39 citations · 312 across the 32 of their papers we have counts for
4 papers · 1 filter
Symmetry reduction for central force problems
Robert I McLachlan, Klas Modin, Olivier Verdier
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 leve…
Geometry of discrete-time spin systems
Robert I. McLachlan, Klas Modin, Olivier Verdier
Classical Hamiltonian spin systems are continuous dynamical systems on the symplectic phase space . In this paper we investigate the underlying geometry of a time discreti…
Symplectic integrators for spin systems
Robert I. McLachlan, Klas Modin, Olivier Verdier
We present a symplectic integrator, based on the canonical midpoint rule, for classical spin systems in which each spin is a unit vector in . Unlike splitting methods…
A minimal-variable symplectic integrator on spheres
Robert I. McLachlan, Klas Modin, Olivier Verdier
We construct a symplectic, globally defined, minimal-coordinate, equivariant integrator on products of 2-spheres. Examples of corresponding Hamiltonian systems, called spin systems…