Abstract
Given a point transformation from a certain domain in ℝm onto a space of lower dimension, we offer a general method to extend it to a canonical transformation increasing the number of variables, in the sense of Scheifele. It has the property of becoming completely automatic after a choice of some adequate constraints, and can even be performed by symbolic manipulation. Questions of degeneration associated to the introduction of redundant variables are also considered, as well as the relations with the corresponding generalized Lagrangean formalism. The paper is completed by examples showing the most popular among those transformations, so that the convenience of the new approach can be easily appreciated.
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Ferrándiz, JM., Sansaturio, ME. Extended canonical transformations with redundant variables: Hamiltonian and Lagrangean formulations and degeneration. Z. angew. Math. Phys. 45, 458–477 (1994). https://doi.org/10.1007/BF00945931
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DOI: https://doi.org/10.1007/BF00945931