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Content available remote Interactive visualization of magnetic fields
In this paper, we present an interactive method for visualizing three-dimensional nonlinear, unsteady vector fields. Visualization of three-dimensional electromagnetic fields is a difficult issue because the user has to be able to assess the distribution of the vector in the context of complex geometry. The authors propose a novel scheme to visualize the flow of vectors.
The article is devoted to a motion control problem for a differentially driven mobile robot in the task of trajectory tracking in the presence of skid-slip effects. The kinematic control concept presented in the paper is the Vector Field Orientation (VFO) feedback approach with a nonlinear feed-forward skid-slip influence compensation scheme. The VFO control law guarantees asymptotic convergence of the position tracking error to zero in spite of the disturbing influence of skid-slip phenomena. The paper includes a control law design description, stability and convergence analysis of a closed-loop system, and practical verification of the proposed control concept. The experimental results illustrate control quality obtained on a laboratory setup equipped with vision feedback, where the Kalman filter algorithm was used in order to practically estimate skid-slip components.
This paper is devoted to the way point following motion task of a unicycle where the motion planning and the closed-loop motion realization stage are considered. The way point following task is determined by the user-defined sequence of way-points which have to be passed by the unicycle with the assumed finite precision. This sequence will take the vehicle from the initial state to the target state in finite time. The motion planning strategy proposed in the paper does not involve any interpolation of way-points leading to simplified task description and its subsequent realization. The motion planning as well as the motion realization stage are based on the Vector-Field-Orientation (VFO) approach applied here to a new task. The unique features of the resultant VFO control system, namely, predictable vehicle transients, fast error convergence, vehicle directing effect together with very simple controller parametric synthesis, may prove to be useful in practically motivated motion tasks.
Content available remote To the question of vector field canonic reper in four-dimensional equiaffine space
In four-dimensional equiaffine space the set of geometric objects of vector field has been built, the invariant straight has been defined. Canonic reper has been built for a particular case.
W czterowymiarowej przestrzeni afinicznej został zbudowany zestaw obiektów geometrycznych oraz zdefiniowana stała. Reper kanoniczny został zbudowany dla szczególnych przypadków.
Content available remote Some natural operations on functions
Let F : FMm &rarr FM be a bundle functor. We describe all FMm,n- natural operators L transforming functions f : Y &rarr R, Y is an element of Obj(FMm,n), into functions L(f) : FY &rarr R.
In this paper we show that the set of solutions to the following integral equation.
Content available remote On some Gołąb connections
The aim of this paper is to study the notion of almost 1-principal Gołąb connections. We characterize some deformation algebras having the same principal vector fields. The last section is devoted to the study of some Gołąb connections on hypersurfaces.
In the paper there is presented the method designed for vector fields classification. It is based on the algorithm proposed by Lund (1963). The replacement of Pearson correlation coefficient with vector correlation coefficient defined by Crosby (1993) is the essential change that makes this technique suitable for treatment of vector fields. The correlation threshold, set a priori in scalar analyses, is calculated objectively, with the help of PVCR index introduced by Huth (1996). PVCR index expresses the proportion of average similarity between objects classified into different categories to objects grouped in the same classes. PVCR is computed for selected range of threshold values and minimum value indicates the ,,best" correlation threshold. The classification was carried out for wind fields at the 250 hPa surface over Europe for winter season during 1958-2003 period. 20 classes of jet stream patterns were distinguished, which constitute 60.7% of the sample. Basic statistics, i.e. average and maximum frequency and duration time, were calculated for the first six key jet types. The main features of upper circulation field as well as temperature and pressure distribution in the lower troposphere associated with the jet types were also described.
Content available remote On the leaves of a prefoliation of a K-differential space
The definition of a prefoliation (M,F) of a K-differential space and the theorem about regularity of the inclusion of a leaf of a prefoliation are reminded. An example of a pair (M, F) of SC-differential spaces with the same set of points, which shows that even if the identity of .M is an immersion F -> M and (top M, top F) is a topological foliation in the sense of Ehresmann then (M, F) has not to be a prefoliation, is given. In the end, we show that if L is a proper leaf of a prefoliation (M, F) then the both structures of a K-differential spaces coincide on L.
Content available remote On some right invertible operators in differential spaces
In this paper we consider the right invertibility problem of some linear operators defined on the algebra of smooth function on a differential space.
For any product-preserving bundle functor F denned on the category F2 M of fibered-fibered manifolds, we determine all natural operators transforming projectable-projectable vector fields on Y 6 Ob(F2M) to vector fields on FY. We also determine all natural affinors on FY and prove a composition property analogous to that concerning Weil bundles.
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