What does mg(theta) means in the equation of motion?

[Aerodfocker]

In the case of inverted pendulum attached in a cart with external force U on it,

the equation of motion is like
U - mg(theta1) - mg(theta2) = m*dv/dt

I don't really understand the mg*theta part what does it mean ...should not be sine or cosine fn there with theta ?

can anyone give me some insight on this
thanks in advance ...really appreciate it.

p.s. I HAVE ATTACHED THE FULL QUESTION HERE AS WELL

 

[vanhees71]

It's just the equations of motion for the cart and the two pendulums. If you want to get more information you need to provide us with some first. E.g., we have to know what you are supposed to assume (e.g., are you supposed to use the least-action principle). Also it looks pretty much like a homework problem, which you should post in the corresponding subforum!

 

[jtbell]

should not be sine or cosine fn there with theta ?

The problem statement says "small neighborhood of the equilibrium" which means the θ's are small so you can use approximations like sin θ ≅ θ.