Time & Fitness-Dependent Hamiltonian Biomechanics

TL;DR

This paper introduces a novel time and fitness-dependent Hamiltonian model for human biomechanics that accounts for energy dissipation and biochemical factors, extending traditional autonomous Hamiltonian frameworks.

Contribution

It develops a comprehensive geometric framework incorporating fibre bundles and jet manifolds to model non-conservative, fitness-dependent human biomechanical systems.

Findings

Derived time-dependent dissipative Hamiltonian equations.

Formulated a fitness evolution equation for biomechanics.

Extended Hamiltonian biomechanics to include biochemical energy loss.

Abstract

In this paper we propose the time & fitness-dependent Hamiltonian form of human biomechanics, in which total mechanical + biochemical energy is not conserved. 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, jet manifolds, polysymplectic geometry and Hamiltonian connections. In this way we derive time-dependent dissipative Hamiltonian equations and the fitness evolution equation for the general time & fitness-dependent human biomechanical system. Keywords: Human biomechanics, configuration bundle, Hamiltonian connections, jet manifolds, time & fitness-dependent dynamics