Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems

DOI10.1007/s10958-012-0650-5zbMath1353.37121OpenAlexW2069113748MaRDI QIDQ2256715

M. V. Shamolin, Valerij V. Trofimov

Publication date: 20 February 2015

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-012-0650-5

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Dynamical systems in classical and celestial mechanics (37N05)

Related Items (21)

Tensor invariants of geodesic, potential, and dissipative systems on tangent bundles of two-dimensional manifolds ⋮ Integrable systems in the dynamics on the tangent bundle of a two-dimensional sphere ⋮ Integrable cases in the dynamics of a multi-dimensional rigid body in a nonconservative field in the presence of a tracking force ⋮ Integrable systems with variable dissipation on the tangent bundle of a sphere ⋮ Integrable nonconservative dynamical systems on the tangent bundle of the multidimensional sphere ⋮ New cases of integrability of equations of motion of a rigid body in the \(n\)-dimensional space ⋮ Transcendental first integrals of dynamical systems on the tangent bundle to the sphere ⋮ Classification of integrable cases in the dynamics of a four-dimensional rigid body in a nonconservative field in the presence of a tracking force ⋮ Integrable seventh and ninth order dynamic systems with dissipation ⋮ Invariant volume forms of geodesic, potential, and dissipative systems on a tangent bundle of a four-dimensional manifold ⋮ Invariant forms of geodesic, potential, and dissipative systems on tangent bundles of finite-dimensional manifolds ⋮ Invariants of fifth-order homogeneous systems with dissipation ⋮ Invariant volume forms of variable dissipation systems with three degrees of freedom ⋮ New cases of integrable odd-order systems with dissipation ⋮ New cases of homogeneous integrable systems with dissipation on tangent bundles of two-dimensional manifolds ⋮ New cases of homogeneous integrable systems with dissipation on tangent bundles of three-dimensional manifolds ⋮ New cases of homogeneous integrable systems with dissipation on tangent bundles of four-dimensional manifolds ⋮ Phase portraits of dynamical equations of motion of a rigid body in a resistive medium ⋮ Family of Phase Portraits in the Spatial Dynamics of a Rigid Body Interacting with a Resisting Medium ⋮ Integrable third and fifth order dynamical systems with dissipation ⋮ New cases of integrability of systems of geodesics and potential and dissipative systems on tangent bundles of finite-dimensional manifolds

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