lambert_algorithm

Lambert Problem solver by Gauss', Battin's, Analytic Gradient methods

User guide

lambert_gauss(T, lambda)
lambert_battin(T, lambda)

${T = \sqrt {\frac {8\mu}{s^3}}(t_2 - t_1)}$ and $\lambda$ represent a semi perimeter

output $x = {\sin}^2{\frac{1}{2}E}$ where $E = \frac{1}{2}(E_2-E_1)$

lambert_analytic_gradient(r1, r2, phi, tf, muC)

$r_1, r_2$ are scalar, and $\phi$ is true anomaly difference (deg)

$t_F$ is transfer time, and $\mu$ represents standard gravitational parameter

output x is a flight-path angle

References

Gauss method

theory of the motion of the heavenly bodies moving about the sun in conic sections

Introducing free parameters

An Elegant Lambert Algorithm (https://doi.org/10.2514/3.19910)

Richard H. Battin and Robin M. Vaughan

An Improvement of Gauss' method for Solving Lambert's Problem

Vaughan, Robin M

Analytic Gradient method

Lambert Algorithm Using Analytic Gradients (https://doi.org/10.2514/1.62091)

Jaemyung Ahn and Sang-Il Lee