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IGRF model Implementation (Calculating the Partial Derivatives of the Legendre Polynomials)

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Abinay Brown
Abinay Brown 2021년 6월 6일
댓글: Abinay Brown 2021년 6월 7일
I was implementing the IGRF-13 Geomagnetic model, and a parts of the equation (3 a, b, and c) requires calculating the Associated Legendre polynomials with Schmidt quasi-Normalization and its partial derivatives.
For the Associated Legendre polynomials, I used the function Legendre(n, x, 'sch') and it works perfectly. But now how would I calculate their partial derivatives?
Equations 19 a, b, and c provides some recursive formulae, but I am not getting the correct result possibly because I might have implemented them incorrectly. Even the sample MATLAB code provided in the paper is not producing the proper results.
I would really appreciate it if someone could provide a proper implementation for calculating the Partial derivatives of these Legendre Polynomials.
Thank you,
Abinay Brown
Reference: https://hanspeterschaub.info/Papers/UnderGradStudents/MagneticField.pdf

답변(1개)

Bjorn Gustavsson
Bjorn Gustavsson 2021년 6월 7일
Have a look at the IGRF implementations available on the file exchange: international-geomagnetic-reference-field-igrf-model, international-reference-ionosphere-iri-model, earth-magnetic-field-with-igrf-13th-gen and igrf-magnetic-field. I've used one of the packages bby Drew Compston.
HTH
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Abinay Brown
Abinay Brown 2021년 6월 7일
I checked out the package by Drew Compston earlier, he happened to use a similar set of recursive equations for calculating the Partial Derivative but he hasn't explained the source of the equations.

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