Monocular Kinematics Based on Geometric Algebras

2019 ◽  
pp. 121-129 ◽  
Author(s):  
Marek Stodola
Keyword(s):  
Geometric Algebras

scholarly journals Relativity in Clifford's Geometric Algebras of Space and Spacetime

2004 ◽  
Vol 43 (10) ◽  
pp. 2061-2079 ◽  
Author(s):  
William E. Baylis ◽  
Garret Sobczyk
Keyword(s):  
Geometric Algebras

2D, 3D, and 4D Geometric Algebras

2009 ◽  
pp. 63-92
Author(s):  
Eduardo Bayro-Corrochano
Keyword(s):  
Geometric Algebras

scholarly journals Explicit Baker–Campbell–Hausdorff–Dynkin formula for spacetime via geometric algebra

2021 ◽  
Author(s):  
Joseph Wilson ◽  
Matt Visser
Keyword(s):  
Efficient Method ◽  
Geometric Algebra ◽  
Clifford Algebras ◽  
Matrix Representation ◽  
Spin Representation ◽  
Lorentz Transformations ◽  
Rodrigues Formula ◽  
Dimension Formula ◽  
Spacetime Algebra ◽  
Geometric Algebras

We present a compact Baker–Campbell–Hausdorff–Dynkin formula for the composition of Lorentz transformations [Formula: see text] in the spin representation (a.k.a. Lorentz rotors) in terms of their generators [Formula: see text]: [Formula: see text] This formula is general to geometric algebras (a.k.a. real Clifford algebras) of dimension [Formula: see text], naturally generalizing Rodrigues’ formula for rotations in [Formula: see text]. In particular, it applies to Lorentz rotors within the framework of Hestenes’ spacetime algebra, and provides an efficient method for composing Lorentz generators. Computer implementations are possible with a complex [Formula: see text] matrix representation realized by the Pauli spin matrices. The formula is applied to the composition of relativistic 3-velocities yielding simple expressions for the resulting boost and the concomitant Wigner angle.

Lectures on Clifford (Geometric) Algebras and Applications

2004 ◽  
Author(s):  
Rafal Ablamowicz ◽  
William E. Baylis ◽  
Thomas Branson ◽  
Pertti Lounesto ◽  
Ian Porteous ◽  
...  
Keyword(s):  
Geometric Algebras

scholarly journals GEOMETRIC ALGEBRAS AND EXTENSORS

2007 ◽  
Vol 04 (06) ◽  
pp. 927-964 ◽  
Author(s):  
V. V. FERNÁNDEZ ◽  
A. M. MOYA ◽  
W. A. RODRIGUES
Keyword(s):  
Differential Geometry ◽  
Gravitational Field ◽  
Geometric Algebras ◽  
Geometrical Algebra

This is the first paper in a series (of four) designed to show how to use geometric algebras of multivectors and extensors to a novel presentation of some topics of differential geometry which are important for a deeper understanding of geometrical theories of the gravitational field. In this first paper we introduce the key algebraic tools for the development of our program, namely the euclidean geometrical algebra of multivectors [Formula: see text] and the theory of its deformations leading to metric geometric algebras [Formula: see text] and some special types of extensors. Those tools permit obtaining, the remarkable golden formula relating calculations in [Formula: see text] with easier ones in [Formula: see text] (e.g. a noticeable relation between the Hodge star operators associated to G and GE). Several useful examples are worked in details for the purpose of transmitting the "tricks of the trade".

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