Time-Dependent Lagrangian Biomechanics

TL;DR

This paper develops a time-dependent extension of human musculo-skeletal biomechanics by incorporating real-time dynamics into the configuration manifold, enabling more accurate modeling of human movement over time.

Contribution

It introduces a novel geometric framework for time-dependent biomechanics using jet spaces and evolving mass-inertia matrices, extending traditional autonomous models.

Findings

Formulation of a time-dependent biomechanical Lagrangian dynamics

Incorporation of geometric evolution of mass-inertia matrix

Extension of configuration manifold with real time axis

Abstract

In this paper we present the time-dependent generalization of an 'ordinary' autonomous human musculo-skeletal biomechanics. We start with the configuration manifold of human body, given as a set of its all active degrees of freedom (DOF). This is a Riemannian manifold with a material metric tensor given by the total mass-inertia matrix of the human body segments. This is the base manifold for standard autonomous biomechanics. To make its time-dependent generalization, we need to extend it with a real time axis. On this extended configuration space we develop time-dependent biomechanical Lagrangian dynamics, using derived jet spaces of velocities and accelerations, as well as the underlying geometric evolution of the mass-inertia matrix. Keywords: Human time-dependent biomechanics, configuration manifold, jet spaces, geometric evolution