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

AI Thread Summary
The discussion centers on the equation of motion for an inverted pendulum attached to a cart, specifically questioning the term mg(theta) in the equation. The user is confused about why sine or cosine functions are not used with theta in this context. It is clarified that since the problem refers to a "small neighborhood of the equilibrium," small angle approximations can be applied, allowing sin(theta) to be approximated as theta. The conversation emphasizes the importance of understanding the assumptions in the problem, such as the application of the least-action principle. Overall, the discussion highlights the relevance of small angle approximations in simplifying the equations of motion for pendulums.
Aerodfocker
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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
 

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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!
 
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Aerodfocker said:
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.
 
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