Setup

pip install numpy pyglet matplotlib panda3d

matplotlib is not necessary if not plotting

Note:

new_energy_n_body.py and n_body.py are the only ones that will currently run due to changes made to rendering. Other files haven't been updated with the new syntax yet.

To-do

• Gravity on Earth
• Build a 2d renderer based on Pyglet
  • Implement multi-object rendering
  • Reuse old shapes
• Implement inelastic collision models
  • Come up with different models for bodies colliding
  • Supoort for different types of collisions (and respective energy+momentum changes)
• Build a 3d renderer based on Panda3D
• Switch to Barnes-Hut method for approximations for particles
• Springs
• Diff eq. support
• Two-body problems
  • One fixed body
• N-body problems
  • basic N-body problems
  • implement fast multipole method
  • parallelization
  • energy conservation
• Particle simulation
  • similar to N-body sims, with perfectly elastic collisions
• Fluid simulation

Switched from RK4 to velocity verlet for significant performance gains, and energy+momentum conservation.

Example System

Energy and momentum graphs for an 27 body gravitational system with velocity verlet (time step = 0.05): Total energy = -24902.30544431605; Total energy final (1000 seconds) = -24902.30544250108

Note: Not sure what the spikes are. They are likely due to improper "collision" handling (there is no collision handling, instead 0 acceleration is added if the delta position is less than sum of radii, where the radii have a minimum radius of 1, despite "true" raidus being proportional to cbrt of mass, which would give sub pixel radii)

Zoomed in energy plot

<p_x, p_y, p_z> represent each of the 3 lines. Total momentum = <687898.600061, 198487.305684, 0>; Total momentum final (1000 seconds) = <-733713.21844474, 3488328.45607243, 0.>