Abstract
Hori, in his method for canonical systems, introduces a parameter τ through an auxiliary system of differential equations. The solutions of this system depend on the parameter and constants of integration. In this paper, Lagrange variational equations for the study of the time dependence of this parameter and of these constants are derived. These variational equations determine how the solutions of the auxiliary system will vary when higher order perturbations are considered. A set of Jacobi's canonical variables may be associated to the constants and parameter of the auxiliary system that reduces Lagrange variational equations to a canonical form.
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References
Hori, G.: 1966,Publ. Astron. Soc. Japan 18, 287.
Lanczos, C.: 1970,The Variational Principles of Mechanics, 4th ed., Chapter VIII, Univ. of Toronto Press, Toronto.
Landau, L. and Lifchitz, E.: 1966,Mécanique, Chapter VII, MIR, Moscou.
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Sessin, W. Lagrange variational equations from Hori's method for canonical systems. Celestial Mechanics 29, 361–366 (1983). https://doi.org/10.1007/BF01228529
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DOI: https://doi.org/10.1007/BF01228529