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

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12070/3008
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