Nonregular abnormal extremals of 2-distribution: Existence, second variation, and rigidity

被引：18

作者：

Zelenko I. ^{[1
]}

机构：

[1] Department of Mathematics, Technion-Israel Inst. of Technology, Haifa

来源：

Journal of Dynamical and Control Systems | 1999年 / 5卷 / 3期

关键词：

Nonholonomic distribution; abnormal extremal; Legendre-Clebsch condition; Lagrangian Grassmannian; Jacobi curve;

D O I：

10.1023/A:1021766616913

中图分类号：

学科分类号：

摘要：

We study existence and rigidity (W∞1-isolatedness) of nonregular abnormal extremals of completely nonholonomic 2-distribution (nonregularity means that such extremals do not satisfy the strong generalized Legendre-Clebsch condition). Introducing the notion of diagonal form of the second variation, we generalize some results of A. Agrachev and A. Sarychev about rigidity of regular abnormal extremals to the nonregular case. In order to reduce the second variation to the diagonal form, we construct a special curve of Lagrangian subspaces, a Jacobi curve. We show that certain geometric properties of this curve (like simplicity) imply the rigidity of the corresponding abnormal extremal.

引用

页码：347 / 383

页数：36

共 21 条

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