O ct 2 00 1 A generalized Kowalevski Hamiltonian and new integrable cases on e ( 3 ) and so ( 4 ) . Vladimir
نویسنده
چکیده
A generalized Kowalevski Hamiltonian and new integrable cases on e(3) and so(4). 1 A new integrable case for the Kirchhoff equation. The Kirchhoff equations (see for example [1]) for the motion of a rigid body in an ideal fluid read as follows M t = M × ∂H ∂M + Γ × ∂H ∂Γ , Γ t = Γ × ∂H ∂M ,
منابع مشابه
ar X iv : m at h - ph / 0 51 00 88 v 1 2 6 O ct 2 00 5 Quasi - Chaplygin Systems and Nonholonimic Rigid Body Dynamics ∗
We show that the Suslov nonholonomic rigid body problem studied in [10, 13, 26] can be regarded almost everywhere as a generalized Chaplygin system. Furthermore, this provides a new example of a multidimensional nonholonomic system which can be reduced to a Hamiltonian form by means of Chaplygin reducing multiplier. Since we deal with Chaplygin systems in the local sense, the invariant manifold...
متن کاملO ct 2 00 3 On two recent generalizations of the Harry Dym equation
Two generalized Harry Dym equations, recently found by Brunelli, Das and Popowicz in the bosonic limit of new supersymmetric extensions of the Harry Dym hierarchy, are transformed into previously known integrable systems: one—into a pair of decoupled KdV equations , the other one—into a pair of coupled mKdV equations from a bi-Hamiltonian hierarchy of Kupershmidt.
متن کامل2 8 M ay 2 00 4 Integrable quadratic Hamiltonians on so ( 4 ) and so ( 3 , 1 ) Vladimir
In this paper we consider the following family of Poisson brackets {Mi,Mj} = εijk Mk, {Mi, γj} = εijk γk, {γi, γj} = κ εijk Mk. (1.1) Here Mi and γi are components of 3-dimensional vectors M and Γ, εijk is the totally skew-symmetric tensor, κ is a parameter. It is well-known that any linear Poisson bracket is defined by an appropriate Lie algebra. The cases κ = 0, κ > 0 and κ < 0 correspond to ...
متن کاملKowalevski top revisited
We review the separation of variables for the Kowalevski top and for its generalization to the algebra o(4). We notice that the corresponding separation equations allow an interpretation of the Kowalevski top as a B (1) 2 integrable lattice. Consequently, we apply the quadratic r-matrix formalism to construct a new 2× 2 Lax matrix for the top, which is responsible for its separation of variable...
متن کاملIntegrable quadratic classical Hamiltonians on so(4) and so(3, 1)
We investigate a special class of quadratic Hamiltonians on so(4) and so(3, 1) and describe Hamiltonians that have additional polynomial integrals. One of the main results is a new integrable case with an integral of sixth degree. PACS numbers: 02.30.Hq, 02.30.Ik, 45.30.+s Mathematics Subject Classification: 34M55, 37J35, 37N15
متن کامل