On the dynamics of mechanical systems with the homogeneous polynomial potential \(V = ax ^{4} + cx ^{2} y ^{2}\)

DOI10.1007/S10884-009-9144-7zbMath1196.37097OpenAlexW2005164933MaRDI QIDQ735063

Claudio Vidal, Manuel J. Falconi, Ernesto A. Lacomba

Publication date: 14 October 2009

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-009-9144-7

zbMATH Keywords

potentialpolynomial, Hamiltonian system

Mathematics Subject Classification ID

Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30) Hamiltonian and Lagrangian mechanics (70H99)

Related Items (3)

Classification of global phase portraits and bifurcation diagrams of Hamiltonian systems with rational potential ⋮ Dynamics of mechanical systems with polynomial potentials ⋮ Global phase portraits and bifurcation diagrams for Hamiltonian systems of linear plus quartic homogeneous polynomials symmetric with respect to the \(y\)-axis

Cites Work

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• On the dynamics of mechanical systems with homogeneous polynomial potentials of degree \(4\)
• Darboux points and integrability of Hamiltonian systems with homogeneous polynomial potential
• Chaos in a quartic dynamical model
• The inverse problem of dynamics: basic facts

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