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Robin S

3D mechanics: motion of a sphere

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I am interested in creating a pseudo-3D game in which the player manoeuvres a ball around an environment. The following forces will be taken into account: [1] Locally constant forces (weight / buoyancy etc.) [2] Velocity-dependent forces (drag and possibly wind of some description) [3] Driving torque [4] Normal reaction force [5] Friction My first problem is this: I know that [1], [2] and [4] should affect linear momentum only, while [3] should affect angular momentum only and [5] should be capable of affecting both. However, I don't know how to determine the linear force F and torque τ caused by friction for a ball moving along a plane surface. If I know the values of [1], [2], [3] and [4], as well as the coefficient of friction between the ball and the plane, how can F and τ be found? My second problem is that I do not know how the linear and angular momentum of a rotating ball are affected by a collision. I know that for a non-rotating ball, post-collision linear momentum would be determined simply by multiplying pre-collision linear momentum by the coefficient of restitution between the ball and the surface, but do not know what happens in the case of a rotating ball. Finally, from what I have been able to work out it seems that my model as it stands would mean that friction disappeared entirely for a rolling, non-slipping ball. This is clearly inaccurate; is there a simple way for me to correct this error?

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I'm not sure how much help I will be of here for now... but I might come back later and try answer some more things.

Anyhows from what I know there are 3 main types of friction, those being "static friction", "dynamic/kinetic friction", and "rolling friction". I will paste some notes I've made from a computer physics course I done :). Hmm, sorry if you already know such things :\.

// static friction
// an object will only move if the total force applied is greater than 'static friction max'
// static friction max = Csf * normal force
// thus, static friction is relative to the coefficient of static friction, and the normal force

// dynamic/kinetic friction
// once an object has a velocity greater than zero, dynamic friction then takes the place of static friction
// the coefficient of dynamic friction is always smaller than the coefficient of static friction
// dynamic friction max = Cdf * normal force
// thus, dynamic friction is relative to the coefficient of dynamic friction, and the normal force

// rolling friction
// occurs on an object that neither rests nor slides on a surface, such as a wheel or ball.
// rolling friction max = Crf * normal force
// thus, rolling friction is relative to the coefficient of rolling friction, and the normal force
// note, you can approximate the coefficient of rolling friction by dividing the length of contact area by the radius of the object

I'll leave it at that for now. Hmm, you might find Gaffer on Games and/or Rigid Body Simulation Tutorial helpful, but I dunno.


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