Hamiltonian systems are considered to be the prime tool of classical and quantum
mechanics. The proper investigation of such systems usually requires deep results from …

Изучается аналог волчка Эйлера в случае псевдоевклидова пространства. В случае
равенства нулю либо геометрического интеграла, либо интеграла площадей были …

In this paper, we consider in detail the 2-body problem in spaces of constant positive
curvature S 2 and S 3. We perform a reduction (analogous to that in rigid body dynamics) …

In the theory of integrable Hamiltonian systems, an important role is played by the study of
Liouville foliations and bifurcations of their leaves. In the compact case, the problem is …

Bertrand theorem's states that, among central-force potentials with bound orbits, there are
only two types of central-force scalar potentials with the property that all bound orbits are …

Posing Kepler's problem of motion around a fixed “sun” requires the geometric mechanician
to choose a metric and a Laplacian. The metric provides the kinetic energy. The fundamental …

The problem of two fixed centers was introduced by Euler as early as in 1760. It plays an
important role both in celestial mechanics and in the microscopic world. In the present paper …

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 …

A Proof of Bertrand’s Theorem Using the Theory of Isochronous Potentials | SpringerLink Skip
to main content Advertisement SpringerLink Log in Menu Find a journal Publish with us Search …

Исследуются натуральные механические системы, описывающие движение частицы
по двумерному риманову многообразию вращения в поле центрального гладкого …