I'm working on a game. I need to work out what the impulse is at different points on a body as a result of a collision.
For example, in the following diagram, if there is a collision that results in an impulse being applied to the body at A, what will the resulting impulse be at B? I know the mass, center of mass and dimensions of the body.
An impulse is an instantaneous change in velocity. You can calculate the velocity of a point before and after an impulse has been applied to the body. The velocity of a point is:
V = Vcm + omega cross r V is the velocity of a point on a rigid body. Vcm is velocity at the center of mass. Omega would be angular velocity, and r is the vector from center of mass to a particular point on the body.
A simple way to perform your needed operation is to record the velocity before and after an impulse is applied and look at the difference.
omega cross r - I don't understand. How can you get the cross product of a scalar and a vector? \$\endgroup\$ A rigid body is generally defined as one which has a fixed shape. This means that its center of mass moves at a certain speed, and additionally the object may be rotating around its center of mass. The net impulse because of the latter term is zero (impulse is a vector field; opposite values cancel.)
Note that the impulse of a single point is zero, unless you have point masses. The impulse of an object is the volume integral of its mass multiplied by its local speed.
The simplest model retaining a physical sensibility would be to regard each collision as instantaneous, with momentum (linear and angular) conserved and energy conserved but with an inelastic loss simulated by a percentage calculated form the properties of the colliding objects.
For two objects such as hard ball bearings a loss of perhaps 0.5% to 1% is probably realistic.
This of course assumes that both objects in collision are rigid, and the very small collision time frames are not of interest.
