Differential Equations for Geomagnetic Field Lines in Space.

by W. L. Sibley

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The presentation of mathematical detail used in, but omitted from, R-368. The report expressed spherical harmonics in rectangular form, a necessary step in evaluating the expressions for the components of the gradient of the earth's magnetic field. This memorandum provides both the mathematical notation for making such a transformation and a method for generating a magnetic field line in rectangular coordinates. The tables shown are valuable in studies of Explorer I and IV, radiation belts, and a variety of other problems in which rectangular rather than spherical symmetry may be present. The presentation of mathematical detail used in, but omitted from, R-368. The report expressed spherical harmonics in rectangular form, a necessary step in evaluating the expressions for the components of the gradient of the earth's magnetic field. This memorandum provides both the mathematical notation for making such a transformation and a method for generating a magnetic field line in rectangular coordinates. The tables shown are valuable in studies of Explorer I and IV, radiation belts, and a variety of other problems in which rectangular rather than spherical symmetry may be present. 22 pp

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