Topological classification of the Goryachev integrable case in rigid body dynamics. (11th March 2016)

• Record Type: Journal Article
• Authors: Nikolaenko, S S
• Is Part Of: Sbornik. Volume 207:Number 1(2016)
• Page Start: 113
• Page End: 139
• Publication Date: 2016-03-11
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1070/SM8520
• Languages: English
• ISSNs: 1064-5616

Abstract

Abstract: A topological analysis of the Goryachev integrable case in rigid body dynamics is made on the basis of the Fomenko-Zieschang theory. The invariants (marked molecules) which are obtained give a complete description, from the standpoint of Liouville classification, of the systems of Goryachev type on various level sets of the energy. It turns out that on appropriate energy levels the Goryachev case is Liouville equivalent to many classical integrable systems and, in particular, the Joukowski, Clebsch, Sokolov and Kovalevskaya-Yehia cases in rigid body dynamics, as well as to some integrable billiards in plane domains bounded by confocal quadrics -- in other words, the foliations given by the closures of generic solutions of these systems have the same structure. Bibliography: 15 titles.