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What I am looking for is how to determine the bounce vector of a disc hitting the edge of an object. The disc can be at any angle to the edge. I have a program that does the calculation without taking in to account the torque caused by the angle of the disc.

I want the direction that the disc will take after the bounce. If the plane of the disc is perpendicular to the direction of the edge when it hits, the direction of the bounce can be calculated by adding the unit vector from the contact point to the center of the disc to one half the velocity unit vector of the disc. If the disc is not perpendicular to the edge some energy will go to spinning the disc. That will change the direction of the bounce.

Any suggestions?

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Bob
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1 Answers1

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If the disk strikes at an angle, this will not change the direction that the centre of mass (CM) will take when it rebounds. But the disk will also rotate as it rebounds. To be more precise, the collision will change the linear momentum of the CM and also the angular momentum of the disk about the CM.

The code which you have must calculate the impulse = change in linear momentum. Call this vector $P$. The change in angular momentum (also a vector) will be $r \times P$ where $r$ is the position of the point of contact relative to the CM. Change in angular momentum $\Delta L$ is related to change in angular velocity $\Delta \omega$ by $\Delta L = J\Delta \omega$, where $J$ is the moment of inertia of the disk.

The effect of the change in angular momentum could be quite difficult to calculate. The easiest case is when velocity vector of the disk and the impulse vector from the contact are always in the same plane. This is then a 2D problem. However, the moment of inertia has different values depending on which axis is used - it is a tensor. If the disk strikes obliquely, the collision could change the axis about which the disk rotates, as well as changing the rate of rotation.

See :
What is the initial angular momentum of a rigid body given an offset impulsed force?

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sammy gerbil
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