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Quaternion Optimization Problems in Engineering

  • Ljudmila Meister

Abstract

The interconnection between algebraic and geometric descriptions of space-time properties has attracted and ravished mathematicians since the time of Euclid. The last two centuries have been marked by several great contributions to this subject; among them Clifford and Grassmann algebras and Hamilton’s quaternions. Quaternions were invented by Hamilton to simplify mathematical modelling of rigid body motion in three dimensions. A fascinating history of quaternions is presented in many books, see, for instance, [ 1]. The joint work of many mathematicians revealed the fundamental connections of Clifford’s, Grassmann’s, and Hamilton’s approaches. The result of all this work is Geometric Algebra (see [ 13]).

Keywords

Reference Frame Loss Function Position Vector Geometric Algebra Quaternion Multiplication 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Ljudmila Meister

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