Matrix of moments of the Legendre polynomials and its application to problems of electrostatics
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- 作者：A. O. Savchenko
- 关键词：Legendre polynomials ; matrix of moments ; charge ; ball ; dipole moment ; electric field ; potential
- 刊名：Computational Mathematics and Mathematical Physics
- 出版年：2017
- 出版时间：January 2017
- 年：2017
- 卷：57
- 期：1
- 页码：175-187
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Computational Mathematics and Numerical Analysis;
- 出版者：Pleiades Publishing
- ISSN：1555-6662
- 卷排序：57
文摘
In this work, properties of the matrix of moments of the Legendre polynomials are presented and proven. In particular, the explicit form of the elements of the matrix inverse to the matrix of moments is found and theorems of the linear combination and orthogonality are proven. On the basis of these properties, the total charge and the dipole moment of a conducting ball in a nonuniform electric field, the charge distribution over the surface of the conducting ball, its multipole moments, and the force acting on a conducting ball situated on the axis of a nonuniform axisymmetric electric field are determined. All assertions are formulated in theorems, the proofs of which are based on the properties of the matrix of moments of the Legendre polynomials.