syms k1 k2 k3

eqn = k1 * cos(ell1.theta)^2 + 2*k2 * cos(ell1.theta)^2 + k3
S = solve(eqn)

[Giuseppe]

I followed your coding but I get a wrong result, becasue the unknown is cos(theta_1) and not k1 and k2.

How to fix this?

[KSSV]

syms theta

eqn = k1 * cos(theta)^2 + 2*k2 * cos(theta)^2 + k3 == 0;
S = solve(eqn,theta)     % cos(ell1.theta) is the unknown!