Affine connections and distributions with applications to nonholonomic mechanics

DOI10.1016/S0034-4877(98)80008-6zbMath0976.53015OpenAlexW2058113136MaRDI QIDQ1289588

Andrew D. Lewis

Publication date: 8 January 2002

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0034-4877(98)80008-6

zbMATH Keywords

distributionintegrabilitytransformationsaffine connectiongeodesic invariance

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Local submanifolds (53B25) Linear and affine connections (53B05)

Related Items

Jacobi fields in nonholonomic mechanics ⋮ Invariant nonholonomic Riemannian structures on three-dimensional Lie groups ⋮ Restricted Jacobi Fields ⋮ The physical foundations of geometric mechanics ⋮ Pseudo-Riemannian foliations and their graphs ⋮ Virtual nonholonomic constraints: a geometric approach ⋮ Unnamed Item ⋮ The automorphism groups of foliations with transverse linear connection ⋮ Nonholonomic mechanical systems and Kaluza-Klein theory ⋮ Nonholonomic and constrained variational mechanics ⋮ General framework for nonholonomic mechanics: Nonholonomic systems on Lie affgebroids ⋮ Nonholonomic connections, time reparametrizations, and integrability of the rolling ball over a sphere ⋮ On some aspects of the geometry of non integrable distributions and applications ⋮ Radial kinetic nonholonomic trajectories are Riemannian geodesics! ⋮ GEOMETRIC INTERPRETATIONS OF THE SYMMETRIC PRODUCT IN AFFINE DIFFERENTIAL GEOMETRY AND APPLICATIONS ⋮ On mechanical control systems with nonholonomic constraints and symmetries ⋮ Horizontal connection and horizontal mean curvature in Carnot groups ⋮ Trajectory design for mechanical control systems: from geometry to algorithms ⋮ THE CARTAN FORM FOR CONSTRAINED LAGRANGIAN SYSTEMS AND THE NONHOLONOMIC NOETHER THEOREM ⋮ A LINEAR CONNECTION FOR BOTH SUB-RIEMANNIAN GEOMETRY AND NONHOLONOMIC MECHANICS (II) ⋮ Cartan meets Chaplygin

Cites Work

• Hamiltonian systems with constraints and their meaning in mechanics
• Manifolds, tensor analysis, and applications.
• Reduction of some classical non-holonomic systems with symmetry
• Examples of gauge conservation laws in nonholonomic systems
• Reduction of constrained mechanical systems and stability of relative equilibria
• On nonholonomic and vakonomic dynamics of mechanical systems with nonintegrable constraints
• Nonholonomic mechanical systems with symmetry
• Variational principles for constrained systems: Theory and experiment
• Simple mechanical control systems with constraints
• Configuration Controllability of Simple Mechanical Control Systems
• On the geometry of non-holonomic Lagrangian systems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item