Thursday, October 10, 2019

[hmbqavtf] Gravity in 2 and 4 dimensions

Simulate and plot particles moving under gravity in a 2D universe.  This should be easy.  Force should probably be 1/r , not 1/r^2 as it is in 3D.  One gets circular and flower-shaped periodic orbits for fine-tuned initial conditions, otherwise non-periodic Lissajous-like paths.

Planiverse by Dewdney.

For the purposes of entertainment, other exponents can also be explored.

Simulate gravity in 4D: inverse cube law.  Simulation is probably easy, but depicting it is hard.  Like 2D, no stable periodic orbits, but plotting a mess could still be pretty.

Motivating observation: in 2D and 3D, a collection of particles in orbits decaying due to friction forms a 2D accretion disc.  What happens in 4D?

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