Abstract:
In the case of two degrees of freedom the simultaneous diagonalization of pairs of Hamiltonians quadratic on momenta that commute with respect to the standard Poisson bracket is considered. A general scheme of partial separation of variables for such pairs is discussed. As an example the Clebsch top is considered.
Keywords:
separation of variables, the Clebsch top.
Citation:
V. G. Marikhin, V. V. Sokolov, “Transformation of a pair of commuting Hamiltonians quadratic in momenta to canonical form and real partial separation of variables for the Clebsch top”, Regul. Chaotic Dyn., 15:6 (2010), 652–658
\Bibitem{MarSok10}
\by V. G. Marikhin, V. V. Sokolov
\paper Transformation of a pair of commuting Hamiltonians quadratic in momenta to canonical form and real partial separation of variables for the Clebsch top
\jour Regul. Chaotic Dyn.
\yr 2010
\vol 15
\issue 6
\pages 652--658
\mathnet{http://mi.mathnet.ru/rcd524}
\crossref{https://doi.org/10.1134/S1560354710510167}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2747175}
\zmath{https://zbmath.org/?q=an:1209.37105}
Linking options:
https://www.mathnet.ru/eng/rcd524
https://www.mathnet.ru/eng/rcd/v15/i6/p652
This publication is cited in the following 5 articles:
Fournier F., Snobl L., Winternitz P., “Cylindrical Type Integrable Classical Systems in a Magnetic Field”, J. Phys. A-Math. Theor., 53:8 (2020), 085203
V. G. Marikhin, “Quasi-Stäckel Hamiltonians and electron dynamics in an external field in the two-dimensional case”, Theoret. and Math. Phys., 199:2 (2019), 652–658
V G Marikhin, “On three-dimensional quasi-Stäckel Hamiltonians”, J. Phys. A: Math. Theor., 47:17 (2014), 175201
V. E. Adler, V. G. Marikhin, A. B. Shabat, “Quantum tops as examples of commuting differential operators”, Theoret. and Math. Phys., 172:3 (2012), 1187–1205
Andrey V. Tsiganov, “On the Poisson Structures for the Nonholonomic Chaplygin and Veselova Problems”, Regul. Chaotic Dyn., 17:5 (2012), 439–450
Citation in format AMSBIB
Contact us: