Rotations Quaternions And Double Groups Dover Books On Mathematics -

quaternions and spatial rotation wikipedia - unit quaternions also known as versors provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions compared to euler angles they are simpler to compose and avoid the problem of gimbal lock compared to rotation matrices they are more compact more numerically stable and more efficient quaternions have applications in computer, quaternion from wolfram mathworld - the quaternions are members of a noncommutative division algebra first invented by william rowan hamilton the idea for quaternions occurred to him while he was walking along the royal canal on his way to a meeting of the irish academy and hamilton was so pleased with his discovery that he scratched the fundamental formula of quaternion algebra i 2 j 2 k 2 ijk 1 1 into the stone of the, visualizing quaternions the morgan kaufmann series in - an excellent treatment of the topic whether you re interested in how quaternions are actually used in graphics control etc or want to start to learn about the surrounding mathematical theory of lie groups spinors clifford algebras and fibre bundles, on quaternions and octonions john horton conway derek - this book investigates the geometry of quaternion and octonion algebras following a comprehensive historical introduction the book illuminates the special properties of 3 and 4 dimensional euclidean spaces using quaternions leading to enumerations of the corresponding finite groups of symmetries, intuitive concepts in quantum mechanics scriptural physics - to make interacting photons the team shone a weak laser through a cloud of cold rubidium atoms rather than emerging from this cloud separately the photons within the laser merged bound in groups of three