Computer program constructs a sequence of optimal solutions to dynamically-approximate linear equations. Specification of the number and type of subarcs in the optimal solution allows simultaneous satisfaction of all switching criteria

Cope, D. D.

Eskridge, C. D.

Hanafy, L. M.

English

NASA Technical Reports Server

November 1968
	 Brief 68-10422 
NASA TECH BRIEF 
NASA Tech Briefs are issued to summarize specific innovations derived from the U.S. space program, 
to encourage their commercial application. Copies are available to the public at 15 cents each 
from the Clearinghouse for Federal Scientific and Technical Informatiow, Springfield, Virginia 22151., 
Generalized Newton—Raphson Trajectory Optimization-Generator I 
The problem: 
To devise a method to replace the precise integra-
tion of the nonlinear motion and Euler-Lagrange 
equations used in previous indirect approaches to the 
optimal solution of trajectory problems. In these 
methods, optional switching points for changing from 
the thrust-on modes to the thrust-off modes are de-
termined by monitoring a coasting-switch function. 
The solution• 
A computer program designed to construct a se-
quence of optimal solutions to dynamically-approxi-
mate linear equations, the sequence converging to the 
solution of the nonlinear problem. Without signif-
icant loss in generality, specification of the number 
and type of subarcs in the optimal solution allows 
simultaneous satisfaction of all switching criteria and 
removes from this technique the objectional sensitivi-
ties of a monitored switch function. 
How it's done: 
The Generalized Newton-Raphson scheme is for-
mulated for the two-dimensional, vacuum-flight tra-
jectory in which it is desired to minimize the expendi-
ture of mass required to fulfill a given mission. The 
formulation is developed for the following mission 
options: (I) rendezvous with a passive satellite in 
circular orbit; and (2) transfer to a circular orbit of 
specified altitude, with flight time and range angle at 
injection free.
Optimum orbit transfer and rendezvous, from any 
initial condition to circular orbit, including optimum 
time to initiate and terminate coasting arcs, can be 
accomplished in one process with crude initial starting 
functions. The extremely wide area of convergence for 
this technique significantly increases the probability 
of obtaining a solution and reduces the manhours and 
computer time required to a level far below that neces-
sary with all other techniques. 
Notes: 
I. This program is written in Fortran H for use on the 
IBM 360 computer. 
2. Inquiries should be directed to: 
COSMIC 
Computer Center 
University of Georgia 
Athens, Georgia 30601 
Reference: B68-10422 
Patent status: 
No. patent action is contemplated by NASA. 
Source: D. D. Cope, C. D. Eskridge, 
and L. M. Hanafy 
of The Boeing Company 
under contract to 
Marshall Space Flight Center 
(M FS- 15020) 
Category 06 
This document was prepared under the sponsorship of the National 
Aeronautics and Space Administration. Neither the United States 
Government nor any person acting on behalf of the United States
Government assumes any liability resulting from the use of the 
information contained in this document, or warrants that such use 
will be free from privately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19680000422 2020-03-12T06:01:42+00:00Z



Generalized Newton-Raphson trajectory optimization-generator 1

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server