Bemerkungen zum Biot-Savartschen Gesetz

Übersicht Die folgende Arbeit verfolgt u. a. auch didaktische Absichten. Das Biot-Savartsche Gesetz wird oft falsch oder mindestens sehr mißverständlich dargestellt und auch auf unzulässige Weise benutzt. Ausgangspunkt der Mißverständnisse ist die auch in vielen Lehrbüchern anzutreffende unkorrekte Aussage, man könne einem von StromI durchflossenen Linienelement ds ein magnetostatisches Feld dB [entsprechend der Gleichung (32) des folgenden Beitrags] zuordnen. Im folgenden werden derartige Aussagen untersucht und in modifizierter Form korrekt dargestellt.

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Remarks concerning the Law of Biot-Savart

Contents The following paper is at least partly of a didactic nature. The Biot-Savart law of magnetostatics is often interpreted in an illegitimate manner and consequently applied incorrectly. The source of these misunderstandings and errors is the incorrect statement that a magnetic field dB [as given by equation (32) of this paper] is caused by an electric currentI flowing along a line element ds, a statement very popular also in many textbooks. Questions related to this problem are investigated and widespread misleading statements are replaced by correct ones.

     

Guaranteed inclusions for the complex generalized eigenproblem

A method is described which produces guaranteed bounds for a solution of the generalized complex eigenproblem. The method extends a similar approach for general systems of nonlinear equations to the special case of complex pencils, where under weaker assumptions stronger assertions can be proved.     

Twisted axially loaded rod with shear and compressibility

Summary Stability of a twisted and axially compressed elastic rod is analysed using the Euler method of adjacent equilibrium configuration. The constitutive equations of the rod are assumed in the form that takes into account both shear of the cross-sections and compressibility of the rod axis. It is shown that bifurcation points of the non-linear system of equations describing equilibrium are determined from the linearized system of equations. The influence of shear and compressibility on the critical values of twisting couple and compressive force is obtained. Moreover, the bifurcation pattern is examined by using the Liapunov-Schmidt method.     

INTEGER analysis of two-dimensional polygonal objects

A consistent modelling scheme for digital images is presented, with the grey-level raster image as input and the list-oriented polygonal image as output. The output information consists of two parts: The metric of the polygonal object, represented by coordinates of marked positions, and the global topology, which takes the form of a two-dimensional topologic order. The central problem, which has to be solved, is to select a digital polygon, approximating a digital arc such that the essential feature of the arc is represented at a predefined precision level. The proposed algorithm uses simple incremental calculations of INTEGER quantities to solve the problem.     

Influence of various types of load-dependent supports on the stability of a compressible column model

Summary The nonlinear behaviour and static stability of a compressible elastic column whose flexural resistance changes as it is loaded is studied. A two-degree-of-freedom, compressible rod model of the column is analysed. Various types of load-stiffness relationships are considered. Post-buckling behaviour under static unidirectional loads is investigated. Singularities of the equilibrium paths of the column are classified according to the slenderness ratio of the column and the load-stiffness relationship of its support.On leave from Department of Mechanical Engineering, University of Toronto, 5 King's College Road Toronto, Ontario, Canada, M5S 1A4