Strong minimality of abnormal geodesics for \(2\)-distributions

DOI10.1007/BF02254637zbMath0951.53029OpenAlexW2025597993MaRDI QIDQ1972690

Yanyan Li

Publication date: 13 April 2000

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02254637

zbMATH Keywords

abnormal geodesicsub-Riemannian geodesicstrong generalized Legendre condition

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Geodesics in global differential geometry (53C22) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10) Sub-Riemannian geometry (53C17)

Related Items (15)

On the role of abnormal minimizers in sub-Riemannian geometry ⋮ Méthodes géométriques et analytiques pour étudier l'application exponentielle, la sphère et le front d'onde en géométrie sous-riemannienne dans le cas Martinet ⋮ Sub-Riemannian Metrics: Minimality of Abnormal Geodesics versus Subanalyticity ⋮ Abnormal sub-Riemannian geodesics: Morse index and rigidity ⋮ Rigid paths of generic 2-distributions on 3-manifolds ⋮ Asymptotics of accessibility sets along an abnormal trajectory ⋮ Extremal controls for chained systems ⋮ Optimal Strokes at Low Reynolds Number: A Geometric and Numerical Study of Copepod and Purcell Swimmers ⋮ Sub-Riemannian sphere in Martinet flat case ⋮ On variational approach to differential invariants of rank two distributions ⋮ Left-Invariant Sub-Riemannian Engel Structures: Abnormal Geodesics and Integrability ⋮ On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures ⋮ Optimal transportation under nonholonomic constraints ⋮ Geometric approach to Pontryagin's maximum principle ⋮ Normal forms for the endpoint map near nice singular curves for rank-two distributions

Cites Work

• Rigidity of integral curves of rank 2 distributions
• Local invariants of smooth control systems
• Abnormal sub-Riemannian geodesics: Morse index and rigidity
• Applications of the theory of quadratic forms in Hilbert space to the calculus of variations
• The High Order Maximal Principle and Its Application to Singular Extremals
• Abnormal Minimizers
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