Quaternion Optimization Problems in Engineering
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]).
KeywordsReference Frame Loss Function Position Vector Geometric Algebra Quaternion Multiplication
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