Titlebook: Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession; The Theory of Gyrogr Abraham A. Ungar Book 2001 Springer Science+Bus

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Beyond the Einstein Addition Law and its Gyroscopic Thomas PrecessionThe Theory of Gyrogr

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0168-1222 ing the role of hy- perbolic geometry in the special theory of relativity, initiated by Minkowski, by emphasizing the central role that hyperbolic geometry play978-0-7923-6910-3978-94-010-9122-0Series ISSN 0168-1222 Series E-ISSN 2365-6425

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Thomas Precession: The Missing Link,y of gyrogroups and gyrovector spaces. The theory of gyrogroups and gyrovector spaces provides a most natural generalization of its classical counterparts, the theory of groups and the theory of vector spaces. Readers who wish to start familiarizing themselves with the theory may, therefore, start r

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The Einstein Gyrovector Space,n turn, results in the emergence of the hyperbolic analytic geometry of the Einstein gyrovector space, which turns out to be the familiar Beltrami ball model of hyperbolic geometry. The ball V. is equipped with the coordinates it inherits from its real inner product space V, relative to which gyrove

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The Ungar Gyrovector Space,by coordinate velocities which, in turn, are determined by coordinate time .. It would be useful, however, to understand the special theory of relativity through more than a single model. In this chapter we propose to study special relativity in terms of proper velocities, which are determined by pr

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Gyrogeometry,n gives rise. We indicate in this chapter that gyrogeometry is the super geometry that naturally unifies Euclidean and hyperbolic geometry. The classical hyperbolic geometry of Bolyai and Lobachevski emerges in gyrogeometry with a companion, called cohyperbolic geometry.

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,Gyrooperations — The ,(2, ,) Approach,ion. Reading this chapter would be useful for readers who are familiar, or wish to familiarize themselves, with the standard .(2,.) formalism and its Pauli spin matrices, and who wish to see how these lead to gyrogroups and gyrovector spaces. Starting from the Pauli spin matrices and a brief descrip