Jet methods in time-dependent Lagrangian biomechanics

• Authors: Tijana Ivancevic
• Languages of publication: EN

Abstracts

EN

In this paper 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 associated to the extended musculo-skeletal configuration manifold, called the configuration bundle. We start with an ordinary configuration manifold of human body motion, given as a set of its all active degrees of freedom (DOF) for a particular movement. 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. By this extension, using techniques from fibre bundles, we defined the biomechanical configuration bundle. On the biomechanical bundle we define vector-fields, differential forms and affine connections, as well as the associated jet manifolds. Using the formalism of jet manifolds of velocities and accelerations, we develop the time-dependent Lagrangian biomechanics. Its underlying geometric evolution is given by the Ricci flow equation.

Keywords

EN

Human time-dependent biomechanics; configuration bundle; jet spaces; Ricci flow

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2010
• Volume: 8
• Issue: 5
• Pages: 737-745

Dates

published

1 - 10 - 2010

online

22 - 7 - 2010

Contributors

author

Tijana Ivancevic

References

• [1] G. Giachetta, L. Mangiarotti, G. Sardanashvily, New Lagrangian and Hamiltonian Methods in Field Theory (World Scientific, Singapore, 1997) 744
• [2] R. S. Hamilton, J. Differ. Geom. 17, 255 (1982)
• [3] H. Hatze, Biol. Cybern. 28, 143 (1978) http://dx.doi.org/10.1007/BF00337136[Crossref]
• [4] A. V. Hill, P. R. Soc. B 76, 136, (1938)
• [5] T. Ivancevic, L. Jain, J. Pattison, A. Hariz, Nonlinear Dynam., 56, 23 (2009) http://dx.doi.org/10.1007/s11071-008-9376-9[Crossref]
• [6] T. Ivancevic, B. Jovanovic, M. Djukic, S. Markovic, N. Djukic, Journal of Facta Universitatis - Series: Sport 6, 51 (2008)
• [7] T. Ivancevic, B. Jovanovic, S. Djukic, M. Djukic, S. Markovic, Complex Sports Biodynamics: With Practical Applications in Tennis (Springer, Berlin, 2009)
• [8] V. Ivancevic, T. Ivancevic, Applied Differential Geometry: A Modern Introduction (World Scientific, Singapore, 2007)
• [9] V. Ivancevic, T. Ivancevic, Geometrical Dynamics of Complex Systems: A Unified Modelling Approach to Physics, Control, Biomechanics, Neurodynamics and Psycho-Socio-Economical Dynamics (Springer, Dordrecht, 2006)
• [10] V. Ivancevic, T. Ivancevic, High-Dimensional Chaotic and Attractor Systems (Springer, Berlin, 2006)
• [11] V. Ivancevic, T. Ivancevic, Int. J. Hum. Robot. 5, 699 (2008) http://dx.doi.org/10.1142/S0219843608001595[Crossref]
• [12] V. Ivancevic, T. Ivancevic, Human-Like Biomechanics: A Unified Mathematical Approach to Human Biomechanics and Humanoid Robotics (Springer, Dordrecht, 2006)
• [13] V. Ivancevic, T. Ivancevic, Natural Biodynamics (World Scientific, Singapore 2006)
• [14] V. Ivancevic, T. Ivancevic, Neuro-Fuzzy Associative Machinery for Comprehensive Brain and Cognition Modelling (Springer, Berlin, 2007) [WoS]
• [15] E. Massa, E. Pagani, Ann. I. H. Poincare-Phy. 61, 17 (1994)
• [16] J. Park, W.-K. Chung, IEEE T. Robot. 21, 850 (2005) http://dx.doi.org/10.1109/TRO.2005.852253[Crossref]
• [17] G. Sardanashvily, J. Math. Phys. 39, 2714 (1998) http://dx.doi.org/10.1063/1.532416[Crossref]
• [18] D. J. Saunders, Lond. Math. Soc. Lect. Notes Ser. (Cambridge University Press, 1989) 142
• [19] M. Vukobratovic, B. Borovac, D. Surla, D. Stokic, Biped Locomotion: Dynamics, Stability, Control, and Applications (Springer, Berlin, 1990)
• [20] D. R. Wilkie, Brit. Med. Bull. 12, 177 (1956)

Identifiers

DOI

10.2478/s11534-009-0148-z