A geometric characterization of certain first integrals for nonholonomic systems with symmetries

DOI10.3842/SIGMA.2016.018zbMath1366.70019arXiv1510.08314OpenAlexW1859698088MaRDI QIDQ254662

Paula Balseiro, Nicola Sansonetto

Publication date: 8 March 2016

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.08314

zbMATH Keywords

nonholonomic systemsfirst integralsgauge symmetries and gauge momentaLie group symmetries

Mathematics Subject Classification ID

Momentum maps; symplectic reduction (53D20) Nonholonomic systems related to the dynamics of a system of particles (70F25) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

Related Items (9)

First integrals and symmetries of nonholonomic systems ⋮ Conserved quantities and Hamiltonization of nonholonomic systems ⋮ On the geometry of the Hamilton-Jacobi equation and generating functions ⋮ Integrability and chaos in figure skating ⋮ Hamiltonization of solids of revolution through reduction ⋮ Symmetries of line bundles and Noether theorem for time-dependent nonholonomic systems ⋮ Gauge momenta as Casimir functions of nonholonomic systems ⋮ Symmetries and conservation laws of Hamiltonian systems ⋮ Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Conservation of `moving' energy in nonholonomic systems with affine constraints and integrability of spheres on rotating surfaces
• Dirac structures, nonholonomic systems and reduction
• The Jacobiator of nonholonomic systems and the geometry of reduced nonholonomic brackets
• Conservation laws, hierarchy of dynamics and explicit integration of nonholonomic systems
• The reaction-annihilator distribution and the nonholonomic Noether theorem for lifted actions
• Geometric control and numerical aspects of nonholonomic systems
• Reduction of almost Poisson brackets and Hamiltonization of the Chaplygin sphere
• Gauge conservation laws and the momentum equation in nonholonomic mechanics
• Nonholonomic Noether theorem and reduction of symmetries
• Reduction of nonholonomic mechanical systems with symmetries
• Various approaches to conservative and nonconservative nonholonomic systems
• Nonholonomic reduction
• Examples of gauge conservation laws in nonholonomic systems
• Linear conservation laws of nonholonomic systems with symmetry
• Momentum maps and Hamiltonian reduction
• Linear weakly Noetherian constants of motion are horizontal gauge momenta
• On the Hamiltonian formulation of nonholonomic mechanical systems
• Chaplygin's ball rolling problem is Hamiltonian
• Nonholonomic mechanics and control. With the collaboration of J. Baillieul, P. Crouch, and J. Marsden. With scientific input from P. S. Krishnaprasad, R. M. Murray, and D. Zenkov.
• Rolling of a ball on a surface. New integrals and hierarchy of dynamics
• Reduction of constrained mechanical systems and stability of relative equilibria
• Gauge transformations, twisted Poisson brackets and Hamiltonization of nonholonomic systems
• Nonholonomic mechanical systems with symmetry
• On the number of weakly Noetherian constants of motion of nonholonomic systems
• Conserved quantities and Hamiltonization of nonholonomic systems
• THE CARTAN FORM FOR CONSTRAINED LAGRANGIAN SYSTEMS AND THE NONHOLONOMIC NOETHER THEOREM
• Reduction of nonholonomic systems in two stages and Hamiltonization
• Dirac Brackets in Constrained Dynamics
• First integrals of non-holonomic systems and their generators

This page was built for publication: A geometric characterization of certain first integrals for nonholonomic systems with symmetries