In this paper we propose the time & fitness-dependent Hamiltonian form of human biomechanics, in which total mechanical + biochemical energy is not conserved. 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, jet manifolds, polysymplectic geometry and Hamiltonian connections. In this way we derive time-dependent dissipative Hamiltonian equations and the fitness evolution equation for the general time & fitness-dependent human biomechanical system. Keywords: Human biomechanics, configuration bundle, Hamiltonian connections, jet manifolds, time & fitness-dependent dynamics
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