Poisson Structures for Aristotelian Model of Three Body Motion

Abstract

We present explicitly Poisson structures, for both time-dependent and time-independent Hamiltonians, of a dynamical system with three degrees of freedom introduced and studied by Calogero et al [2005]. For the time-independent case, new constant of motion includes all parameters of the system. This extends the result of Calogero et al [2009] for semi-symmetrical motion. We also discuss the case of three bodies two of which are not interacting with each other but are coupled with the interaction of third one.

References in corpus (3)

• New solutions of the Jacobi equations for three-dimensional Poisson structures
• A constant of motion in 3D implies a local generalized Hamiltonian structure
• Understanding complex dynamics by means of an associated Riemann surface

Cited by in corpus (1)

• Bi-Hamiltonian Structure of Gradient Systems in Three Dimensions and Geometry of Potential Surfaces