Three Body Problem

• This is my attempt to solving the three body problem. It seems like the major issue is finding additional facts about the system that remain constant. For example, a three-body system always has linear momentum, angular momentum, change in the Hamiltonian, and velocity of the center of mass always conserved. Many people refer to this as the integrals of motion. We need to find additional integrals of motion that remain constant to allow us to solve the differential equation. The 3-body problem has 18 differential equations and we would thus need 18 independent integrals of motion but only have 10 (3 for linear moment, 3 for angular momentum, 1 for energy, and 3 for the center of mass motion). So, we need 8 more. The primary approach we take is "guessing" at combinations of mass, position, and velocity such that they remain constant for all three-body systems.
• We first need an expression generator. It's sort of working now but our parentheses generation needs to be implemented recursively so we can achieve all possible expressions. We have to somehow also allow linear combinations later on.
• Finally, we need to do the physics and check if any of these expressions are valid lol. Lots of computation time.