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| Volume 29 Number 7 |
May / June 2004 |
Cranium Cruncher
by Douglas Yazell, ViceChair-Technical
Norman Chaffee/NASA (retired) continued a tradition of publishing a monthly
puzzle in Horizons, and the names of the people who sent him the correct
answers were published. Sophia Bright/Boeing suggested that our section's
technical branch committees continue the tradition. Please send your answers
to me at douglas.yazell@honeywell.com or phone me (for hints or discussion or
to deliver an answer) at 281-244-3925. I am submitting this one as a member
of our section's Guidance, Navigation, and Control technical committee,
which is chaired by Ellen Gillespie/USA. Like all of our committees in
the technical branch of our section, we are always looking for new members:
students, young professionals, experts, etc. We don't impose much on our
members' time, but there are many potential benefits. Other members on the
GN&C TC are: Daniel Nobles (Oceaneering), George Platanitis (Texas A&M,
recent PhD graduate in aerospace engineering), Jeff Tave (Lockheed Martin),
Ron Sostaric (NASA), and Murugan Subramaniam (Dynacs).
"Given an aircraft's velocity vector's coordinates in two coordinate systems
with the same origin, can we find the orientation between the two coordinate
systems? Is it unique? If not, describe all solutions."
Hints:
- This can be solved for full credit with no equations, using words
like circles, cones, lines, axes, coordinate systems, etc.
- There is more than one solution.
Applications and background:
One of many applications is a flight control system design engineer who has a
trim case (equilibrium among the rotational forces on the vehicle) for a new
vehicle's flight simulation, where the velocity vector is horizontal and due
north in the North, East, Down coordinate system. Having trimmed the vehicle,
the same vector is known in the body-fixed coordinate system. New trim
cases for simulation can be created easily if the direction cosine matrix
(describing the orientation between the two coordinate systems) is known.
For example, the velocity vector could point due east and horizontal.
Thanks are already due to Murugan Subramaniam. I created this puzzle
(creativity: the art of concealing one's sources), and he helped me to find
and visualize a complete solution. Thanks also go to Guillaume Francois
(Awty International School), a French ninth grade student who visited our
office for a week as part of his school's curriculum. He and others listened
and helped in other ways.
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