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 members 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 issues have been optimum keep watch over, constitution and regulate of nonlinear structures, stabilization and observers, differential algebra and platforms idea, nonlinear facets of Hoc concept, inflexible and versatile mechanical platforms, nonlinear research of indications. we're indebted to the medical 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 prefer to thank Chris BYRNES for arranging for the e-book of those lawsuits throughout the sequence "Progress in platforms and keep watch over Theory"; BIRKHAUSER. eventually, we're very thankful to the subsequent associations who via their monetary help contributed primarily to the luck of this convention : CNRS, precise 12 months " Systemes Dynamiques", DRET, MEN-DAGIC, GRECO-AUTOMATIQUE, Claude Bernard Lyon I college, Entreprise Rhone-Alpes foreign, Conseil basic du RhOne, the towns of LYON and VILLEURBANNE.

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V. Van der Schaft, Nonlinear Dynamical Control Systems, Springer-Verlag, New York, 1990. J. ), pp. 81-131, Marcel Dekker, NY 1990. Francesca Albertini Eduardo D. edu The Behavior of Super-Articulated Mechanisms Subject to Periodic Forcing J. BAILLIEUL Abstract Super-articulated mechanisms with symmetries are studied. It is shown that averaging may be applied to capture nonholonomic effects produced by subjecting the systems of interest to high-frequency periodic forcing. Using a Hamiltonian representation for the forced system, it is shown that the result of averaging is another Hamiltonian system having a certain Hermitian structure.

1988 IEEE Int'l Conf. on Robotics and Automation, Philadelphia, April 24-29. pp. 152-158. [7] J. GUCKENHEIMER & P. HOLMES, 1983. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Vol. 42, Applied Mathematical Sciences Series, Springer-Verlag, New York. K. HALE, 1969. Ordinary Differential Equations, Wiley, New York. [9] H. J. VAN DER SCHAFT, 1990. Nonlinear Dynamical Control Systems, Springer-Verlag, New York. [10] N. SREENATH, 1989. , Contempomry Mathematics, 97, American Mathematical Society, pp.

We will show the following two properties: 1. for each k 2. if Rk(x) 2: 0 if int Rk(x) = 0 then Rk(x) = 0; = 0 for all k 2: 0 then intR(x) = 0. Combining (1) and (2) we have that if int R(x) = 0 then all int Rk(x) = 0 too, so intR(x) = 0, as desired. We first prove (1). Suppose that Rk(x) =I- 0, so that there exists some sequence ii for which the rank Pk,x(') is equal to n at ii. Since we assume U C closintU, there exists also some ii E int Uk so that Pk,x(U) = n for each U in some neighbourhood of ii.