N-body Dynamics on Curved Spaces

Question

How does the curvature of space change the motion of interacting bodies?

Goals

• Formulate an N-body model on a sphere or hyperbolic surface.
• Simulate orbits and examine conserved quantities.

Method

Replace flat-space distance and motion with those determined by a curved metric.

• Choose coordinates, a metric, and an interaction potential on the curved space.
• Derive the constrained equations of motion.
• Integrate the system numerically and compare it with a flat-space case.