3D elastic collisions of spheres: angular momentum

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SUMMARY

This discussion focuses on modeling 3D elastic collisions of spheres in a space combat game, specifically addressing the calculation of final velocities using conservation of linear momentum. The formulas provided for final velocities are: v1f = v1i - ((m2c)/(m1 + m2))(1 + e)n and v2f = v2i + ((m1c)/(m1 + m2))(1 + e)n, where e represents the coefficient of restitution. The main inquiry is about determining the angular velocities of spinning spheres post-collision and understanding the transfer of spin and angular momentum to linear momentum.

PREREQUISITES
  • Understanding of 3D vector mathematics
  • Familiarity with conservation laws in physics, specifically linear and angular momentum
  • Knowledge of the coefficient of restitution in elastic collisions
  • Basic programming skills for implementing collision algorithms
NEXT STEPS
  • Research the mathematical principles of angular momentum conservation in collisions
  • Explore the concept of moment of inertia and its impact on angular velocity
  • Learn about the transfer of angular momentum in elastic collisions
  • Investigate existing physics engines, such as Bullet Physics or Unity's Rigidbody, for collision handling
USEFUL FOR

Game developers, physics simulation engineers, and anyone interested in implementing realistic collision mechanics in 3D environments.

protolocke
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Hi, I'm helping my friend with a space combat game he is programming. What I'm trying to figure out is how to model the collisions between spheres in 3D.

So far I've figured out how to calculate final velocities of 2 colliding spheres using conservation of linear momentum. I found a http://www.wheatchex.com/projects/collisions/" which gives me this formula:

v1f = v1i - ((m2c)/(m1 + m2))(1 + e)n
v2f = v2i + ((m1c)/(m1 + m2))(1 + e)n

where

v1i = the initial velocity of object 1
v2i = the initial velocity of object 2
m1 = the mass of object 1
m2 = the mass of object 2
e = the coefficient of restitution (e = 1 for elastic collision)
n = normal unit vector drawn from object 1 to object 2
c = n . (v1i - v2i)

My question is, using conservation of angular momentum, how would I work out the angular velocities of spinning spheres after they collide? How much spin is transferred from one sphere to another? How much angular momentum, if any, would be converted to linear momentum?

Thanks for your time
 
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Take a look at this thread, where we discuss something similar, that resulted eventually in a working program.
 

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