Classic techniques have been established to characterize N × N proper orthogonal matrices using the N-dimensional Euler’s theorem and the Cayley transform. These techniques provide separate descriptions of N-dimensional orientation in terms of the constituent principal rotations or a minimum-parameter representation. The two descriptions can be linked by the canonical form of the extended Rodrigues parameters. This form is developed into a new minimum-parameter representation that directly links to the principal rotations. The new representation is solved using analytic and geometric approaches for N = 3 and N = 4, and numerical solutions are found for N= 5. In fact multiple solutions, which are related geometrically by different coordinatizations of the principal planes, have been found. The new parameters represent a projection of the principal rotations onto the planes formed by the body coordinates.


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    Title :

    Minimum-Parameter Representations of N-Dimensional Principal Rotations


    Additional title:

    J of Astronaut Sci


    Contributors:

    Published in:

    Publication date :

    2005-09-01


    Size :

    19 pages




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English




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