Jet-Ricci Geometry of Time-Dependent Human Biomechanics

2009/07/07 by Tijana T. Ivancevic, Ivancevic, Tijana T.
Mathematics · Physics and Astronomy · #Biological Physics (physics.bio-ph) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #math.DG #physics.bio-ph

paper · pdf · doi:10.48550/arxiv.0907.1204

13 pages 4 figures

arxiv created 2009/07/07 · arxiv updated 2009/12/01

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

Related

• Time-Dependent Lagrangian Biomechanics
• Time & Fitness-Dependent Hamiltonian Biomechanics
• Ricci Flow and Nonlinear Reaction--Diffusion Systems in Biology, Chemistry, and Physics
• Cross-Modal Diffusion for Biomechanical Dynamical Systems Through Local Manifold Alignment
• A Flow Tangent to the Ricci Flow via Heat Kernels and Mass Transport