Nonregular Abnormal Extremals
نویسنده
چکیده
We study existence and rigidity (W1-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.
منابع مشابه
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\The skull seems broken as with some big weapon, but there's no weapon at all lying about, and the murderer would have found it awkward to carry it away, unless the weapon was to small to be noticed." \Perhaps the weapon was too big to be noticed," said the priest, with an odd little giggle. Gilder looked round at this wild remark, and rather sternly asked Brown what he meant. \Silly way of put...
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