how can i decoupling this system of equation? and solve it by ode.

Answer 1

[Torsten]

This is a linear system of equations in theta1_dotdot and theta2_dotdot.

Solve it explicitly for theta1_dotdot and theta2_dotdot (e.g. using Cramer's rule).

theta1_dotdot = f1(theta1,theta2,theta1_dot,theta2_dot)
theta2_dotdot = f2(theta1,theta2,theta1_dot,theta2_dot)

Then define

y1 = theta1, y2 = theta1_dot, y3 = theta2, y4 = theta2_dot

and write your system as a system of 4 first order differential equations:

y1_dot = y2;
y2_dot = f1(y1,y3,y2,y4)
y3_dot = y4;
y4_dot = f2(y1,y3,y2,y4)

Use "ode45" to solve it with initial conditions for theta1, theta2, theta1_dot and theta2_dot.