JDCS, vol. 1, #4 (1995), pp. 447-596

1. I.Kolmanowsky, N.H.McClamroch, V.T.Coppola
NEW RESULTS ON CONTROL OF MULTIBODY SYSTEMS WHICH CONSERVE ANGULAR MOMENTUM, pp. 447-462
A planar system of rigid bodies interconnected by one degree of freedom rotational joints is considered. This multibody system is referred to as a multilink, and the rigid bodies are referred to as links. The angular momentum of the multilink is conserved but is not necessarily zero. We show that if the number of links is at least four, then periodic joint motions can make the absolute orientation of a specified base link track exactly a specified function of time whose time derivative is periodic. This result on the use of periodic joint motions for orientation tracking extends previous work on using periodic joint motions for rest-to-rest reorientation. It has interesting physical consequences. Specifically, in the case of non-zero angular momentum periodic joint motions can maintain the orientation of the base link constant. In the case of zero angular momentum periodic joint motions can change the orientation of the base link at a specified angular rate. We also demonstrate that if the multilink consists of at least three links, then for any value of the angular momentum joint motions can reorient the multilink arbitrarily over an arbitrary time interval. This result extends similar results in [15] for zero angular momentum and in [20] that apply for nonzero angular momentum but not for an arbitrary time interval. In terms of their control-theoretic aspects, the problems treated in the paper can be viewed as controllability problems for a class of nonlinear control systems with time-dependent drift.
2. A.A.Davydov, L.Ortiz-Bobadilla
SMOOTH NORMAL FORMS OF FOLDED ELEMENTARY SINGULAR POINTS, pp. 463-482
In this work the smooth and topological normal forms of the first order implicit differential equations in the plane near its folded degenerate elementary singular point are found, and thereby, the smooth and topological classification of folded elementary singular points of these equations is completed.
3. G.K.Immink
MULTISUMMABILITY AND THE STOKES PHENOMENON, pp. 483-534
We define elementary acceleration operators and accelero-Laplace transformations on certain classes of (germs of) hyperfunctions on R. The type of accelero-Laplace transforms considered here generalize the notion of multisum of a formal power series. We describe the corresponding Stokes phenomenon, i.e., the difference of two accelero-Laplace transforms of the same germ in different (multi-) directions , with the aid of operators introduced by J.Ecalle.
4. Chr. Gole, R.Karidi
A NOTE ON CARNOT GEODESICS IN NILPOTENT LIE GROUPS, pp. 535-549
We show that strictly abnormal geodesics arise in graded nilpotent Lie groups. We construct a group, with a left invariant bracket generating distribution, for which some Carnot geodesics are strictly abnormal and, in fact, not normal in any subgroup. In the 2-step case we also prove that these geodesics are always smooth. Our main technique is based on the equations for the normal and abnormal curves, which we derive (for any Lie group) explicitly in terms of the structure constants.
5. V.P.Kostov
A GENERALIZATION OF THE BURNSIDE THEOREM AND OF SCHURS LEMMA FOR REDUCIBLE REPRESENTATIONS, pp. 551-580
We show that any reducible group generated by a finite number of matrices from GL(n,C) can be conjugated to a block upper-triangular form such that
  1. if the matrices from the centralizer of the group are blok-decomposed as the group itself, then their blocks are either scalar or 0 (generalization of Schurs lemma),
  2. the linear space S spanned in gl(n,C) by the matrices of the group is described as follows: all entries of a part of the blocks of the matrices of S are parameters and the rest of the blocks are linearly expressed by them by means of equations of the kind aP+...+cQ=0, where a,...,c are in C and P,...,Q denote blocks of the matrices S (generalization of the Burnside theorem.)
6. G.Grammel
CONTROLLABILITY OF DIFFERENTIAL INCLUSIONS, pp.581-595
We consider autonomous differential inclusions on compact Riemannian manifolds and characterize regions of complete controllability, the so-called control sets. Therefore we introduce appropriate dynamical systems and relate control sets to minimal sets. We get robustness and continuity results for control sets under perturbation of the attainable set semiflow. The results are applied to nonlinear singularly perturbed control systems.