solve the mass spring system where the mass matrix depends explicitly on time

Hello everyone,

I was wondering how to solve a system of two ODEs where the mass matrix is time dependent. The system of differential equation is in the following form:

[M]*X_double_dot +K*X=0;

where K=[2 1;5 8] and [M]=[t 0; 0 t], t is the time.

My question is : is it possible to solve this kind of ODEs with ode functions (ode45, ode15s,...) or one should evaluate the mass matrix at each time step ?

Best Regards,

Nado

[Sam Chak]

Yes, possible. The total rocket mass also decreases as the acceleration of the rocket increases due to fuel mass burns away.

Answer 1

[Torsten]

Setting y1' = y3 and y2' = y4, you arrive at the following code:

M = @(t) [t 0; 0 t];
K = [2 1;5 8];
MM = @(t)[eye(2),zeros(2);zeros(2),M(t)];
KK = [zeros(2),-eye(2);K,zeros(2)];
fun = @(t,y) -KK*y;
options = odeset('Mass',MM,'MStateDependence','none');
y0 = [0 0 1 1];
[T,Y] = ode45(fun,[0 1],y0);
plot(T,Y)

[nado]

Thank you man !!! awesome :)