Further classification of 2D integrable mechanical systems with quadratic invariants

DOI10.1134/S1560354709040121zbMath1229.70056MaRDI QIDQ653253

H. M. Yehia

Publication date: 9 January 2012

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

zbMATH Keywords

quadratic invariantsintegrable Lagrangian systemstime-irreversible systems

Mathematics Subject Classification ID

Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Integrable cases of motion in rigid body dynamics (70E40)

Related Items (1)

Integrable 2D time-irreversible systems with a cubic second integral

Cites Work

• Commuting quadratic Hamiltonians with velocity dependent potentials
• On integrable Hamiltonians with velocity-dependent potentials
• An integrable motion of a particle on a smooth ellipsoid
• Integrable and superintegrable Hamiltonian systems in magnetic fields
• Variable separation for natural Hamiltonians with scalar and vector potentials on Riemannian manifolds
• Integrable Hamiltonian systems with vector potentials
• Atlas of two-dimensional irreversible conservative Lagrangian mechanical systems with a second quadratic integral
• Integrable Hamiltonian systems with velocity-dependent potentials
• Generalized natural mechanical systems of two degrees of freedom with quadratic integrals
• Superintegrable systems on the two-dimensional sphere S2 and the hyperbolic plane H2
• Motions of a particle on a sphere and integrable motions of a rigid body

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