Bifurcations of quasi-periodic solutions from relative equilibria in the Lennard-Jones 2-body problem

DOI10.1007/s10569-021-10041-9zbMath1484.37060OpenAlexW3201716186MaRDI QIDQ2052959

Daniel Strzelecki

Publication date: 29 November 2021

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10569-021-10041-9

zbMATH Keywords

periodic solutionsHamiltonian systems\(N\)-body problemLennard-Jones potentialLyapunov center theorem

Mathematics Subject Classification ID

Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Bifurcations and instability for nonlinear problems in mechanics (70K50) Dynamical systems in classical and celestial mechanics (37N05) (n)-body problems (70F10) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46)

Cites Work

• The two-body problem with generalized Lennard-Jones potential
• Solutions of the generalized Lennard-Jones system
• Periodic solutions for the generalized anisotropic Lennard-Jones Hamiltonian
• Introduction to Hamiltonian dynamical systems and the \(N\)-body problem.
• Symmetric Liapunov center theorem for minimal orbit
• Equilibrium points and central configurations for the Lennard-Jones 2- and 3-body problems
• Periodic solutions of symmetric Hamiltonian systems
• Homographic solutions of the \(N\)-body generalized Lennard-Jones system
• Normal modes for nonlinear Hamiltonian systems
• Periodic orbits near an equilibrium and a theorem by Alan Weinstein