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Teoreticheskaya i Matematicheskaya Fizika, 1994, Volume 99, Number 3, Pages 355–363
(Mi tmf1597)
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Completely integrable one-dimensional classical and relativistic time-dependent hamiltonians
S. Bouquet CEA, Service de Physique Théorique
Abstract:
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.
Citation:
S. Bouquet, “Completely integrable one-dimensional classical and relativistic time-dependent hamiltonians”, TMF, 99:3 (1994), 355–363; Theoret. and Math. Phys., 99:3 (1994), 641–647
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https://www.mathnet.ru/eng/tmf1597 https://www.mathnet.ru/eng/tmf/v99/i3/p355
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Abstract page: | 228 | Full-text PDF : | 83 | References: | 33 | First page: | 2 |
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