transferorbit / lamberts-problem-for-exponential-sinusoids

Library made for calculating the LOW-thrust solution to Lambert's problem as formulated by Dario Izzo. (https://doi.org/10.2514/1.21796)

LOW Thrust Lambert Targeter

This repository serves as both a (1) feature under development for use with Tudat and an (2) example for the use of Cython to wrap C++ libraries in Python accessible modules.

Warning

No unit tests or module tests are in place to ensure correct installation or implementation as of yet! This will be resolved soon.

Versioning

Version	Note
v1.0.0	First release with exponential sinusoids formulated for Lambert's Problem (Izzo, 2006).

Upcoming features

• Class for three dimensional use of the 2D Lambert formulation of exponential sinusoids for LOW thrust.
• Routines for optimal computation of Lambert solution fitness, thrust-guidance law and propulsion system feasibility check.

Installing (Python)

Clone the repository:

git clone https://github.com/ggarrett13/lamberts-problem-for-exponential-sinusoids.git

Install Cython (preferably in a virtual environment):

pip3 install Cython

Use your flavour of text editor commands to add the TudatBundle absolute path to the setup.ini config file.

cd lamberts-problem-for-exponential-sinusoids
gedit setup.ini

Install. Note that if you do not correctly define the TudatBundle path, installation will fail.

python3 setup.py build_ext --inplace

Examples

from lambert_exponential_sinusoid import ExponentialSinusoidFamily
import numpy as np
import matplotlib.pyplot as plt

# Define exponential sinusoid family parameters.
winding_parameter = k2 = 1 / 8.
initial_radial_distance = r1 = 1.
final_radial_distance = r2 = 1.5
angle_ccw_from_r1_to_r2 = psi = np.pi / 6
number_of_revolutions = N = 1

# Instantiation of exponential sinusoid family class.
exponential_sinusoid = ExponentialSinusoidFamily(k2, r1, r2, psi, N)

# Retrieve flight path limits.
flight_path_limits = exponential_sinusoid.get_flight_path_limits()

# Figure plotting.
plt.figure(figsize=(8, 8), dpi=400)
ax = plt.subplot(111, projection='polar')
for initial_flight_path_angle in np.linspace(flight_path_limits[0] * 0.4, flight_path_limits[1] * 0.4, 50):
    _r = exponential_sinusoid.get_radial_distance_array(initial_flight_path_angle)
    _theta = exponential_sinusoid.get_theta_array()
    ax.plot(_theta, _r)
ax.grid(True)
ax.set_title("Class $k_2=1/{}$ Exponential Sinusoid\n".format(int(1/k2)) +
             "$r_1={}$;      ".format(r1) +
             "$r_2={}$;      ".format(r2) +
             "$\psi=\pi/{}$;      ".format(int(np.pi/psi)) +
             "N={}".format(number_of_revolutions)
             , va='bottom')
plt.savefig("example1.png")