Three families of isochrone-type canonical transformations

Autores: Sebastián Ferrer Martínez , Martín Lara Coira
Localización: Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza, ISSN 1132-6360, Nº. 35, 2011, págs. 41-52
Idioma: inglés
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Resumen
- Hénon’s isochrone Hamiltonian is formulated in extended phase space including a time transformation. Then, the Hamilton-Jacobi equation a la Poincar´e is used to find suitable canonical transformations that reduces the original Hamiltonian to a function of only the momenta. We focus on three different time transformations, for each of which we build a family of canonical transformations where the new Hamiltonian remains unspecified. Materialization of particular transformations based on specific requirements lead to a partial differential equation which the new Hamiltonian ought to satisfy. Specifically, we show how different canonical transformations in the Literature may be recovered from our families.