Solve Nonlinear ODE Symbolically

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Jonathan Frutschy
Jonathan Frutschy 2024-4-12，17:15
移动：Torsten 2024-4-12，17:46
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(t)), damping C, mass M, and force F. The nonlinearity is introduced by the spring stiffness matrix K(X(t)), where X(t) is a vector of the displacements of masses 1&2. That is, X(t) = [x1(t); x2(t)].
I would like to solve this ODE symbolically for expressions for x1(t) and x2(t). Can this be done with either ODE45() or dsolve()? Is there another better option that I'm missing?

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Torsten
Torsten 2024-4-12，17:46
移动：Torsten 2024-4-12，17:46
This is a nonlinear system of ODEs. An analytical solution with symbolic math is not possible.
The only way to solve it is numerically using one of the ODE integrators (e.g. ode45).

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