On certain two-dimensional conservative mechanical systems with a cubic second integral

DOI10.1088/0305-4470/35/44/314zbMath1070.70009OpenAlexW2022951943MaRDI QIDQ4468025

H. M. Yehia

Publication date: 10 June 2004

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0305-4470/35/44/314

zbMATH Keywords

Goryachev-Chaplygin problemHall-Toda systemsintegrable two-dimensional Lagrangian systems

Mathematics Subject Classification ID

Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Dynamical systems in classical and celestial mechanics (37N05) Lagrange's equations (70H03) Integrable cases of motion in rigid body dynamics (70E40)

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Integrable magnetic geodesic flows on 2-surfaces ^* ⋮ Integrable 2D time-irreversible systems with a cubic second integral ⋮ On the application of KBM method for the 3-D motion of asymmetric rigid body ⋮ New integrable problems in rigid body dynamics with quartic integrals ⋮ Topological atlas of the Kovalevskaya-Yehia gyrostat ⋮ First integrals of motion for two dimensional weight-homogeneous Hamiltonian systems in curved spaces ⋮ Integrability analysis of natural Hamiltonian systems in curved spaces ⋮ Erratum to: ``On a class of integrable systems with a cubic first integral ⋮ Atlas of two-dimensional irreversible conservative Lagrangian mechanical systems with a second quadratic integral ⋮ New Families of Integrable Two-Dimensional Systems with Quartic Second Integrals ⋮ Differential invariants for cubic integrals of geodesic flows on surfaces ⋮ On two-dimensional integrable models with a cubic or quartic integral of motion ⋮ New integrable problems in the dynamics of particle and rigid body

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