Functions

‍A static library of functions used in astrodynamics.

Features

• Fully-normalized Associated Legendre functions through standard forward column recursive approach (Holmes & Featherstone, 2002). First and second order derivatives are also supported.
• Fully-normalized 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).

TO DO

• Eccentricity functions

Setup

Makefile

1. Clone this repository into your external folder

   git clone https://github.com/gabri-aero/functions

2. Build the library

   cd functions
   make 

3. Link to your project accordingly

   # Define path to functions repository
   FUNCTIONS_DIR = $(EXTERNAL_DIR)/functions
    
   # Define flags for compiler
   FUNCTIONS_INCLUDE = -I$(FUNCTIONS_DIR)/include/ -I$(FUNCTIONS_DIR)  # include flags
   FUNCTIONS_LIB_FLAGS = -L$(FUNCTIONS_DIR)/lib -lfunctions            # link flags

4. Include headers in your code

   // Include single headers
   #include <functions/Flmp.hpp>
   #include <functions/Plm.hpp>
   #include <functions/Nlm.hpp>
   // Alternatively all at once
   #include <functions>

References

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