Jet-Ricci Geometry of Time-Dependent Human Biomechanics

TL;DR

This paper introduces a novel geometric framework for modeling time-dependent human biomechanics, incorporating biochemical energy decay and Ricci flow to describe energy evolution on the configuration manifold.

Contribution

It develops a mathematical model using jet manifolds and Ricci flow to analyze non-conservative, time-dependent biomechanics with biochemical energy considerations.

Findings

Energy decay modeled by Ricci flow on the configuration manifold

Framework captures biochemical resource exhaustion effects

Provides a geometric perspective on biomechanics dynamics

Abstract

We propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds derived from the extended musculo-skeletal configuration manifold. The corresponding Riemannian geometrical evolution follows the Ricci flow diffusion. In particular, we show that the exponential-like decay of total biomechanical energy (due to exhaustion of biochemical resources) is closely related to the Ricci flow on the biomechanical configuration manifold. Keywords: Time-dependent biomechanics, extended configuration manifold, configuration bundle, jet manifolds, Ricci flow diffusion