# Question:Convert ODE system to matrix form

## Question:Convert ODE system to matrix form

Maple

Sorry for disturbing you. I am wondering if there is an easier approach in Maple that could convert a system of second order differential equations into matrix form. Of course, we could do it by hand easily if the degrees of freedom is small. I would like to know if we could use Maple to do so.

Here is an example with 6 degrees of freedom: the variables are u, v, w, alpha, beta and gamma. And, this is a uncoupled system.

Vector(6, {(1) = 2*R^2*(diff(w(t), t))*Pi*Omega*h*rho+R^2*(diff(u(t), t, t))*Pi*h*rho-R^2*u(t)*Pi*Omega^2*h*rho = 0, (2) = R^2*(diff(v(t), t, t))*Pi*h*rho = 0, (3) = -2*R^2*(diff(u(t), t))*Pi*Omega*h*rho+R^2*(diff(w(t), t, t))*Pi*h*rho-R^2*w(t)*Pi*Omega^2*h*rho = 0, (4) = (1/4)*R^4*Pi*(diff(alpha(t), t, t))*h*rho+(1/12)*R^2*Pi*(diff(alpha(t), t, t))*h^3*rho+(1/6)*R^2*Pi*(diff(gamma(t), t))*Omega*h^3*rho-(1/12)*R^2*Pi*alpha(t)*Omega^2*h^3*rho = 0, (5) = (1/2)*R^4*Pi*(diff(beta(t), t, t))*h*rho-(1/2)*R^4*Pi*beta(t)*Omega^2*h*rho = 0, (6) = (1/4)*R^4*Pi*(diff(gamma(t), t, t))*h*rho+(1/12)*R^2*Pi*(diff(gamma(t), t, t))*h^3*rho-(1/6)*R^2*Pi*(diff(alpha(t), t))*Omega*h^3*rho-(1/12)*R^2*Pi*gamma(t)*Omega^2*h^3*rho = 0});

The objective is to reform it into matrix form : M*diff(X(t), t, t)+C*diff(X(t), t)+K*X(t)=F.

Thank you in advance for taking a look.

﻿