Contemporary Trends in Nonlinear Geometric Control Theory - download pdf or read online

By F. Monroy-Perez, B. Bonnard, J. P. Gauthier

ISBN-10: 9810248415

ISBN-13: 9789810248413

ISBN-10: 9812778071

ISBN-13: 9789812778079

Selection of papers proposing new effects, correct open difficulties, and significant purposes relating to educational and real-world difficulties.

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Extra info for Contemporary Trends in Nonlinear Geometric Control Theory and Its Applications

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F+{M) that satisfy the conditions i.

An(t) denote a frame attached to the body with both frames centered at a fixed point O of the body. We may orient the absolute frame so that the gravitational force is of the form F = Ce\ where C is a gravitational constant. 43 Denote by R{t) the isometry that relates the moving frame to the absolute frame. If q = (qi,... ,qn)T denotes the coordinate vector of a point OP in the absolute space, and if Q = (Qi,... ,Qn)T denotes the coordinate vector of the same point relative to the moving frame then q = RQ .

It is known that the quadratic forms which are SO„(ffi) invariant are scalar multiples of the trace form (A,B) = - | l r a c e ( A B ) . In particular, both the problem of Dubins and the problem of EulerGriffiths are invariant in the above sense, and that fact considerably simplifies their solutions as we shall soon see. 1 Hamiltonians and the Extremal Curves The Maximum Principle The Maximum Principle, as a general necessary condition of optimality, leads to the appropriate Hamiltonians on the cotangent bundle of the ambient manifold.

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Contemporary Trends in Nonlinear Geometric Control Theory and Its Applications by F. Monroy-Perez, B. Bonnard, J. P. Gauthier

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