A reversible bifurcation analysis of the inverted pendulum

DOI10.1016/S0167-2789(97)00201-7zbMath1194.70029MaRDI QIDQ992207

Igor Hoveijn, Henk W. Broer, Martijn van Noort

Publication date: 11 September 2010

Published in: Physica D (Search for Journal in Brave)

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Forced motions for nonlinear problems in mechanics (70K40) Hamilton's equations (70H05) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

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Uses Software

• DSTool

Cites Work

• Equivariant singularity theory with distinguished parameters: two case studies of resonant Hamiltonian systems
• The Hamiltonian Hopf bifurcation
• Singularities and groups in bifurcation theory. Volume I
• A normally elliptic Hamiltonian bifurcation
• Geometrical aspects of stability theory for Hill's equations
• Stability of the Inverted Pendulum—A Topological Explanation
• Equivalence and Decomposition of Vector Fields About an Elementary Critical Point
• Averaging methods in nonlinear dynamical systems
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