Conservative motion of a discrete, tetrahedral top on a smooth horizontal plane
Author:
Donald Greenspan
Journal:
Quart. Appl. Math. 58 (2000), 17-36
MSC:
Primary 70E18; Secondary 65P40, 70-08
DOI:
https://doi.org/10.1090/qam/1738556
MathSciNet review:
MR1738556
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Abstract: Tetrahedral tops are simulated as discrete, rigid bodies in rotation by introducing a molecular mechanics formulation. The contact point of the top with the $\left ( X, Y \right )$-plane is allowed to move in the plane. The conservative, dynamical differential equations are solved numerically in such a fashion that all the system invariants are preserved. Examples, which include cusp formation, and looping, are described and discussed.
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D. Greenspan, Technical Report #314, Mathematics Dept., UT Arlington, Arlington, TX, 1996
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D. Greenspan, Supercomputer simulation of cracks and fractures by quasimolecular simulation, J. Phys. Chem. Solids 50, 1245 (1989)
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D. Greenspan, Arithmetic Applied Mathematics, Pergamon Press, Oxford, 1980
D. Greenspan, Completely conservative, covariant numerical methodology, Comput. Math. Applic. 29, 37–43 (1995)
D. Greenspan, Technical Report #314, Mathematics Dept., UT Arlington, Arlington, TX, 1996
D. Greenspan, Quasimolecular modelling, World Sci. Press, Singapore, 1991
A. Gray, Gyrostatics and Rotational Motion, Dover, NY, 1959
L. D. Landau and E. M. Lifshitz, Mechanics (3rd Edition), Pergamon Press, Oxford, 1976, p. 112
D. Greenspan, Supercomputer simulation of cracks and fractures by quasimolecular simulation, J. Phys. Chem. Solids 50, 1245 (1989)
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Article copyright:
© Copyright 2000
American Mathematical Society
