solving coupled system of second order differential equations
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aakash dewangan
on 25 May 2021
Commented: aakash dewangan
on 30 May 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 Comments
Paul
on 28 May 2021
Do you have a simple example for M, K, and F? Preferably one that you know what that solution should be?
Accepted Answer
Sulaymon Eshkabilov
on 25 May 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 Comments
Sulaymon Eshkabilov
on 28 May 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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