Symmetry reduction for central force problems

Robert I McLachlan, Klas Modin, Olivier Verdier

Published 2015-12-15Version 1

We given an elementary illustration of symmetry reduction for central force problems, drawing phase portraits of the reduced dynamics as the intersection of Casimir and energy level sets in three dimensions. These systems form a classic example of symplectic reduction which can usefully be compared to the more-commonly seen case of the free rigid body.