Second Order Differential Equations

I have seen all of the documentation of converting second order diffeq's to first order, but what if your equations are coupled...for instance:

y''[t] = 3x''[t] -4y[t];
x''[t] =  2y''[t] + 6x[t];

Answer 1

[Brian B]

You can rewrite that system with a constant mass matrix M. That is, the system above is equivalent to

   M * d/dt[x1; x2; x3; x4] = [x2; x4; -4 x3; 6 x1]

where

   M = [1 0 0 0; 0 0 1 0; 0 -3 0 1; 0 1 0 -2].

Use odeset to specify the mass matrix.

[Helge]

Hi Community,

isn't it possible to rewrite the above differential equations, so they aren't coupled anymore in terms of the second derivative? I would do it as follows:

1. Insert the 2nd eqn into the first, which gives: y''[t] = 3*(2y''[t] + 6x[t]) - 4y[t] and solve this for y''[t]:: y''[t] = -18/5 * x[t] + 4/5 y[t]
2. Re-Insert this in the 2nd eqn from "Leila" above, which gives x''[t] = 2(-18/5 * x[t] + 4/5 * y[t]) + 6 * x[t] and solve for x''[t]:: x''[t] = 8/5 * y[t] - 6/5 * x[t]
3. Now these two equations can be brought to State Space Representation and solved with ode45()

I tried to solve my problem this way and now I am unsure if that is even possible or do I have two use the mass matrix M in any case?

Best wishes, Helge

[Torsten]

Everything is all right with your way of solving the above system.

Best wishes

Torsten.