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# How metal cube bounces off the ground?

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Hi. I am trying to simulate a metal cube bouncing off the ground with spinning (torques) etc.. I am not sure what forces will cause the cube to bounce off the ground. I dont just want to inverse velocity and multiply it by some restitution (The ratio of speed ) so it will loose some energy and bounce off the ground like a standard ball simulation would do. I would like to use real physics to calculate this effect first find out exactly what forces are generated when crashing into ground and when bouncing off. Is it just a spring with high spring constant ? or its more? I think I know how to calculate torques so I am not worrying about it now. If you know anything about it then please let me know. Thank you.

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The restitution depends of the elasticity of the floor. If your floor is in metal, the restitution is likely to be 0 as your cube won't penetrate and the surface of the floor will stay flat (heat dissipation is neglected). If it is made of plastic, you can assume your floor will bend, this is caused by the energy of your cube. You could approximate this situation with a network of strings (ie. like a mesh of triangles but with edges made of strings). The springs constant will determinate the elasticity of your material, you should read docs about cloths simulation. The forces and energy will apply on the nodes in contact with your cube. A good analogy is the trampoline, with its high elasticity coefficient.

When the mesh bends, it gets part of the energy and tries to launch your cube in the air, check the inelastic collision formula as some energy is lost during the collision. If the energy accumulated by the ground is too low, it will oscillates and at the end, it will keep its curved shape with the metal cube on it. Strings simulations always use a damping factor (for stability reasons too).

If the energy is too high, the floor will break and your cube will fall through The only problem is to get all the numerical parameters for the elasticity definition, this model is of course a rough approximation and some finetuning is necessary. Maybe there's another approach than the network of strings.

http://hyperphysics.phy-astr.gsu.edu/hbase/inecol.html
http://freespace.virgin.net/hugo.elias/models/m_cloth.htm

[edited by - bucheron on September 3, 2003 6:55:35 AM]

Cédric

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Ok. Explain what my problem is. I am working on a rally car simulator. The car''s body sits on springs and wobbles when I''m driving on small bumps. Suspension works as it should but then I am trying to jump from a high cliff (extreme example) the car lands on ground (obviously pulled by gravity) and all 4 springs frist are compressed to its min length. When they''re at its minimum length they become a solid material not a spring. Now this is why I gave you a simpler example on a cube not to confuse with a car as I think its the same problem. Now there must be some other impulse forces sending the car back in teh air like a ball but I am not sure what they are.

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Your springs get a lot of energy but that''s still springs, they are not like dense cylinders or whatever, and as you say, they want to send the car back in the air, what about Hooke law, F = -k*x - loss ? where loss is a constant to simulate the conversion to heat. But (good) springs on a car have a non-linear behaviour, there''s a shock absorber at the end. The liquid in the absorber is compressed and dissipates part of the energy. Even without an absorber, I doubt they are linear. [Speculating] An exponential curve into the Hooke law should help, kinda a hack I suppose that the response of your spring in time is not constant - fast to compress, slow to decompress. [/Speculating]

Ok, I stop speculating, I found a good site about that. Read the doc, it has some explanations about the physics.

http://www.racer.nl/

You should have a look at the "physics of racing" series too
http://www.gamedev.net/reference/list.asp?categoryid=28#39

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Ok, I just tested the engine of Racer and it''s pretty good. The simulation is far from perfect (sending smoke each time you turn the wheels is not cool) but I watched how it transfered weights and the physics is ok (they use ODE). You definitely have to look how they implemented their springs.

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