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    Re: Spacecraft Attitude Determination and Control
    From: Dan Allen
    Date: 2003 Feb 13, 19:20 -0800

    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
         - 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.

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