Poisson manifolds in generalised Hamiltonian biomechanics

Abstract

In this paper the generalised Hamiltonian approach to the modelling of dynamical systems is developed no via the standard formalism of symplectic geometry but rather via Poisson manifolds and evolution equations. This alternative approach has the merit of being available in a wider context than the former. Application is made to three biomechanical models, one in which the symplectic–geometry approach also applies (the motion of a body segment) and two in which it does not (Schwan's model of blood and lymph circulation and Davydov's molecular model of muscle contraction).