I want to calculate the final angular (w) and linear velocity (v) of a sphere that collides with a plane. I assume no energy loss and no slipping occurs during the collision. (each vector has x y z components)
My current work summary: I can set up conservation expressions where I am left with 3 equations (two for angular momentum conservation about the contact point and one for kinetic energy). My assumption is that the incoming vertical velocity is reflected, and that the vertical component of the angular momentum has no interaction with the plane (no torque can be applied to it). This allows me to simplify my equations to be in terms of 4 variables instead of 6.
This is still an underdetermined system.
*An extension out of curiousity (no need to answer this): What are standard ways to incorporate friction and energy losses into these calculations without evaluating any material properties... would applying a dampening factor be a good approximation for these sorts of events? (I want to make a ping pong simulation)
Another extension because why not :) (no need to answer this again): Is it possible to emulate the effects of slipping without worrying much about the material interactions/forces? (I assume not) *
To further simplify the problem I wonder if I can split my kinematic conservation equation into two equations. My idea is that an angular velocity along the x axis will only cause an effect in the linear velocity along the y axis, and so I only need to consider the kinematic energy balance between these two varaibles (same for w_y and v_x). Is this a valid assumption to make?