Comparison of complete integrability cases in dynamics of a two-, three-, and four-dimensional rigid body in a nonconservative field

DOI10.1007/s10958-012-1068-9zbMath1277.37104OpenAlexW2066790455MaRDI QIDQ1948590

M. V. Shamolin

Publication date: 24 April 2013

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

Full work available at URL: https://doi.org/10.1007/s10958-012-1068-9

zbMATH Keywords

complete integrabilitydynamics of a rigid body

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical systems in classical and celestial mechanics (37N05) Integrable cases of motion in rigid body dynamics (70E40)

Related Items (14)

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 ⋮ New examples of integrable systems with dissipation on the tangent bundles of multidimensional spheres ⋮ Integrable motions of a pendulum in a two-dimensional plane ⋮ 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 systems with dissipation on the tangent bundles of 2- and 3-dimensional spheres ⋮ Integrable variable dissipation systems on the tangent bundle of a multi-dimensional sphere and some applications ⋮ Low-dimensional and multidimensional pendulums in nonconservative fields. I ⋮ Low-dimensional and multidimensional pendulums in nonconservative fields. II ⋮ Phase portraits of dynamical equations of motion of a rigid body in a resistive medium ⋮ Variety of integrable cases in dynamics of low- and multi-dimensional rigid bodies in nonconservative force fields

Cites Work

• Body motion in a resisting medium
• New integrable, in the sense of Jacobi, cases in the dynamics of a rigid body interacting with a medium.
• Some questions of the qualitative theory of ordinary differential equations and dynamics of a rigid body interacting with a medium
• Valeriĭ Vladimirovich Trofimov (1952--2003)
• A case of complete integrability in the dynamics on the tangent bundle of a two-dimensional sphere
• An integrable case of dynamical equations on $ so(4)\times\mathbb R^4$
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