A header-only library of functions used in astrodynamics.

• Associated Legendre functions through standard forward column recursive approach (Holmes & Featherstone, 2002). First and second order derivatives are also supported.
• Inclination function computation through FFT (Wagner, 1983). First derivatives can also be computed similarly. Besides, cross-track inclination functions computation is provided (Balmino et al., 1996).
• Full-normalization constants (Heiskanen & Moritz, 1967). Fully-normalized versions of the functions are also available.

• Eccentricity functions

1. Clone functions and fft repository into your external folder

mkdir -p external
cd external
git clone https://github.com/gabri-aero/functions
git clone https://github.com/gabri-aero/fft

1. Link to your project accordingly

# Define path to external repositories
FUNCTIONS_DIR = $(EXTERNAL_DIR)/functions
FFT_DIR = $(EXTERNAL_DIR)/fft

# Define flags for compiler
INCLUDE_FLAGS = -I$(FUNCTIONS_DIR) -I$(FFT_DIR) # include flags

1. Include headers in your code

// Include headers
#include <functions>

The unit tests can be built and run as follows:

make test

Balmino, G., Schrama, E., & Sneeuw, N. (1996). Compatibility of first-order circular orbit perturbations theories; consequences for cross-track inclination functions. Journal of Geodesy, 70(9), 554–561. https://doi.org/10.1007/bf00867863

Heiskanen, W., & Moritz, H. (1967). Physical Geodesy. W. H. Freeman.

Holmes, S. A., & Featherstone, W. E. (2002). A unified approach to the Clenshaw summation and the recursive computation of very high degree and order normalised associated Legendre functions. Journal of Geodesy, 76(5), 279–299. https://doi.org/10.1007/s00190002-0216-2

Kaula, W. M. (1966). Theory of Satellite Geodesy: Applications of Satellites to Geodesy. Blaisdell Publishing Company.

Wagner, C. A. (1983). Direct determination of gravitational harmonics from low-low GRAVSAT data. Journal of Geophysical Research: Solid Earth, 88(B12), 10309–10321. https://doi.org/10.1029/jb088ib12p10309