|Jan3-13, 05:44 PM||#1|
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?
|Jan3-13, 05:50 PM||#2|
show us what you've tried, and where you're stuck, and then we'll know how to help!
|Jan3-13, 06:03 PM||#3|
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 2-dimensional 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.
|Jan3-13, 06:11 PM||#4|
|function, pendulum, spherical|
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