Pendulum Equilibrium: Can It Pass Balance Point Twice?

AI Thread Summary
A pendulum can swing in all directions within a sphere, and the discussion centers on whether it can be released from a height such that it does not pass the balance point on the first swing but does on the return. The possibility hinges on specific initial conditions and heights, which remain undefined in the conversation. Participants express a belief that this scenario is feasible but lack proof or detailed guidance on how to achieve it. The discussion also raises questions about the time-reversed process of the pendulum's motion. Overall, the feasibility of this pendulum behavior invites further exploration and mathematical analysis.
walter1998
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Consider a pendulum in it's balance point hanging from ceiling. It can swing in all the directions in the space. The pendulum can only swing in a sphere(the string can't bend). Now, is it possible to release the pendulum in a particular height and with a initial condition that in the first go(the same height as the first place) it doesn't pass the balance point but in the return it does? (don't count air or friction)
If it is possible what initial conditions and height(s) are required?
If not why?
 
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What do you think?
 
mfb said:
What do you think?
I think it is possible but i cannot prove it; I'd be glad if you could guide me or more glad if you solve it.
 
walter1998 said:
I think it is possible
In which way?

Also, how would the time-reversed process look like?

What do you know about angular momentum?
 

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