Generalized coordinates - Rotating pendulum

AI Thread Summary
In the context of a rotating pendulum, the angle of rotation about the axis is not considered a generalized coordinate because it does not contribute to the dynamics of the system in the same way as other coordinates. The discussion highlights that if the rotation around the axis is not influenced by gravity, this coordinate becomes cyclic, meaning its conjugate momentum is conserved. The relationship between the angle and angular velocity is crucial, especially when determining the Hamiltonian for the system. The confusion arises from whether to include the angle in the Hamiltonian formulation, which depends on the constancy of angular velocity. Understanding these concepts is essential for accurately modeling the dynamics of the rotating pendulum.
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My question is kinda simple but it has been causing me some trouble for a while. In the problem of the pendulum rotating about an axis, why isn't the angle of rotation about the axis a generalized coordinate? The doubt appears when i try to write the hamiltonian for the system and i don't know if i include the term relative to that angle.
How that's related to the fact that the angular velocity is or not constant.
Thanks in advance.
( The problem considered is of a simple pendulum, but with its axis of oscillation rotating)
 
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What is the orientation of that axis? If rotation around it is not influenced by gravity, the coordinate is cyclic (I think this is what you are looking for?) and its time-derivative is conserved.
 

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