solve the mass spring system where the mass matrix depends explicitly on time
10 vues (au cours des 30 derniers jours)
Afficher commentaires plus anciens
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
1 commentaire
Sam Chak
le 12 Avr 2023
Yes, possible. The total rocket mass also decreases as the acceleration of the rocket increases due to fuel mass burns away.
Réponse acceptée
Torsten
le 12 Avr 2023
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)
Plus de réponses (0)
Voir également
Catégories
En savoir plus sur Ordinary Differential Equations dans Help Center et File Exchange
Produits
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!