Constants of motion associated with canonoid transformations for non-autonomous systems

• G.F. Torres del Castillo ^[1] ; R. Azuaje ^[1]
  1. [1] Benemérita Universidad Autónoma de Puebla

     Benemérita Universidad Autónoma de Puebla

     México

     
• Localización: Revista Mexicana de Física, ISSN-e 0035-001X, Vol. 68, Nº. 2, 2022, págs. 230-237
• Idioma: inglés
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• Resumen

  • We consider non-autonomous systems of ordinary differential equations that can be expressed in Hamiltonian form in terms of two different coordinate systems, not related by a canonical transformation. We show that the relationship between these coordinate systems leads to a, possibly time-dependent, tensor field, S^(α)_(β), whose eigenvalues are constants of motion. We prove that if the Nijenhuis torsion tensor of S^(α)_(β) is equal to zero then the eigenvalues of S^(α)_(β) are in involution, and that these eigenvalues may be in involution even if the Nijenhuis tensor is not zero.