NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Spacecraft Attitude Determination and Control
From: Aubrey O?Callaghan
Date: 2003 Feb 14, 08:39 +0000
From: Aubrey O?Callaghan
Date: 2003 Feb 14, 08:39 +0000
William Rowan Hamilton was Irish studied at Trinity College Dublin.... I'm quite proud of having read Engineering there. Our Maths Prof. never allowed us forget Hamilton ! Just did a quick google search, as I never followed up much on this before: http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Hamilton.html Aubrey. At 03:20 14-02-03, you wrote: >On Thursday, February 13, 2003, at 05:20 PM, Robert Eno wrote: > >>What is a quaternion? > >In the world of mathematics there are a variety of numbers: > >* scalars > - single numbers (3.14, 58) >* complex numbers > - pairs of numbers like x,y points (1,2) > - also written as real + imaginary (1+2i) > - a set of arithmetic operations are defined such that > the square root of -1 is an imaginary number called i >* vectors > - several numbers (often 2-4) grouped together (1,2,3) > - often used to represent dimensions of space and time > - special operations like dot and cross product defined > - used in navigation, i.e., a 2D vector is distance & course >* tensors > - a matrix of numbers used in advanced physics & relativity >[(1,2,3)(4,5,6)] > - a generalization of vectors >* quaternions > - 4 numbers grouped together (q1,q2,q3,q4) > - used in rigid body rotations and computer graphics > - invented by Sir William Rowan Hamilton, circa 1866. > - allows multiple rotations be to computed with fewer operations > - think of them as a cross between a 3D vector and a complex number > - shares some properties of both vectors and complex numbers > >http://www.cs.berkeley.edu/~laura/cs184/quat/quaternion.html for more. > >Dan