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Poisson manifolds in generalised Hamiltonian biomechanics

Published online by Cambridge University Press:  17 April 2009

V. Ivancevic  and
C. E. M. Pearce
V. Ivancevic
Affiliation:
Torson Productions Pty Ltd, Adelaide SA 5034, Australia
C. E. M. Pearce
Affiliation:
Applied Mathematics Department, The University of Adelaide, Adelaide SA 5005, Australia
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Abstract

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In this paper the generalised Hamiltonian approach to the modelling of dynamical systems is developed no via the standard formalism of symplectic geometry but rather via Poisson manifolds and evolution equations. This alternative approach has the merit of being available in a wider context than the former. Application is made to three biomechanical models, one in which the symplectic–geometry approach also applies (the motion of a body segment) and two in which it does not (Schwan's model of blood and lymph circulation and Davydov's molecular model of muscle contraction).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 3 , June 2001 , pp. 515 - 526
Copyright
Copyright © Australian Mathematical Society 2001

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