Computation of Spherical Harmonics and Approximation by Spherical Harmonic Expansions,

Abstract

A technique is developed for generating spherical harmonics by exact computation (in integer mode) thereby circumventing any source of rounding errors. Essential results of the theory of spherical harmonics are recapitulated by intrinsic properties of the space of homogeneous harmonic polynomials. Exact computation of (maximal) linearly independent and orthonormal systems of spherical harmonics is explained using exclusively integer operations. The numerical efficiency is discussed. The development of exterior gravitational potential in a series of outer (spherical) harmonics is investigated. Some numerical examples are given for solving exterior Dirichlet's boundary-value problems by use of outer (spherical) harmonic expansions for not-necessarily spherical boundaries. Keywords: Homogeneous harmonic polynomials; Spherical harmonics; Exact computation in integer mode; Series expansion into spherical harmonics; Exterior dirichlet's problem.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1985
Accession Number
ADA160445

Entities

People

  • W. Freeden

Organizations

  • Ohio State University

Tags

Communities of Interest

  • C4I
  • Space

DTIC Thesaurus Topics

  • Air Force
  • Air Force Facilities
  • Applied Mathematics
  • Artificial Satellites
  • Boundaries
  • Boundary Value Problems
  • Computations
  • Contracts
  • Coordinate Systems
  • Differential Equations
  • Earth Sciences
  • Equations
  • Geodesy
  • Geophysics
  • Polynomials
  • Spherical Harmonics
  • United States

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis

Technology Areas

  • Space