arora Module¶

Summary¶

Functions

arora2013

Solves Lambert problem using Arora’s devised algorithm

Description¶

A module hosting all algorithms devised by Arora

Module Details¶

lamberthub.universal_solvers.arora.arora2013(mu, r1, r2, tof, M=0, is_prograde=True, is_low_path=True, maxiter=35, atol=1e-05, rtol=1e-07, full_output=False)[source]¶

Solves Lambert problem using Arora’s devised algorithm

Parameters:

mu: float: Gravitational parameter, equivalent to \(GM\) of attractor body.
r1: numpy.array: Initial position vector.
r2: numpy.array: Final position vector.
tof: float: Time of flight between initial and final position vectors.
M: int: Number of revolutions. Must be equal or greater than 0 value.
is_prograde: bool: If True, specifies prograde motion. Otherwise, retrograde motion is imposed.
is_low_path: bool: If two solutions are available, it selects between high or low path.
maxiter: int: Maximum number of iterations.
atol: float: Absolute tolerance \(abs(x_{i+1} - x_{i})\)
rtol: float: Relative tolerance \(abs(\frac{x_{i+1}}{x_{i}} - 1)\)
full_output: bool: If True, the number of iterations and time per iteration are also returned.

Returns:

v1: numpy.array: Initial velocity vector
v2: numpy.array: Final velocity vector
numiter: int: Number of iterations.
tpi: float: Time per iteration in seconds.

Notes

Lambert’s problem solver using the method proposed by Nitin Arora and Ryan P. Rusell in 2013, see [1]. This algorithm exploits the universal formulae by defining a new cosine-based transformation and developing a robust initial guess. Although based on arbitrary conditions, the algorithm shows a high performance.

References

[1] Arora, N., & Russell, R. P. (2013). A fast and robust multiple revolution Lambert algorithm using a cosine transformation. Paper AAS, 13, 728.