The motion equations for a Lagrangian 0264-9381/13/5/030/img6, depending on the curvature 0264-9381/13/5/030/img7 of the particle world line, embedded in a spacetime of constant curvature, are considered and reformulated in terms of the principal curvatures. It is shown that, for an arbitrary Lagrangian function 0264-9381/13/5/030/img6, the general solution of the motion equations can be obtained by integrals. By analogy with the flat spacetime case, the constants of integration are interpreted as the particle mass and its spin. As examples, we completely investigate Lagrangians linear and quadratic in 0264-9381/13/5/030/img9 and the model of a relativistic particle with maximal proper acceleration, in a spacetime with constant curvature.

COMPLETE INTEGRABILITY FOR LAGRANGIANS DEPENDENT ON ACCELERATION IN A SPACETIME OF CONSTANT CURVATURE

FEOLI A;
1996-01-01

Abstract

The motion equations for a Lagrangian 0264-9381/13/5/030/img6, depending on the curvature 0264-9381/13/5/030/img7 of the particle world line, embedded in a spacetime of constant curvature, are considered and reformulated in terms of the principal curvatures. It is shown that, for an arbitrary Lagrangian function 0264-9381/13/5/030/img6, the general solution of the motion equations can be obtained by integrals. By analogy with the flat spacetime case, the constants of integration are interpreted as the particle mass and its spin. As examples, we completely investigate Lagrangians linear and quadratic in 0264-9381/13/5/030/img9 and the model of a relativistic particle with maximal proper acceleration, in a spacetime with constant curvature.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12070/3008
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 34
  • ???jsp.display-item.citation.isi??? 37
social impact