The main purposes of this research are to obtain Lagrange function for the relativistic rotation of the rigid body, which is generated by metric properties of Riemann space of general relativity and to derive the differential equations, determining the rigid body rotation in the terms of the Rodrigues-Hamilton parameters. The Lagrange function for the relativistic rotation of the rigid body is derived from the Lagrange function of the nonrotation point of masses system in the relativistic approximation.
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The paper presents comments and observations resulting from research of electrical power devices. Drive motors are essential elements of the processing chain in industrial plants. Synchronous and asynchronous motors are about the most important group among the drive motors, due to their power properties and the simplicity of power and control systems. During failures of synchronous and asynchronous machines, a burnout of coil turns takes place. RMS values of phase currents during the short-circuit of turn do not show a significant asymmetry, which consequently results in a lack of effective protection against short-circuit of individual turns. The authors propose a solution of this issue based upon the phase angle control of different currents. The phenomenon of current phase angle asymmetry occurring during turn short-circuit has been utilized.
PL
W artykule zostały przedstawione uwagi i spostrzeżenia wynikające z fragmentu badań urządzeń elektroenergetycznych. W zakładach przemysłowych jednym z podstawowych elementów ciągu technologicznego są silniki napędowe. Wśród silników napędowych ze względu na własności energetyczne oraz prostotę układów zasilania i sterowania najważniejszą grupę stanowią silniki synchroniczne i asynchroniczne. Podczas awarii maszyn synchronicznych i asynchronicznych dochodzi do wypalenia zwojów cewek zainstalowanych w korpusie. Wartości skuteczne prądów fazowych podczas zwarcia zwoju nie wykazują większej asymetrii, co ostatecznie skutkuje brakiem skutecznego zabezpieczenia od zwarć pojedynczych zwojów. Autorzy zaproponowali rozwiązanie polegające na kontroli kątów przesunięcia fazowego poszczególnych prądów. Wykorzystano zjawisko asymetrii kątów fazowych występujące podczas zwarcia zwojowego.
In this paper we identify those shifts (continuous functions) of the term structure of interest rates, against which a given bond portfolio (BP) is immunized. The set of such shifts (IMMU) happens to be an (m − 1)-dimensional linear subspace in an m-dimensional linear space of all admissible shifts. In the proof we use triangular (Lagrange) functions, by means of which we build a base for IMMU. How this IMMU space varies in response to changes in the cash flow generated by bond portfolio, BP, is also discussed in the last section of the paper.
The paper deals with a single-phase reluctance motor used to test the motion equations of an electromechanical system. The identification of the motor electric parameters as a function of the rotation angle of the rotor was carried out using AC 50 Hz voltage source. A mechanical part of the system was designed as a physical pendulum containing the motor rotor and a metal bar mounted on the rotor axis. The parameters of the mechanical part were measured during the pendulum oscillations. The work presents the characteristics and motion equation parameters of the motor dynamics. The reluctance motor motion equation does not fullfil the power balance. The parameters of the motion equations obtained from the experiment and from the second order Lagrange’a equations are compared. The derivation of motion equation, together with a discussion of holonomicity of electromechanical systems is also presented.
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The aim of this paper is to providing a simple method to build a Lagrange functional for the complex interactions of thermal, mechanical and processes in the gradient thermomechanics. The formal similarity of the mass, momentum and energy balances is used
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