Rolling balls and octonions

DOI10.1134/S0081543807030030zbMath1153.70010arXivmath/0611812OpenAlexW2110794153MaRDI QIDQ2377564

Andrei A. Agrachev

Publication date: 19 January 2009

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611812

zbMATH Keywords

invariantshidden symmetriesvector distributions

Mathematics Subject Classification ID

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) Motion of a rigid body in contact with a solid surface (70E18)

Related Items (19)

Geometrical applications of split octonions ⋮ Homogeneous real \((2,3,5)\) distributions with isotropy ⋮ 𝐺₂ and the rolling ball ⋮ Geometric conditions for the existence of a rolling without twisting or slipping ⋮ A codimension 3 sub-Riemannian structure on the Gromoll-Meyer exotic sphere ⋮ A historical review on nonholomic mechanics ⋮ Symmetries of the rolling model ⋮ Dancing polygons, rolling balls, and the Cartan-Engel distribution ⋮ The dancing metric, ${G}_2$-symmetry and projective rolling ⋮ Twistor space for rolling bodies ⋮ Conservation laws, hierarchy of dynamics and explicit integration of nonholonomic systems ⋮ Rolling Maps and Nonlinear Data ⋮ Chaplygin systems associated to Cartan decompositions of semi-simple Lie groups ⋮ Cartan's incomplete classification and an explicit ambient metric of holonomy \(\mathrm G_2^\ast\) ⋮ Duality on geodesics of Cartan distributions and sub-Riemannian pseudo-product structures ⋮ Cartan meets Chaplygin ⋮ Extremals for a series of sub-Finsler problems with 2-dimensional control via convex trigonometry ⋮ DUALITY OF (2, 3, 5)-DISTRIBUTIONS AND LAGRANGIAN CONE STRUCTURES ⋮ Ants and bracket generating distributions in dimensions 5 and 6

Cites Work

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• Rigidity of integral curves of rank 2 distributions
• Geometry of Jacobi curves. I
• Control theory from the geometric viewpoint.
• Feedback-invariant optimal control theory and differential geometry. II. Jacobi curves for singular extremals
• On variational approach to differential invariants of rank two distributions
• Differential equations and conformal structures

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