Symbolic solution for system of equations

Hello. I'm trying to solve symbolically a equation of type M*Z_DDot+C*Z_Dot+K*Z=F, where M, C, K and F are 3x3 matrices. I want to solve for Z, which is a 3x1 vector containing the displacement of 3 masses. I've written a matlab script but it seems i cannot get around a problem regarding the boundary conditions. I'm using dsolve command and so far i was able to define only the initial displacement of the masses. Please tell me how do I define the velocity and acceleration boundary conditions using dsolve command. I can post the matlab script if necessary. Thank you very much.

Answer 1

[Ayush Aniket]

Hi Pavel,

You can specify the initial condition for velocity(Z_Dot) and acceleration (Z_DDot) in the following way:

1. While defining the equation, these derivatives will be incorporoated using the diff keyword in the equation as follows:

eqn = M*diff(Z,t,2) + C*diff(Z,t,1) + K * Z == F;

2. Then you can assign some variable names to the derivatives:

Z_Dot = diff(Z,t,1);
Z_DDot = diff(Z,t,2);

3. Finally, you can provide the initial values and plug the eqn and the initial condition cond into the dsolve command to solve your equation:

cond = [Z(0)==Z0, Z_Dot(0)==Z_Dot0, Z_DDot(0)==Z_DDot0];
ZSol(t) = dsolve(eqn,cond);

Refer to the following documentation which shows an example for the same:

https://www.mathworks.com/help/symbolic/dsolve.html#bve5nw0-1