Statistics – Computation
Scientific paper
Feb 1988
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988jgcd...11...31l&link_type=abstract
Journal of Guidance, Control, and Dynamics (ISSN 0731-5090), vol. 11, Jan.-Feb. 1988, p. 31-38.
Statistics
Computation
4
Earth Gravitation, Geopotential, Legendre Functions, Recursive Functions, Constraints, Errors, Numerical Stability, Spherical Harmonics
Scientific paper
In the spherical harmonic model for the gravitational potential and its derivatives, singularities are encountered at the poles. These singularities, caused by the use of spherical coordinates, can be removed with direction cosines and 'derived' Legendre functions. Using the definition and properties of derived Legendre functions, a set of recursion formulas may be formed for their computation. However, by imposing a set of algorithmic constraints, the set of suitable recursion formulas is reduced to six. Finally, a numerical stability requirement reduces the number of suitable relationships from six to two. The computational precision associated with the acceptable recursions has been examined for degree and order up to 180, as required for some forthcoming satellite missions. The precision of the gravitation force computation obtained with the acceptable recursions was demonstrated to be near the limiting precision of the machine.
Lundberg John B.
Schutz Bob E.
No associations
LandOfFree
Recursion formulas of Legendre functions for use with nonsingular geopotential models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Recursion formulas of Legendre functions for use with nonsingular geopotential models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Recursion formulas of Legendre functions for use with nonsingular geopotential models will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1226741