Invariant nonholonomic Riemannian structures on three-dimensional Lie groups

DOI10.3934/jgm.2016001zbMath1390.70040OpenAlexW2409626691MaRDI QIDQ326670

Rory Biggs, Dennis I. Barrett, Claudiu C. Remsing, Olga Krupková

Publication date: 12 October 2016

Published in: Journal of Geometric Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/jgm.2016001

zbMATH Keywords

invariant nonholonomic Riemannian structureisometric invariantnonholonomic connectionnonholonomic mechanical systemSchouten curvature tensor

Mathematics Subject Classification ID

Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) General properties and structure of real Lie groups (22E15) Sub-Riemannian geometry (53C17) Nonholonomic dynamical systems (37J60)

Related Items

Restricted Jacobi Fields, Non-holonomic equations for the normal extremals in geometric control theory, On the Schouten and Wagner curvature tensors, Nonholonomic connections, time reparametrizations, and integrability of the rolling ball over a sphere, A note about integrable systems on low-dimensional Lie groups and Lie algebras, A note on flat nonholonomic Riemannian structures on three-dimensional Lie groups, Classification of left invariant metrics on 4-dimensional solvable Lie groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sub-Riemannian structures on 3D Lie groups
• On the theory of motion of nonholonomic systems. The reducing-multiplier theorem. Translated from the Russian 1911 original
• Geometric control and numerical aspects of nonholonomic systems
• Integrable nonholonomic systems on Lie groups
• Nonholonomic problems and the theory of distributions
• Invariant measures of Euler-Poincaré equations on Lie algebras
• Affine connections and distributions with applications to nonholonomic mechanics
• The Wagner curvature tensor in nonholonomic mechanics
• Geometric equivalence on nonholonomic three-manifolds
• Nonholonomic LR systems as generalized Chaplygin systems with an invariant measure and flows on homogeneous spaces
• 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.
• About Cartan geometrization of non-holonomic mechanics
• The Bianchi classification in the Schücking-Behr approach
• Uniform projectile motion: Dynamics, symmetries and conservation laws
• Simple mechanical control systems with constraints
• Non-holonomic connections following Élie Cartan
• Geometry and integrability of Euler-Poincaré-Suslov equations
• The relativistic mechanics in a nonholonomic setting: a unified approach to particles with non-zero mass and massless particles
• The hydrodynamic Chaplygin sleigh
• The Poisson equations in the nonholonomic Suslov problem: integrability, meromorphic and hypergeometric solutions
• Nonholonomic mechanics and connections over a bundle map
• Exponential Barycenters of the Canonical Cartan Connection and Invariant Means on Lie Groups
• Geometry VI. Riemannian geometry. Transl. from the Russian by S. A. Vakhrameev