1,437 research outputs found
Non-integrability of the problem of a rigid satellite in gravitational and magnetic fields
In this paper we analyse the integrability of a dynamical system describing
the rotational motion of a rigid satellite under the influence of gravitational
and magnetic fields. In our investigations we apply an extension of the Ziglin
theory developed by Morales-Ruiz and Ramis. We prove that for a symmetric
satellite the system does not admit an additional real meromorphic first
integral except for one case when the value of the induced magnetic moment
along the symmetry axis is related to the principal moments of inertia in a
special way.Comment: 39 pages, 4 figures, missing bibliography was adde
On algebraic construction of certain integrable and super-integrable systems
We propose a new construction of two-dimensional natural bi-Hamiltonian
systems associated with a very simple Lie algebra. The presented construction
allows us to distinguish three families of super-integrable monomial potentials
for which one additional first integral is quadratic, and the second one can be
of arbitrarily high degree with respect to the momenta. Many integrable systems
with additional integrals of degree greater than two in momenta are given.
Moreover, an example of a super-integrable system with first integrals of
degree two, four and six in the momenta is found.Comment: 37 page
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