Solving Motion Equations for 2D Elastic Collisions

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SUMMARY

This discussion focuses on deriving motion equations for 2D elastic collisions involving balls with known speed, mass, and angle of movement. The key principles involved are the conservation of energy and momentum, which dictate the new speed and angles of the balls post-collision. The absence of friction and rotation simplifies the calculations, allowing for a straightforward application of these principles. The discussion emphasizes that one free parameter, the angle after collision, must be determined to fully solve the equations.

PREREQUISITES
  • Understanding of 2D vector mathematics
  • Knowledge of conservation laws in physics (energy and momentum)
  • Familiarity with elastic collision principles
  • Basic skills in programming for simulation (e.g., Python, JavaScript)
NEXT STEPS
  • Study the derivation of 2D elastic collision equations
  • Learn about vector decomposition in physics
  • Explore numerical methods for simulating collisions in programming
  • Investigate graphical representations of collision outcomes
USEFUL FOR

Physics students, game developers, and anyone interested in simulating realistic 2D elastic collisions in their projects.

cghost
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Hi, I'm trying to make a 2d simulation of elastic colliding balls. I have a hard time deriving the motion equations after collision. For each ball i know the speed, the mass and the angle of movement. Can anyone point me in the right direction to find the general equations for this ? I need the new speed after collision and the new angles which the balls will use as direction. I tried some energy and impulse conservation but i didn't came up with something concrete.
Btw: i don't have friction, rotation or things like this. everything is ideal.
 
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Given conservation of energy and momentum, you will have one free parameter, namely the angle after collision.
 

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