linearizing a 2nd order ODE in matlab

I have this equation that needs to linearization

0.0099157 theta double dot + 0.0000781 beta double dot =0.54684 sin (theta)

is there a build in finction on matlab that can be pluged in the values or is there another way to solve it ?

Thank you!

[David Hill]

Is beta double dot constant and are you solving for theta? Boundary conditions?

[Rodwan Baghdadi]

no beta is not constant but i forgot to add another equation which is

0.0000781 theta double dot + 0.0000781 beta double dot = tourque

i attached the full paper if any further information is needed

[Rodwan Baghdadi]

here is the link of the expirament in progress

Swing-Up and Stabilization of a Reaction Wheel Inverted Pendulum - YouTube

Answer 1

[Sulaymon Eshkabilov]

Hi,

Linearization of the given ODE can be done via Jacobian matrices that need to be derived.

Some good appropriate discussions are here:

https://www.mathworks.com/matlabcentral/answers/478845-linearization-of-nonlinear-modes-from-ode-equation

Good luck.

[Rodwan Baghdadi]

Thank you very much!

[Sulaymon Eshkabilov]

You are MOST Welcome!