Classification of integrable cases in the dynamics of a four-dimensional rigid body in a nonconservative field in the presence of a tracking force

DOI10.1007/s10958-015-2220-0zbMath1346.70007OpenAlexW2152121859MaRDI QIDQ893719

M. V. Shamolin

Publication date: 20 November 2015

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

Full work available at URL: https://doi.org/10.1007/s10958-015-2220-0

zbMATH Keywords

integrable casesfour-dimensional rigid body

Mathematics Subject Classification ID

Integrable cases of motion in rigid body dynamics (70E40) Higher-dimensional generalizations in rigid body dynamics (70E45)

Related Items (2)

Low-dimensional and multidimensional pendulums in nonconservative fields. I ⋮ Low-dimensional and multidimensional pendulums in nonconservative fields. II

Cites Work

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• Some questions of qualitative theory in dynamics of systems with the variable dissipation
• Dynamical systems with variable dissipation: approaches, methods, and applications
• On integrability in elementary functions of certain classes of nonconservative dynamical systems
• Phase pattern classification for the problem of the motion of a body in a resisting medium in the presence of a linear damping moment
• Introduction to problem on braking of a body in a resisting medium and new two-parametric family of phase portraits
• New integrable cases and families of portraits in the plane and spatial dynamics of a rigid body interacting with a medium
• New integrable, in the sense of Jacobi, cases in the dynamics of a rigid body interacting with a medium.
• Classes of variable dissipation systems with nonzero mean in the dynamics of a rigid body
• Complete integrability of equations of motion of a spatial pendulum placed in an incident medium
• Levi-Civita symbols, generalized vector products, and new integrable cases in mechanics of multidimensional bodies
• Comparison of complete integrability cases in dynamics of a two-, three-, and four-dimensional rigid body in a nonconservative field
• Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems
• Sessions of the workshop of the Mathematics and Mechanics Department of Lomonosov Moscow State University, ``Topical problems of geometry and mechanics named after V. V. Trofimov
• Averaging operators and real equations of hydromechanics
• Classification of complete integrability cases in four-dimensional symmetric rigid-body dynamics in a nonconservative field
• Valeriĭ Vladimirovich Trofimov (1952--2003)
• Integrability and non-integrability in Hamiltonian mechanics
• The definition of relative robustness and a two-parameter family of phase portraits in the dynamics of a rigid body
• Integrability of some classes of dynamic systems in terms of elementary functions
• A completely integrable case in the dynamics of a four-dimensional rigid body in a non-conservative field
• Topological analysis of Steklov's integrable cases
• Spatial topographical systems of Poincaré and comparison systems
• On integrability in transcendental functions
• Robustness of dissipative systems and relative robustness and non-robustness of systems with variable dissipation
• On limit sets of differential equations near singular critical points
• Some Methods of Analysis of the Dynamic Systems with the Various Dissipation in Dynamics of a Rigid Body
• Geometrical Representation of the Motion of a Body Through a Medium
• A case of complete integrability in the dynamics on the tangent bundle of a two-dimensional sphere
• Sessions of the workshop of the Mathematics and Mechanics Department of Lomonosov Moscow State University, ``Urgent problems of geometry and mechanics named after V. V. Trofimov
• Sessions of the workshop of the Mathematics and Mechanics Department of Lomonosov Moscow State University, ``Urgent problems of geometry and mechanics named after V. V. Trofimov
• Sessions of the workshop of the Mathematics and Mechanics Department of Lomonosov Moscow State University, ``Urgent problems of geometry and mechanics named after V. V. Trofimov

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