I have the following non-linear ODE:
I have the following ODE45 solution:
fun = @(t,X)odefun(X,K,C,M,F(t),resSize);
[t_ode,X_answer] = ode45(fun,tspan,X_0);
The input matrices are stiffness K(X), damping C, mass M, and force F. resSize is the total number of masses in the system.
I would like to find the system's eigenvalues using either the Jacobian matrix, transfer function, or any other viable method.
I have tried using:
[vector,lambda,condition_number] = polyeig(K(X_answer),C,M);
This is tricky since my K matrix is a function handle of X. In other words, K=@(X). X represents a displacement vector of each mass in the system (x_1(t),x_2(t),...x_resSize(t)), where resSize is the total number of masses. My X_answer matrix is a double with dimensions of t_ode by resSize, where each row is the displacement vector of each mass in double form. Is there some way to substitute X_answer into my function handle for K so I can use polyeig()? If not, how would I go about finding my system's transfer function or Jacobian matrix so that I can find it's eigenvalues?
a state-dependent matrix, as illustrated below?
should vary over time.
