solving coupled system of second order differential equations
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aakash dewangan
el 25 de Mayo de 2021
Comentada: aakash dewangan
el 30 de Mayo de 2021
Hello everyone,
I want to solve a "second order coupled ordinary differential equation". I searched a lot but could not find the solution.
Please suggest me how can I solve this.
The structure of my equation is given below,
[M]{x''} + [K]{x} = {F}
where [M], [K] are the matrices, which contain time dependent terms.
{x} vector of unknown dependent variables.
{x''} is the second derivative of the vector {x} with respect to time.
Please note that [M], [K] contains time varying terms
Looking forward for your the response.
Thanks for your time..
4 comentarios
Paul
el 28 de Mayo de 2021
Do you have a simple example for M, K, and F? Preferably one that you know what that solution should be?
Respuesta aceptada
Sulaymon Eshkabilov
el 25 de Mayo de 2021
Hi,
You can employ ode solvers (ode23, ode23tb, ode45, ode113, etc) as suggested or write scripts using function handles or anonymous functions by apply Euler or Runge-Kutta methods.
2 comentarios
Sulaymon Eshkabilov
el 28 de Mayo de 2021
Should you need to obtain an analytical solution, then dsolve() of Symbolic MATH toolbox needs to be employed. E..g.:
syms x(t) Dx(t) DDx(t)
Dx = diff(x, t);
DDx = diff(Dx, t);
M = [??];
K = [??];
EQN = DDx==inv(M)*(F-K*x);
SOL = dsolve(EQN, x(0)==??, Dx(0)==??)
Good luck
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