It is shown that a Lagrangian system whose Legendre transformation degenerates along a hypersurface behaves in a strange manner by jumping from time to time without any "visible cause." In such a jump the system changes instantaneously its coordinates as well as its momenta. Necessary elements of the general theory of such systems are reported and a detailed description of a postrelativistic oscillator showing such a behavior is given.
Discontinuous trajectories of Lagrangian systems with singular hypersurface
PUGLIESE, Fabrizio;VINOGRADOV, Alexandre
2001
Abstract
It is shown that a Lagrangian system whose Legendre transformation degenerates along a hypersurface behaves in a strange manner by jumping from time to time without any "visible cause." In such a jump the system changes instantaneously its coordinates as well as its momenta. Necessary elements of the general theory of such systems are reported and a detailed description of a postrelativistic oscillator showing such a behavior is given.File in questo prodotto:
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