solution to non homogenous time dependent differetial equation using ODE45

I looking to solve the control of planar 2r manipulator for which i need to solve the differential equation using ODE 45.

11.426*y"(t)+(11.426+12.456*cos(y(t)))x"(t)+(12.456*sin(y(t)))*(x'(t))^2+12.456*cos(x(t)+y(t))

i am unsure as to how to write it in matlab, as it is a second order equation and matlab accepts only first order differential equation. Need some help in this regard.

Answer 1

[Bjorn Gustavsson]

You can convert a second order ODE to two coupled first order ODEs:

can be split up into 2 by introducing a second variable, v, that is the first derivative of y:

You can extend this to your 2-variable 2nd-order ODE, just take it step-by-step. One problem more: I don't see the ODE, you've just written an expression with a couple of derivatives, you need to have a look on that.

HTH

[PRAJWAL PRABHU]

Thank you sir. It is very helpful. I got an idea as to how should i proceed further