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Normal forms for skew-symmetric matrices and Hamiltonian systems with first integrals linear in momenta


Author: G. Thompson
Journal: Proc. Amer. Math. Soc. 104 (1988), 910-916
MSC: Primary 58F05; Secondary 15A21, 34C20, 70H05
DOI: https://doi.org/10.1090/S0002-9939-1988-0964872-9
MathSciNet review: 964872
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Abstract | References | Similar Articles | Additional Information

Abstract: Using an appropriate notion of equivalence, those classical Hamiltonian systems which admit a first integral of motion polynomial of degree one in momentum are classified. The classification is effected by means of finding a normal form for a skew-symmetric matrix under the action of orthogonal symmetry.


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

  • [1] R. Abraham and J. E. Marsden, Foundations of mechanics, Benjamin, Reading, Mass., 1978. MR 515141 (81e:58025)
  • [2] G. Darboux, Archives Neerlandaises 6 (1901), 371.
  • [3] B. Dorizzi, B. Grammaticos and A. Ramani, A new class of integrable systems, J. Math. Phys. 24 (1983), 2282-2288. MR 715399 (85m:58089a)
  • [4] J. Hietarinta, Direct methods for the search of the second invariant, preprint, Univ. of Turku, 1986. MR 879243 (88a:70012)
  • [5] A. Ankiewicz and C. Pask, The complete Whittaker theorem for two-dimensional integrable systems and its application, J. Phys. A 16 (1983), 4203-4208. MR 732731 (85a:58039)
  • [6] G. Thompson, Darboux's problem of quadratic integrals, J. Phys. A 17 (1984), 985-988. MR 743179 (85m:58099)
  • [7] E. T. Whittaker, A treatise on the analytical dynamics of particles and rigid bodies, 4th ed., Cambridge Univ. Press, Cambridge, 1959. MR 0103613 (21:2381)
  • [8] J. A. Wolf, Spaces of constant curvature, Publish or Perish, Boston, Mass., 1974. MR 0343214 (49:7958)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0964872-9
Article copyright: © Copyright 1988 American Mathematical Society

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