Abstract
One of the main reasons why the Hamiltonian formalism is more powerful than the Lagrangian formalism is that the set of coordinate transformations that leave invariant the form of the Hamilton equations is much broader than the set of coordinate transformations that leave invariant the form of the Lagrange equations.
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Crampin, M. and Pirani, F.A.E. (1986). Applicable Differential Geometry (Cambridge University Press, Cambridge).
Das, A. (1989). Integrable Models (World Scientific, Singapore).
Eves, H. (1980). Elementary Matrix Theory (Dover, New York).
Fasano, A. and Marmi, S. (2006). Analytical Mechanics: An Introduction (Oxford University Press, Oxford).
Percival, I. and Richards, D. (1982). Introduction to Dynamics (Cambridge University Press, Cambridge).
Perelomov, A.M. (1990). Integrable Systems of Classical Mechanics and Lie Algebras, Vol. I (Birkhäuser, Basel).
Torres del Castillo, G.F. (1999). Symmetry of the Kepler problem in classical mechanics, Rev. Mex. Fís. 45, 234.
Torres del Castillo, G.F. and Herrera Flores, J.E. (2016). Symmetries of the Hamiltonian operator and constants of motion, Rev. Mex. Fís. 62, 135.
Wells, C.G. and Siklos, T.C. (2007). The adiabatic invariance of the action variable in classical mechanics, Eur. J. Phys. 28, 105.
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Torres del Castillo, G.F. (2018). Canonical Transformations. In: An Introduction to Hamiltonian Mechanics. Birkhäuser Advanced Texts Basler Lehrbücher. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-95225-3_5
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DOI: https://doi.org/10.1007/978-3-319-95225-3_5
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