Completely integrable one-dimensional classical and relativistic time-dependent hamiltonians
Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 3, pp. 355-363
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In this paper, we look for first integrals $I(q;p;t)$ of time-dependent one-dimensional Hamiltonians $H(q;p;t)$. We first present a formalism based on the use of canonical transformations, and it is seen that $I(q;p;t)$ can always be written in terms of two variables $I=P(u;v)$, whereu andv are functions of $q$, $p$ andt, without loss of generality. Moreover, it is shown that any Hamiltonian with first integral $I(q;p;t)$ can be made autonomous in the space $(u,v,T)$, where $T$ is a new time. On the other hand, the cases of a particle moving classically and relativistically in a time-dependent potential $V(q;t)$ are studied. In both cases, completely integrable potentials, together with the corresponding first integrals, are derived.
@article{TMF_1994_99_3_a0,
author = {S. Bouquet},
title = {Completely integrable one-dimensional classical and relativistic time-dependent hamiltonians},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {355--363},
publisher = {mathdoc},
volume = {99},
number = {3},
year = {1994},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1994_99_3_a0/}
}
TY - JOUR AU - S. Bouquet TI - Completely integrable one-dimensional classical and relativistic time-dependent hamiltonians JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1994 SP - 355 EP - 363 VL - 99 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1994_99_3_a0/ LA - ru ID - TMF_1994_99_3_a0 ER -
S. Bouquet. Completely integrable one-dimensional classical and relativistic time-dependent hamiltonians. Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 3, pp. 355-363. http://geodesic.mathdoc.fr/item/TMF_1994_99_3_a0/