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

DOI10.1155/2016/8958747zbMath1358.70010OpenAlexW2345877267WikidataQ59122582 ScholiaQ59122582MaRDI QIDQ310361

H. M. Yehia, A. A. Elmandouh

Publication date: 8 September 2016

Published in: Advances in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2016/8958747

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 (5)

Integrable magnetic geodesic flows on 2-surfaces ^* ⋮ Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system ⋮ On the application of KBM method for the 3-D motion of asymmetric rigid body ⋮ First integrals of motion for two dimensional weight-homogeneous Hamiltonian systems in curved spaces ⋮ On the integrability of new examples of two-dimensional Hamiltonian systems in curved spaces

Cites Work

• Unnamed Item
• Unnamed Item
• New integrable systems with a quartic integral and new generalizations of kovalevskaya's and goriatchev's cases
• Further classification of 2D integrable mechanical systems with quadratic invariants
• New integrable problems in the dynamics of particle and rigid body
• A theory of exact and approximate configurational invariants
• Pairs of commuting Hamiltonians quadratic in the momenta
• First integrals versus configurational invariants and a weak form of complete integrability
• Commuting quadratic Hamiltonians with velocity dependent potentials
• Non-homogeneous systems of hydrodynamic type, related to quadratic Hamiltonians with electromagnetic term
• Commutative Poisson subalgebras for Sklyanin brackets and deformations of some known integrable models
• Completely integrable 2D Lagrangian systems and related integrable geodesic flows on various manifolds
• Compatibility conditions for a non-quadratic integral of motion
• Integrals of motion and analytic functions
• Integrability of Hamiltonians with third- and fourth-degree polynomial potentials
• Polynomial constants of motion in flat space
• Atlas of two-dimensional irreversible conservative Lagrangian mechanical systems with a second quadratic integral
• Integrable Hamiltonian systems with velocity-dependent potentials
• On a generalization of certain results of Goriatchev, Chaplygin and Sretensky in the dynamics of rigid bodies
• On certain two-dimensional conservative mechanical systems with a cubic second integral
• On a family of integrable systems on S² with a cubic integral of motion
• Dynamics on strata of trigonal Jacobians and some integrable problems of rigid body motion
• On quasi-Stäckel Hamiltonians
• The master integrable two-dimensional system with a quartic second integral

This page was built for publication: Integrable 2D time-irreversible systems with a cubic second integral