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$\begingroup$ That exactly what I was looking for, except I couldn't find the mentioned reference anywhere on the web, so thanks for the hint. However, I really need a confirmation about the formula correctness including the derivatives too. $\endgroup$

Ayoub
– Ayoub

2020-08-24 16:06:54 +00:00
Commented Aug 24, 2020 at 16:06
$\begingroup$ I don't think there is a digital version of Langel (1987) anywhere online, but I just found I could view enough of the following reference through Google Books to confirm the equations: Wertz, J. R. "Spacecraft Attitude Determination and Control", (1978). Use the "Search inside" option and search for "Appendix H", you can see the first few pages about Schmidt normalisation. $\endgroup$

WJB
– WJB

2020-08-24 16:27:20 +00:00
Commented Aug 24, 2020 at 16:27
$\begingroup$ That was useful, thanks again! So, the factors S are used with Gauss functions to obtain Schmidt functions, where: P_Schmidt = S * P_Gauss. But, it's still a long way to go with. I would love to compute directly the P_Schmidt functions since we know that there's recursion relations for them out there. $\endgroup$

Ayoub
– Ayoub

2020-08-24 17:33:32 +00:00
Commented Aug 24, 2020 at 17:33
$\begingroup$ Are you actually after the final recursive formula for the Schmidt P_n^m(cos(theta)) functions themselves, or are you ultimately trying to write code to calculate these values for geomag problems? I can add links to open source code in a few languages much more easily than I can work back and type up the formula working from those codes right now! $\endgroup$

WJB
– WJB

2020-08-24 19:15:15 +00:00
Commented Aug 24, 2020 at 19:15
$\begingroup$ Exactly I'm trying to implement a code to calculate those values, any open source code is welcomed! but I can't just take the code without the formula since I need to document that. $\endgroup$

Ayoub
– Ayoub

2020-08-24 21:22:53 +00:00
Commented Aug 24, 2020 at 21:22

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