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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2015, Volume 11, Number 2, Pages 343–352
(Mi nd484)
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This article is cited in 7 scientific papers (total in 7 papers)
Translated papers
On the Birkhoff transformation in the case of complete degeneracy of the quadratic part of the Hamiltonian
A. P. Markeev A.Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences pr. Vernadskogo 101-1, Moscow, 119526, Russia
Abstract:
A time-periodic system with one degree of freedom is investigated. The system is assumed to have
an equilibrium position, in the vicinity of which the Hamiltonian is represented as a convergent
series.This series does not contain members of the second degree, whereas the members to some
finite degree $\ell$ do not depend explicitly on time. The algorithm for constructing a canonical
transformation is proposed that simplifies the structure of the Hamiltonian in members to
degree $\ell$, inclusive. As an application, a special case is considered when the expansion of the
Hamiltonian begins with members of the third degree. For this case, sufficient conditions for
instability of the equilibrium are obtained depending on the forms of the fourth and fifth degrees.
Keywords:
Hamiltonian system, canonical transformation, stability.
Received: 08.02.2015 Revised: 24.02.2015
Citation:
A. P. Markeev, “On the Birkhoff transformation in the case of complete degeneracy of the quadratic part of the Hamiltonian”, Nelin. Dinam., 11:2 (2015), 343–352; Regul. Chaotic Dyn., 20:3 (2015), 309–316
Linking options:
https://www.mathnet.ru/eng/nd484 https://www.mathnet.ru/eng/nd/v11/i2/p343
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Abstract page: | 403 | Full-text PDF : | 162 | References: | 37 |
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