Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] Herbert Goldstein, Classical mechanics, 2nd ed., Addison-Wesley Publishing Co., Reading, Mass., 1980. Addison-Wesley Series in Physics. MR 575343
  • [2] Richard P. Feynman, Robert B. Leighton, and Matthew Sands, The Feynman lectures on physics. Vol. 1: Mainly mechanics, radiation, and heat, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1963. MR 0213077
  • [3] Donald Greenspan, Arithmetic applied mathematics, International Series in Nonlinear Mathematics: Theory, Methods and Applications, vol. 1, Pergamon Press, Oxford-New York, 1980. MR 590428
  • [4] D. Greenspan, Completely conservative, covariant numerical methodology, Comput. Math. Appl. 29 (1995), no. 4, 37–43. MR 1321057, https://doi.org/10.1016/0898-1221(94)00236-E
  • [5] D. Greenspan, Technical Report #314, Mathematics Dept., UT Arlington, Arlington, TX, 1996
  • [6] D. Greenspan, Quasimolecular modelling, World Sci. Press, Singapore, 1991
  • [7] A. Gray, Gyrostatics and Rotational Motion, Dover, NY, 1959
  • [8] L. D. Landau and E. M. Lifshitz, Course of theoretical physics. Vol. 1, 3rd ed., Pergamon Press, Oxford-New York-Toronto, Ont., 1976. Mechanics; Translated from the Russian by J. B. Skyes and#J. S. Bell. MR 0475051
  • [9] D. Greenspan, Supercomputer simulation of cracks and fractures by quasimolecular simulation, J. Phys. Chem. Solids 50, 1245 (1989)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 70E18, 65P40, 70-08

Retrieve articles in all journals with MSC: 70E18, 65P40, 70-08

Additional Information

DOI: https://doi.org/10.1090/qam/1738556
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society