| Description |
1 online resource (121 pages) |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; Volume 118, Number 564 |
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Memoirs of the American Mathematical Society ; Volume 118, no. 564.
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| Contents |
Table of Contents -- 1 Introduction -- 2 Three examples -- 2.1 Riemannian geodesies -- 2.2 The Heisenberg algebra case -- 2.3 An abnormal minimizer -- 3 Notational conventions and definitions -- 3.1 Manifolds, charts, bundles, curves and arcs -- 3.2 Hamiltonian functions, Hamilton vector fields, and bicharacteristics -- 3.3 Hamiltonian lifts and characteristics -- 3.4 Distributions, admissible curves, orbits -- 3.5 Nonholonomic distributions; regularity -- 4 Abnormal extremals -- 5 Sub-Riemannian manifolds, length minimizers and extremals |
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5.1 The sub-Riemannian distance, length minimization and time optimality5.2 Extremals -- 5.3 The relationship between minimality and extremality -- 6 Regular abnormal extremals for rank-two distributions -- 6.1 The regular abnormal foliation of a rank-two distribution -- 6.2 Regular abnormal biextremals of a sub-Riemannian manifold -- 7 Local optimality of regular abnormal extremals -- 7.1 The main inequality -- 7.2 The normal form theorem -- 7.3 The optimality theorem -- 8 Strict abnormality -- 9 Some special cases -- 9.1 2- and 3-generating distributions |
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9.2 3-Regular distributions9.3 The 4- and 5-dimensional cases -- 9.4 The three-dimensional case -- 9.5 A Lie group example -- 9.6 A nonsmooth abnormal extremal -- Appendix A: The Gaveau-Brockett problem -- Appendix B: Proof of Theorem 1 -- B.l: Control systems -- B.2: The Maximum Principle -- Appendix C: Local optimality of normal extremals -- Appendix D: Rigid sub-Riemannian arcs and local optimality -- Appendix E: A nonoptimality proof -- References |
| Notes |
"November 1995, Volume 118, Number 564 (second of 5 numbers)"--Cover |
| Bibliography |
Includes bibliographical references |
| Notes |
Print version record |
| Subject |
Geometry, Riemannian.
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Geodesics (Mathematics)
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Geodesics (Mathematics)
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Geometry, Riemannian.
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| Form |
Electronic book
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| Author |
Sussmann, Hector J., 1946- author.
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| ISBN |
9781470401436 |
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1470401436 |
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