Abstract by Nick Freeman
Variational Methods and Numerical Simulation of the N-Body Problem
It is known that Newton’s Law of Gravitation, combined with his second law, produces a system of second-order nonlinear vector differential equations for the motion of N point masses m1, m2, … , mN. The force between masses mi and mj is given by G times their product divided by the square of the distance between them, where G is the universal constant of gravitation. The solution of the resultant system of equations is called the N-body problem.
In this talk, we discuss an introduction of the variational methods used in the N-body problem beginning from 2006. Our simulations implemented a solver for boundary value problems. We emphasize on numerically finding periodic solutions of boundary value problems of 4 bodies in two dimensions.