Optimal control of the sphere \(S^n\) rolling on \(E^n\)

DOI10.1007/s00498-004-0143-2zbMath1064.49021OpenAlexW2078789729MaRDI QIDQ1770228

Jason A. Zimmerman

Publication date: 14 April 2005

Published in: MCSS. Mathematics of Control, Signals, and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00498-004-0143-2

zbMATH Keywords

optimal controlNoether theoremballnonholonomic systemrolling spheresub-Riemannianabnormal extremalscompletely integrable Hamiltonian systemssymmetric integrals

Mathematics Subject Classification ID

Automated systems (robots, etc.) in control theory (93C85) Control of mechanical systems (70Q05) Nonholonomic systems related to the dynamics of a system of particles (70F25) Optimality conditions for problems involving ordinary differential equations (49K15) Motion of a rigid body in contact with a solid surface (70E18) Nonholonomic dynamical systems (37J60)

Related Items (12)

Pure rolling motion of hyperquadrics in pseudo-Euclidean spaces ⋮ Geometric conditions for the existence of a rolling without twisting or slipping ⋮ An intrinsic formulation of the problem on rolling manifolds ⋮ Symmetric spaces rolling on flat spaces ⋮ Rolling sphere problems on spaces of constant curvature ⋮ Rolling Maps and Nonlinear Data ⋮ On the geometry of rolling and interpolation curves on \(S^n\), \(\mathrm{SO}_n\), and Grassmann manifolds ⋮ Rolling Problems on Spaces of Constant Curvature ⋮ Submersions, Hamiltonian Systems, and Optimal Solutions to the Rolling Manifolds Problem ⋮ Rolling Stiefel manifolds ⋮ A unifying approach for rolling symmetric spaces ⋮ Unnamed Item

Cites Work

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• On Hammersley's minimum problem for a rolling sphere
• Abnormal Minimizers
• Nonholonomic Control Systems on Riemannian Manifolds
• Shortest paths for sub-Riemannian metrics on rank-two distributions

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