Integrals of Lipschitz-Hankel type in analysis of magnetostatic fields

• Autorzy: Pawluk K.
• Języki publikacji: EN

Abstrakty

EN

A boundary-integral model of the static magnetic field due to cylindrical permanent magnets that is put in free space is considered. Magnetic scalar potential quantities created by a virtual quantity "surface magnetic charge density" is expressed by means of Lipschitz-Hankel integrals that for the considered case are reducible (by the way of hypergeometric series) to some algebraic expressions, in which elliptic integrals of various kinds occur. This approach seems to be more effective than that can be reached by the use of a typical professional software for the field problems in which numerical integration, being not quite conform to the considered case, is common. The magnet subjected to the analysis has to be virtually subdivided in some number of elementary pieces, inside of which the uniform distribution of the inherent magnetization is supposed.

Słowa kluczowe

EN

magnetic field; magnetisation; magnetostatistics; numerical analysis; boundary integral equation; pernament magnet; elliptic integral; numerical integration

PL

pole magnetyczne; magnesowanie; magnetostatyka; analiza numeryczna; magnes trwały; całka eliptyczna; całkowanie numeryczne

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Journal of Technical Physics
• Rocznik: 2003
• Tom: Vol. 44, no 2
• Strony: 133--144
• Opis fizyczny: Bibliogr. 11 poz., rys., wykr.

Twórcy

autor

Pawluk K.

• Electrotechnical Institute Department of Fundamental Research in Electrotechnics Pożaryskiego 28, 04-793 Warszawa, Poland

Bibliografia

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• 2. K. PAWLUK, M. KUCHARSKA, Vector and scalar models of a quasi-stationary electromagnetic field in boundary-integral approach, Bull, of the Pol. Ac. of Sc., 44, 2, 119-128, 1996.
• 3. M. KUCHARSKA, K. PAWLUK, On the bi-scalar boundary-integral approach to modelling electromagnetic fields, COMPEL, The Int. Jour, for Comp, and Math, in Electr. Eng., 17, 4, 475-488, 1998.
• 4. K. PAWLUK, Z. ŻYCKI, Boundary-integral approach to determine the magnetic field created by a permanent magnet put in free space, COMPEL, The Int. Jour, for Com. and Math, in Electrical and Electronic Eng., 19, 1, 86-94, 2000.
• 5. K. PAWLUK, Z. ZYCKI, The working state of cone-shaped permanent magnets determined by boundary-integral approach, COMPEL, P. Di Barba, A. Savini, S. Wiak [Eds.], The Int. Jour, for Com. and Math, in Electrical and Electronic Eng. 19, 2, 632-638, 2000.
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• 7. G. EASON, B. NOBLE, I.N. SNEDDON, On certain integrals of Lipschnitz-Hankel type involving products of Bessel functions, Phil. Trans, of the Roy. Soc., 247, 195-219, 1954.
• 8. W. PRESS, B. FLANNERY, S. TEUKOLSKY, The art of scientific computing, Cambridge Univ. Press, Cambridge 1968.
• 9. K. PAWLUK, Algorithms based on integrals of Lipschitz-Hankel type for modelling permanent magnet field, Bulletin of the Polish Academy of Sciences, Technical Sciences, 49, 4, 567-580.
• 10. I.M. RYSHIK, I.S. GRADSTEIN, Tables of series, products and integrals, VEB Deutscher Verlag der Wissenschaften, Berlin 1957.
• 11. P.F. BYRD, M.D. FRIEDMAN, Handbook of elliptic integrals for engineers and scientists, Springer- Verlag Berlin, Heidelberg, New York 1971.