Mechanical systems with closed orbits on manifolds of revolution

Journal Article · Sun May 31 00:00:00 EDT 2015 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2015V206N05ABEH004476· OSTI ID:22590456

Kudryavtseva, E A; Fedoseev, D A ^[1]

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1. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

We study natural mechanical systems describing the motion of a particle on a two-dimensional Riemannian manifold of revolution in the field of a central smooth potential. We obtain a classification of Riemannian manifolds of revolution and central potentials on them that have the strong Bertrand property: any nonsingular (that is, not contained in a meridian) orbit is closed. We also obtain a classification of manifolds of revolution and central potentials on them that have the 'stable' Bertrand property: every parallel is an 'almost stable' circular orbit, and any nonsingular bounded orbit is closed. Bibliography: 14 titles.

• OSTI ID: 22590456
• Journal Information: Sbornik. Mathematics, Vol. 206, Issue 5; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
MATHEMATICAL MANIFOLDS
RIEMANN SPACE
TWO-DIMENSIONAL CALCULATIONS