Jet spaces in modern Hamiltonian biomechanics

Tijana Ivancevic 1 , Bojan Jovanovic 2 , Ratko Stankovic 3 , and Sasa Markovic 3
  • 1 QLIWW IP Pty Ltd. & Citech Research IP Pty Ltd., Adelaide, Australia
  • 2 Sports Academy, Belgrade, Serbia
  • 3 Faculty of Sport and Physical Education, University of Nis, Nis, Serbia


In this paper we propose the time-dependent Hamiltonian form of human biomechanics, as a sequel to our previous work in time-dependent Lagrangian biomechanics [1]. This is the time-dependent generalization of an ‘ordinary’ autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. In our view, this time-dependent energetic approach is much more realistic than the autonomous one. 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 and jet manifolds associated to the biomechanical configuration manifold. We derive time-dependent, dissipative, Hamiltonian equations and the fitness evolution equation for the general time-dependent human biomechanical system.

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