Jet Spaces in Modern Hamiltonian Biomechanics

TL;DR

This paper introduces a novel time-dependent Hamiltonian framework for human biomechanics, utilizing advanced geometric tools like fibre bundles and jet manifolds to model dissipative and fitness evolution dynamics.

Contribution

It extends previous Lagrangian biomechanics work by developing a comprehensive Hamiltonian approach with geometric structures for time-dependent, dissipative human biomechanical systems.

Findings

Derived time-dependent Hamiltonian equations for biomechanics

Formulated fitness evolution equations within the Hamiltonian framework

Extended autonomous models to include dissipation and time dependence

Abstract

In this paper we propose the time-dependent Hamiltonian form of human biomechanics, as a sequel to our previous work in time-dependent Lagrangian biomechanics [1]. Starting with the Covariant Force Law, we first develop autonomous Hamiltonian biomechanics. Then we extend it using a powerful geometrical machinery consisting of fibre bundles and jet manifolds associated to the biomechanical configuration manifold. We derive time-dependent, dissipative, Hamiltonian equations and the fitness evolution equation for the general time-dependent human biomechanical system. Keywords: Human biomechanics, covariant force law, configuration manifold, jet manifolds, time-dependent Hamiltonian dynamics