Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

An electrostatic problem in bi-cyclide coordinates


Authors: K. Aikawa, T. Hisamoto and T. Suganuma
Journal: Quart. Appl. Math. 35 (1977), 297-304
MSC: Primary 78.33; Secondary 31A35
DOI: https://doi.org/10.1090/qam/479034
MathSciNet review: 479034
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Abstract: This paper deals with an electrostatic problem for the field between two charged conductors $ \pm {u_0}$ maintained at potential $ \pm V$ in bi-cyclide coordinates ( $ u, v, \psi $). In this coordinate system, Heine functions are used, of which something is known. Heine functions are the solutions of Heine differential equations. Though the problem is to be solved in the same manner as the problem in the case of bispherical coordinates, it has not been clarified because of the complexity of Heine functions. A Heine differential equation is solved to satisfy the boundary condition that the functions and their derivatives are bounded at the ends of interval, and eigenvalues and eigenfunctions are evaluated. A formula giving the capacity between two electrodes is presented and numerically calculated.


References [Enhancements On Off] (What's this?)

  • [1] P. Moon and D. E. Spencer, Field theory handbook, 2nd ed., Springer-Verlag, Berlin, 1988. Including coordinate systems, differential equations and their solutions. MR 947546
  • [2] C. Ito and K. Aikawa, Heine oyobi Wangerin no kansū no sūchi keisan (Numerical calculations of Heine and Wangerin functions), Report of Faculty of Engineering, Yamanashi University, No. 17, 91-98 (1963)
  • [3] Parry Moon and Domina Eberle Spencer, Field theory for engineers, The Van Nostrand Series in Electronics and Communications, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1961. MR 0121018
  • [4] K. Aikawa and Y. Ohki, An approximate formula giving the capacity between two spindle-shaped electrodes placed in rotational symmetry on a straight line, Report of Faculty of Engineering, Yamanashi University, No. 14, 93-100 (1963)

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DOI: https://doi.org/10.1090/qam/479034
Article copyright: © Copyright 1977 American Mathematical Society

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