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

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Giuseppe
Giuseppe 2022-3-2
评论： KSSV 2022-3-2
Ran in:
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!

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采纳的回答

KSSV
KSSV 2022-3-2
syms k1 k2 k3
eqn = k1 * cos(ell1.theta)^2 + 2*k2 * cos(ell1.theta)^2 + k3
S = solve(eqn)
  2 个评论
Giuseppe
Giuseppe 2022-3-2
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
KSSV 2022-3-2
syms theta
eqn = k1 * cos(theta)^2 + 2*k2 * cos(theta)^2 + k3 == 0;
S = solve(eqn,theta) % cos(ell1.theta) is the unknown!

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