Computing approximate random Delta v magnitude probability densities
Abstract
This paper describes the development and use of an algorithm to compute approximate statistics of the magnitude of a single random trajectory correction maneuver (TCM) Delta v vector. The TCM Delta v vector is modeled as a three component Cartesian vector each of whose components is a random variable having a normal (Gaussian) distribution with zero mean and possibly unequal standard deviations. The algorithm uses these standard deviations as input to produce approximations to (1) the mean and standard deviation of the magnitude of Delta v, (2) points of the probability density function of the magnitude of Delta v, and (3) points of the cumulative and inverse cumulative distribution functions of Delta v. The approximates are based on Monte Carlo techniques developed in a previous paper by the author and extended here. The algorithm described is expected to be useful in both preflight planning and inflight analysis of maneuver propellant requirements for space missions.
 Publication:

Astrodynamics 1983
 Pub Date:
 August 1984
 Bibcode:
 1984asdy.confT....C
 Keywords:

 Probability Density Functions;
 Spacecraft Maneuvers;
 Trajectory Optimization;
 Algorithms;
 Approximation;
 Monte Carlo Method;
 Random Processes;
 Vector Analysis;
 Astrodynamics