Computer program for solving attitude error equations related to gimballed platform is described. Program generates matrix elements of attitude error equations when initial matrices and trigonometric identities have been defined. Program is written for IBM 360 computer

Hall, W. A., Jr.

Morris, T. D.

Rone, K. Y.

English

NASA Technical Reports Server

October 1972	 B72-10624 
NASA TECH BRIEF 
Marshall Space Flight Center
	 - 
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Computer Program To Generate Attitude Error Equations 
For A Gimballed Platform 
The problem: 
To find a method by which attitude error equations, 
suitable for use in a flight program, can be generated for 
a platform with a given gimbal order. The generation of 
the equations requires the expansion and reduction of 
seven third-order matrices for a four-gimbal platform. 
Once expanded, the equations can be reduced using 
fundamental trigonometric identities for the sum of two 
angles. The expansion and subsequent reduction of these 
equations is time consuming, tedious, and virtually 
impossible to perform without error. 
The solution: 
A computer program was developed which will gener-
ate the matrix elements of the attitude error equations 
when the initial matrices and trigonometric identities 
have been defined and provided as program input. 
How it's done: 
Through the use of an extension of the OS/360 PL/I 
(F) compiler, known as the PL/I-FORMAC interpreter, 
the matrices whose elements are the sines and cosines of 
the guidance commands and related gimbal angles can be 
multiplied to form the matrix product, and like terms 
can be collected for each element of the product. 
Input to the program consists of up to seven input 
matrices entered in PL/I data-directed format on cards. 
Output is a printout of individual matrix elements for 
each matrix product. A final matrix product after 
reduction of terms using trigonometric identities is also 
printed.
The process used to generate equations in this 
program can be used whenever matrix manipulation is 
required. Use of this program enables one to obtain 
equations in a linear form rather than a matrix form. 
This is useful, as well as cost effective, when a program is 
implemented which will be run many times as in the 
case of simulations. 
Notes: 
1. This program is written in PL/I-FOR.MAC to be 
utilized on the IBM-360/75 computer. 260 K bytes 
of storage, a 9-track tape drive and 2311 disk drive 
are required to run the present version. 
2. Inquiries concerning this program should be directed 
to:
COSMIC 
112 Barrow Hall 
University of Georgia 
Athens, Goergia 30601 
Reference: MFS-21991 
Source: Willaim A. Hall, Jr., 
Thomas D. Morris, and
Kyle Y. Rone of
IBM Corp.
under contract to

Marshall Space Flight Center 
(MFS-21991) 
Category 09 
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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
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Computer program to generate attitude error equations for a gimballed platform

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