Time-Dependent Lagrangian Biomechanics

Details Time-Dependent Lagrangian Biomechanics Time-Dependent Lagrangian Biomechanics

2009-07-07

arxiv.org/abs/0907.1209v1

Physics

Biological Physics

8 pages, 2 figures

Scientific paper

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

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