Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Separation of variables in the generalized 4th Appelrot class

Separation of variables in the generalized 4th Appelrot class We consider an analogue of the 4th Appelrot class of motions of the Kowalevski top for the case of two constant force fields. The trajectories of this family fill a four-dimensional surface $$\mathfrak{O}$$ in the six-dimensional phase space. The constants of the three first integrals in involution restricted to this surface fill one of the sheets of the bifurcation diagram in ℝ3. We point out a pair of partial integrals to obtain explicit parametric equations of this sheet. The induced system on $$\mathfrak{O}$$ is shown to be Hamiltonian with two degrees of freedom having a thin set of points where the induced symplectic structure degenerates. The region of existence of motions in terms of the integral constants is found. We provide the separation of variables on $$\mathfrak{O}$$ and algebraic formulae for the initial phase variables. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

Separation of variables in the generalized 4th Appelrot class

Kharlamov, M.
Regular and Chaotic Dynamics , Volume 12 (3) – Jun 13, 2007
Download PDF
14 pages

Loading next page...
 
/lp/springer-journals/separation-of-variables-in-the-generalized-4th-appelrot-class-flWpMvPAqY

References (11)

Publisher
Springer Journals
Copyright
Copyright © 2007 by Pleiades Publishing, Ltd.
Subject
Mathematics; Dynamical Systems and Ergodic Theory
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/S1560354707030021
Publisher site
See Article on Publisher Site

Abstract

We consider an analogue of the 4th Appelrot class of motions of the Kowalevski top for the case of two constant force fields. The trajectories of this family fill a four-dimensional surface $$\mathfrak{O}$$ in the six-dimensional phase space. The constants of the three first integrals in involution restricted to this surface fill one of the sheets of the bifurcation diagram in ℝ3. We point out a pair of partial integrals to obtain explicit parametric equations of this sheet. The induced system on $$\mathfrak{O}$$ is shown to be Hamiltonian with two degrees of freedom having a thin set of points where the induced symplectic structure degenerates. The region of existence of motions in terms of the integral constants is found. We provide the separation of variables on $$\mathfrak{O}$$ and algebraic formulae for the initial phase variables.

Journal

Regular and Chaotic Dynamics – Springer Journals

Published: Jun 13, 2007

There are no references for this article.