Simulating the motion of the leech: A biomechanical application of DAEs |
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Authors: | Alscher Christian Beyn Wolf-Jürgen |
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Institution: | (1) Department of Mathematics, University of Bielefeld, P.O. Box 100131, D-33501 Bielefeld, Germany |
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Abstract: | In this paper a mathematical model is developed for the dynamical behaviour of a hydrostatic skeleton. The basic configuration
is taken from the worm-like shape of the medicinal leech. It consists of a sequence of hexahedra with damped elastic springs
as edges to model the various parts of the musculature. The system is stabilized by the constraint of constant volume either
in the whole body or in prescribed compartments. We set up Lagrange's equations of motion with the Lagrange multipliers being
the pressure values in the compartments. The equations of motion lead to a large differential-algebraic system which is solved
by an application of semi-explicit numerical methods. Though the model has not yet been adapted to experimental data, first
simulations with a simplified set of parameters show that it is capable of generating basic movements of the leech such as
crawling and swimming.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | Lagrange's equations of motion viscoelasticity semi-explicit methods 92C10 |
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