Abstract
We introduce a new kind of canonical variables that prove very useful when the order of a Hamiltonian system can be reduced by one, as in the case of isoenergetic reduction, and of what we call homogeneous reduction. The Kepler Problem, Geometrical Optics and McGehee Blow-up are discussed as examples. Finally we carry out the isoenergetic reduction of the general N-Body Problem using the new variables, and briefly discuss its application to the problem of collision.
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References
Arnold, V.I.: 1978, Mathematical methods of classical mechanics, Graduate texts in mathematics, 60, Springer Verlag.
Boigey, F.: 1981, Transformations canoniques a variables imposées,. Applications a la mecanique celeste, These, Universite P. et M. Curie (Paris)
Bryant, J.: 1983, Le formalisme de contact en mecanique classique et relativiste, Ann. Inst. Henri Poincare, Physique Theorique, 38, 121–152
Bryant, J.: 1980, Sur une reduction du probleme des N-corps mettant en evidence une structure de contact, C.R. Acad. Sc. Paris, 291 A, 205–208
Libermann, P. and Marie, C-M.: 1987, Symplectic geometry and analytical mechanics, Kluwer Academic,.
McGehee, R.: 1974, Triple collision in the collinear three-body problem, Inv. Math, 27, 191–227
Whittaker, E.T.: 1927, A treatise on the analytical dynamics of particles and rigid bodies, Cambridge University Press
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© 1999 Springer Science+Business Media Dordrecht
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Bryant, J.G. (1999). Canonical Variables of the Second Kind and the Reduction of the N-Body Problem. In: Henrard, J., Ferraz-Mello, S. (eds) Impact of Modern Dynamics in Astronomy. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4527-5_27
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DOI: https://doi.org/10.1007/978-94-011-4527-5_27
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5930-5
Online ISBN: 978-94-011-4527-5
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