Computer program generates trajectories that are optimum with respect to payload placed in an earth orbit. It uses a subroutine package which produces the terminal and transversality conditions and their partial derivatives. This program is written in FORTRAN 4 and FORMAC for the IBM 7094 computer

Heintschel, T. J.

English

NASA Technical Reports Server

July 1968
	
Brief 68-10232 
NASA TECH BRIEF H 
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 Information, Springfield, Virginia 22151. 
HICOV. (Newton-Raphson Calculus of Variation
with Automatic Transversalities) 
The problem: 
In generating trajectories that are optimum with 
respect to payload placed in an earth orbit, there 
arises a need for analytically forming the transversal-
ity equations and their respective partial derivatives. 
The solution: 
A computer program which generates the desired 
trajectories through the use of a subroutine package 
which produces the terminal and transversality condi-
tions and their partial derivatives. 
How it's done: 
The Wierstrass condition defines the control varia-
bles, or steering angles, which appear in the differen-
tial equations of motion, while the transversality con-
ditions are used along with, the physical cutoff 
conditions to determine the nine boundary conditions. 
The partial derivatives are used to solve for the desired 
boundary conditions and then determine the gain 
matrices for the steering angles. The gain matrices are 
used to write the guidance functions which reduce to 
linear polynomials in the state variables. The state 
variables can be stored onboard the vehicle for guid-
ance purposes. 
The transversality generator program along with the 
Formac subroutine package, TAC, generates the 
terminal and transversality conditions and their partial 
derivatives. The package uses a formula manipula-
tion language which is an extension of Fortran. It
allows the programmer to arrive at a single analytic 
solution, following it by multiple numeric evaluations. 
The terminal conditions are input into the program 
and a Fortran IV source deck for the calculation of 
the solutions is generated on tape. Included in the 
tape source deck are a deck name, calling sequence, 
type statements, dimension statements, and analytic 
expressions as desired. The tape can then be punched 
on cards and used directly with a program or called 
in by a program through the use of $1 EDIT. 
Using this subroutine package, the programmer is 
able to automatically arrange his analytic solution(s) 
in form suitable for numeric evaluation. 
Notes: 
I. This program is written in Fortran IV and Formac 
for the IBM 7094 computer. 
2. Inquiries concerning this program may be made to: 
cosmic. 
Computer Center 
University of Georgia 
Athens, Georgia 30601 
Reference: B68-10232 
Patent status: 
No patent action is contemplated by NASA. 
Source: Tommy J. Heintschel 
of General Electric Company 
under contract to 
Marshall Space Flight Center 
(M FS- 14468) 
Category 06 
.,
This document was prepared under the sponsorship of the National 	 Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States 	 information contained in this document, or warrants that such use 
Government nor any person acting on behalf of the United States 	 will be free from privately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19680000232 2020-03-12T06:07:27+00:00Z


HICOV - Newton-Raphson calculus of variation with automatic transversalities

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server