Lagrangians of a non-mechanical type for second order Riccati and Abel equations

Autores: José Fernando Cariñena Marzo , Manuel F. Rañada
Localización: Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza, ISSN 1132-6360, Nº. 33, 2010, págs. 165-176
Idioma: español
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Resumen
- The Helmholtz approach to the inverse problem of the Lagrangian dynamics is studied first in the particular case of the second-order Riccati equation and then in the case of the second-order Abel equation. The existence of two alternative Lagrangian formulations is proved, both Lagrangians being of a non-natural class (neither potential nor kinetic term). These second-order Riccati and Abel equations are studied by means of their Darboux polynomials and Jacobi last multipliers. The existence of a family of constants of the motion is also discussed.