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This article is cited in 11 scientific papers (total in 11 papers)
Pairs of commuting Hamiltonians quadratic in the momenta
V. G. Marikhin, V. V. Sokolov
L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
Abstract:
In the case of two degrees of freedom, we consider pairs of Hamiltonians
quadratic in the momenta and commuting with respect to the standard Poisson
bracket. We find new multiparameter families of such pairs and present
a universal scheme for constructing a complete solution of the Hamilton–Jacobi
equation in terms of integrals over an algebraic curve. For the most
complicated examples, this curve is a nonhyperelliptic covering of an elliptic curve.
Keywords:
integrable Hamiltonian system, separation of variables, algebraic system
DOI:
https://doi.org/10.4213/tmf4224
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English version:
Theoretical and Mathematical Physics, 2006, 149:2, 1425–1436
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Received: 24.05.2006
Citation:
V. G. Marikhin, V. V. Sokolov, “Pairs of commuting Hamiltonians quadratic in the momenta”, TMF, 149:2 (2006), 147–160; Theoret. and Math. Phys., 149:2 (2006), 1425–1436
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/tmf4224https://doi.org/10.4213/tmf4224 http://mi.mathnet.ru/eng/tmf/v149/i2/p147
Citing articles on Google Scholar:
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Related articles on Google Scholar:
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This publication is cited in the following articles:
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Borisov AV, Mamaev IS, Marikhin VG, “Explicit Integration of One Problem in Nonholonomic Mechanics”, Doklady Physics, 53:10 (2008), 525–528
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Borisov AV, Mamaev IS, “Conservation Laws, Hierarchy of Dynamics and Explicit Integration of Nonholonomic Systems”, Regular & Chaotic Dynamics, 13:5 (2008), 443–490
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I. S. Mamaev, “Universalnyi kompleks programm dlya issledovaniya mekhanicheskikh sistem s negolonomnymi svyazyami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2009, no. 2, 147–160
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Marikhin V.G., Sokolov V.V., “Transformation of a Pair of Commuting Hamiltonians Quadratic in Momenta to Canonical Form and Real Partial Separation of Variables for the Clebsch Top”, Regular & Chaotic Dynamics, 15:6 (2010), 652–658
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V. G. Marikhin, “On a two-dimensional Schrцdinger equation with a magnetic field with an additional quadratic integral of motion”, JETP Letters, 94:3 (2011), 243–247
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V. G. Marikhin, “On the two-dimensional classical motion of a charged particle in an electromagnetic field with an additional quadratic integral of motion”, JETP Letters, 97:7 (2013), 425–428
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V. G. Marikhin, “Quasi-Stäckel systems and two-dimensional Schrödinger equations in an electromagnetic field”, Theoret. and Math. Phys., 177:1 (2013), 1352–1360
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A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Geometrizatsiya teoremy Chaplygina o privodyaschem mnozhitele”, Nelineinaya dinam., 9:4 (2013), 627–640
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Yehia H.M., Elmandouh A.A., “Integrable 2D Time-Irreversible Systems with a Cubic Second Integral”, Adv. Math. Phys., 2016, 8958747
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Agapov S.V., Bialy M., Mironov A.E., “Integrable Magnetic Geodesic Flows on 2-Torus: New Examples via Quasi-Linear System of PDEs”, Commun. Math. Phys., 351:3 (2017), 993–1007
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Bolsinov A., Matveev V.S., Miranda E., Tabachnikov S., “Open Problems, Questions and Challenges in Finite-Dimensional Integrable Systems”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 376:2131 (2018), 20170430
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