ISSN:
1432-1394
Keywords:
Key words: Legendre functions – Spherical harmonics – Vector spherical harmonics – D-functions
Source:
Springer Online Journal Archives 1860-2000
Topics:
Architecture, Civil Engineering, Surveying
Notes:
Abstract. The relation between D- and d-functions, spherical harmonic functions and Legendre functions is reviewed. D-matrices and irreducible representations of the rotation group O(3) and SU(2) group are briefly reviewed. Two new recursive methods for calculations of D-matrices are presented. Legendre functions are evaluated as part of this scheme. Vector spherical harmonics in the form of generalized spherical harmonics are also included as well as derivatives of the spherical harmonics. The special d-matrices evaluated for argument equal to π/2 offer a simple method of calculating the Fourier coefficients of Legendre functions, derivatives of Legendre functions and vector spherical harmonics. Summation of a Legendre series or a full synthesis on the unit sphere of a field can then be performed by transforming the spherical harmonic coefficients to Fourier coefficients and making the summation by an inverse FFT (Fast Fourier Transform). The procedure is general and can also be applied to evaluate derivatives of a field and components of vector and tensor fields.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01090814
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