SPACE: THE LINEAR FRONTIER

By:  Tammy Spadaccini

 

         Man and woman, of course, have always been curious and explored regions previously beyond reach.  For roughly the past 50 years we have reached toward space.  Navigating our way off of this planet toward orbit, other planets, or a cruise through the galaxy; linear algebra has played a distinct role.  Aside from the fact that there are literally thousands of bits of space debris to avoid, it has been important for us to maintain control of vehicles to achieve proper orbit, turn to the correct position to release a satellite, or hit the heavenly body for which we aimed.

 

         From the Apollo missions to today’s space station, the challenge of “gimbal-lock” has created controversy as well as protocol solutions related to situations occurring before and during spaceflight.  Rotational matrices are used to create all possible orientation movements of the spacecraft.  Certain situations produce “gimbal-lock” causing problems which require a change in thinking and priority on the part of the powers that be; i.e. those in charge of the spacecraft and its payload.

 

         Relationships will be addressed between rotational matrices, “gimbal-lock” and spacecraft to include Apollo missions using the Saturn 5, MIR space station, Space Shuttle, and our current International Space Station.  We will discover the ancient mathematics used in today’s most progressively daring exploration of our “linear frontier”.

 

References:

http://www.apollosaturn.com/gnc.htm

http://www.eas.asu.edu/~cse470/resources/documents/orientation.pdf

http://www.gimblelock.com/Biography/gldefinedheader.html

http://www.hq.nasa.gov/office/pao/History/alsj/gimbals.html

http://www.hq.nasa.gov/pao/History/alsj/e-1344.htm

http://www.softdocwiz.com/IMUText.htm

http://www.worldhistory.com/wiki/g/gimbal.htm

http://www.worldhistory.com/wiki/g/gimbal-lock.htm

http://www.worldhistory.com/wiki/g/gyroscope.htm

http://www.worldhistory.com/wiki/E/Euler-angles.htm

http://www.worldhistory.com/wiki/E/Euclidean-space.htm

http://www.worldhistory.com/wiki/v/vector-space.htm

http://www.yarchive.net/space/spacecraft/gimbal_lock.html

http://www.caisu.ca

http://www.science.ksc.nasa.gov

http://www.spaceflight.nasa.gov

http://www.anticz.com

http://www.gamasurta.com

http://www.cadd.cern.cL

 

Linear Algebra:  Modules for Interactive Learning Using Maple 6; by The Linear Algebra Modules Project [LAMP], Herman, Pepe, Moore, King; Addison-Wesley; Copyright 2001.

 

Elementary Linear Algebra 5th Edition; by Larson, Edwards, Falvo; Houghton Mifflin Company; Copyright 2004.

 

Class MAT 2240 Notes dictated by Dr. Sarah J. Greenwald from June 7, 2004 through July 1, 2004.