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Spherical Pendulum 
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#1
Jan313, 05:44 PM

P: 34

I thought of this question the other day, and I was unable to solve it. A Google search has not helped, so I thought I might post it here.
A point mass hangs from a rod of length "l" from the center of a pendulum. The only forces acting upon the point mass are the force of gravity and the force of constraint (keeping it distance "l" from the center). Is there a function that describes the motion of the point mass? 


#2
Jan313, 05:50 PM

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hi praeclarum!
show us what you've tried, and where you're stuck, and then we'll know how to help! 


#3
Jan313, 06:03 PM

P: 34

OK. It's not as complicated as a double pendulum. It's just a single pendulum where the mass is constrained to a sphere (rather than the 2dimensional case where you have a circle).
Well, one thought I had was to solve for the potential energy of the system, since that's just mgh+1/2mv^2 = C The mass is just a constant, and we can get rid of it. From this point, I am stuck, however, and I don't know where to go from here. I was thinking the initial velocity must be perpendicular to the force of constraint and was wondering if you could split up the motion into just x and y components to solve it, but that seemed fruitless upon inspection. I am looking for a general function that describes the motion of the point around the sphere. Your help is appreciated greatly. 


#4
Jan313, 06:11 PM

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Spherical Pendulum
so it's basically a mass moving on the inside of a sphere?
hmm … in linear problems we usually use conservation of energy and conservation of momentum, sooo … have you tried conservation of angular momentum ? 


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