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Old Nov 11th 2015, 07:08 AM   #1
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Block sliding off edge of platform

I'm trying to model the motion of a block sliding off an edge for a platform game I am making but I am stuck please help!
Here is the concept: http://imgur.com/CTf9GZq
Here is my work so far: http://imgur.com/MBOFh9k

What are the equations of displacement and rotation in terms of time? x(t), y(t), and theta(t) for the rigid block falling and sliding off the edge?

I have found the accelerations ax and ay in terms of theta and theta in terms of x but don't know what to do from here to get it in terms of time.

ax = gcos(theta)sin(theta)
ay = -gsin2 (theta)
theta'' = 12gx/(h2 + L2)

Since theta'' changes as x changes and vise versa I don't know how to decouple the equations to solve this analytically. Any ideas?
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Old Nov 11th 2015, 02:57 PM   #2
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I would suggest taking moments about the tipping point - I think that would give you a better indication of rotational acceleration. Your equations assume that the block rotates about its center point O, but it actually rotates about the contact point, and that point changes as the block slides. I also don't see how you got a normal force at the contact point of N=mg cos(theta).

I think what you'll most likely end up with are three equations with no closed form solution. So it's likely you will have to use numerical techniques to approximate the block's motion.
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Old Nov 12th 2015, 09:33 AM   #3
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Okay thanks. I got N=mg cos(theta) from assuming that the block remains in contact with the edge so it does not raise off or lower into the edge therefore the forces at that point, normal to the block are zero. And knowing that the force due to gravity at that point is mg cos(theta) I thought that would be the normal force.

It seemed like such a simple situation when I first looked at it (know initial conditions, only forces due to gravity) so I am surprised it is so hard (impossible?) to find an analytical solution.
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block, edge, platform, platform game, rigid body motion, sliding



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