Controlled Lagrangians and stabilization of Euler-Poincaré equations with symmetry breaking nonholonomic constraints

DOI10.1007/S00332-024-10066-YMaRDI QIDQ6599776

Jorge S. Garcia, Tomoki Ohsawa

Publication date: 6 September 2024

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

zbMATH Keywords

Lie groupsemidirect productbroken symmetrynonholonomic Euler-Poincaré equationspendulum skate

Mathematics Subject Classification ID

Control of mechanical systems (70Q05) Nonholonomic systems related to the dynamics of a system of particles (70F25) Motion of a rigid body in contact with a solid surface (70E18) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65) Lagrange's equations (70H03)

Cites Work

• Title not available (Why is that?)
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• Dirac reduction for nonholonomic mechanical systems and semidirect products
• Hamiltonization of the generalized Veselova LR system
• Symmetries and reduction in nonholonomic mechanics
• Currents on Lie groups with nonholonomic connection and integrable non- Hamiltonian systems
• On stabilization by means of the Energy-Casimir method
• The Euler-Poincaré equations and semidirect products with applications to continuum theories
• Nonlinear systems. Analysis, stability, and control
• The Lyapunov-Malkin theorem and stabilization of the unicycle with rider
• Nonholonomic LR systems as generalized Chaplygin systems with an invariant measure and flows on homogeneous spaces
• Integrability and chaos in figure skating
• Controlled Lagrangians and the stabilization of Euler-Poincaré mechanical systems
• Controlled Lagrangians and the stabilization of mechanical systems. I: The first matching theorem.
• Non-holonomic Euler-Poincare´ equations and stability in Chaplygin's sphere
• Semidirect Products and Reduction in Mechanics
• Nonholonomic constraints: A new viewpoint
• On Hamel’s equations
• Quasivelocities and symmetries in non-holonomic systems
• Geometric Mechanics

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