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.