Detecting stable-unstable nonlinear invariant manifold and homoclinic orbits in mechanical systems

DOI10.1007/s11071-010-9787-2zbMath1215.70015OpenAlexW2043393553MaRDI QIDQ547210

Stefano Lenci, Giuseppe Rega

Publication date: 30 June 2011

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-010-9787-2

zbMATH Keywords

homoclinic orbitsinvariant manifoldbuckled beamsaddle-center

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Bifurcation and buckling (74G60) Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics (70K44) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items

Convergent analytic solutions for homoclinic orbits in reversible and non-reversible systems

Uses Software

• AUTO
• HomCont

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Invariant manifolds for flows in Banach spaces
• Dimension reduction of homoclinic orbits of buckled beams via the non-linear normal modes technique
• Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle- center
• Normally hyperbolic invariant manifolds in dynamical systems
• Optimal numerical control of single-well to cross-well chaos transition in mechanical systems.
• Horseshoes in two-degree-of-freedom Hamiltonian systems with saddle-centers
• A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam
• Stability of homoclinic orbits and diffusion in phase space.
• Detection of symmetric homoclinic orbits to saddle-centres in reversible systems
• Dimension reduction of dynamical systems: methods, models, applications
• NUMERICAL COMPUTATION OF HOMOCLINIC ORBITS FOR FLOWS
• FROM SINGLE WELL CHAOS TO CROSS WELL CHAOS: A DETAILED EXPLANATION IN TERMS OF MANIFOLD INTERSECTIONS
• Irregular dynamics and homoclinic orbits to Hamiltonian saddle centers
• CALCULATING STABLE AND UNSTABLE MANIFOLDS
• Orbits homoclinic to centre manifolds of conservative PDEs
• Multibump homoclinic solutions to a centre equilibrium in a class of autonomous Hamiltonian systems
• Cascades of homoclinic orbits to a saddle-centre for reversible and perturbed Hamiltonian systems
• Invariant manifolds
• Nonlinear modal analysis of structural systems using multi-mode invariant manifolds