Download Analysis of Controlled Dynamical Systems: Proceedings of a by Dirk Aeyels (auth.), Bernard Bonnard, Bernard Bride, PDF

By Dirk Aeyels (auth.), Bernard Bonnard, Bernard Bride, Jean-Paul Gauthier, Ivan Kupka (eds.)

The convention "Analysis of managed Dynamical platforms" was once held in July 1990 on the college of LYON FRANCE. approximately hundred contributors attended this convention which lasted 4 days : there have been 50 audio system from departments of Engineering and arithmetic in east and west Europe, united states and USSR. the final topic of the convention was once process idea. the most themes have been optimum keep an eye on, constitution and keep an eye on of nonlinear platforms, stabilization and observers, differential algebra and platforms thought, nonlinear points of Hoc thought, inflexible and versatile mechanical structures, nonlinear research of indications. we're indebted to the clinical committee John BAILLIEUL, Michel FLIESS, Bronislaw JAKUBCZYCK, Hector SUSSMANN, Jan WILLEMS. We gratefully recognize the time and suggestion they gave to this activity. we might additionally wish to thank Chris BYRNES for arranging for the booklet of those court cases throughout the sequence "Progress in structures and regulate Theory"; BIRKHAUSER. ultimately, we're very thankful to the subsequent associations who via their monetary help contributed primarily to the good fortune of this convention : CNRS, precise 12 months " Systemes Dynamiques", DRET, MEN-DAGIC, GRECO-AUTOMATIQUE, Claude Bernard Lyon I collage, Entreprise Rhone-Alpes foreign, Conseil basic du RhOne, the towns of LYON and VILLEURBANNE.

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2 2 2 4 II cos 'I' + 12 sm ¢> _~(w2 + ~2 )(Il(sin27jJ + sin2 ¢>cos27jJ) + I2cos2 ¢>cos 2 7jJ) - cos¢>cos7jJ. This is a conserved quantity for the averaged rotating spatial link dynamics where V(¢>,7jJ) = K2 (Ilsin27jJ+ (II-I2)2sin2¢>cos~¢>cos27jJ) 4 h cos 2 ¢> + 12 sm2 ¢> _~(W2 + ~2 )(Il(sin2 7jJ + sin2 ¢> cos 27jJ) + 12 cos 2 ¢> cos 2 7jJ) - cos ¢>cos 7jJ. V is called the averaged potential, and relative minima of this function define the stable equilibrium points of the averaged spatial link dynamics (23).

Iii) follows immediately from the form of these Lagrangians, and (iv) follows from writing the O-symmetry reduction of the two control systems. 0 The remainder of this section will be devoted to the dynamics of single link chains subject to periodic forcing. Assuming that the single link is axially symmetric, and that the link length, link mass, and the force of gravity have been suitably normalized, the Lagrangians (20) and (21) specialize to . ,p)2 + .. ,p + Ou 2 SUPER-ARTICULATED MECHANISMS, PERIODIC FORCING 47 respectively.

52 L. BARATCHART A moment's thinking shows that the optimal p is really a function of q for each n, obtained by projecting orthogonally f onto the subspace Rn[z]/q of H:;. Let L(q)/q stand for this projection, and put t/J(q) = Ilf - L(q)/qI12. We can thus replace the former criterion by t/J and look for inf qER;;[zj t/J(q). Doing so, we are brought down to perform optimization on a bounded domain of Rn. By this, we mean that if we assume q to be monic, which is always possible, and identify q = zn + qn_lzn-1 + ...

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