The Kustaanheimo–Stiefel transformation in geometric algebra
نویسندگان
چکیده
منابع مشابه
The Kustaanheimo–Stiefel transformation in geometric algebra
The Kustaanheimo–Stiefel (KS) transformation maps the non-linear and singular equations of motion of the three-dimensional Kepler problem to the linear and regular equations of a four-dimensional harmonic oscillator. It is used extensively in studies of the perturbed Kepler problem in celestial mechanics and atomic physics. In contrast to the conventional matrixbased approach, the formulation o...
متن کاملExtensors in Geometric Algebra
This paper, the third in a series of three introduces the basics of the theory of extensors that are need for the a theory of multvector and extensor fields in arbitrary manifolds, developed in a following series of five papers. Key notions such as the extension and generalization operators of a given linear operator (a (1, 1)-extensor) acting on a real vector space V are introduced and studied...
متن کاملConformal Mappings in Geometric Algebra
I n 1878 William Kingdon Clifford wrote down the rules for his geometric algebra, also known as Clifford algebra. We argue in this paper that in doing so he laid down the groundwork that is profoundly altering the language used by the mathematical community to express geometrical ideas. In the real estate business everyone knows that what is most important is location. We demonstrate here that ...
متن کاملCrystal Cells in Geometric Algebra
This paper focuses on the symmetries of space lattice crystal cells. All 32 point groups of three dimensional crystal cells are exclusively described by vectors (three for one particular cell) taken from the physical cell. Geometric multiplication of these vectors completely generates all symmetries, including reflections, rotations, inversions, rotary-reflections and rotary-inversions. The set...
متن کاملEngineering Graphics in Geometric Algebra
We illustrate the suitability of geometric algebra for representing structures and developing algorithms in computer graphics, especially for engineering applications. A number of example applications are reviewed. Geometric algebra unites many underpinning mathematical concepts in computer graphics such as vector algebra and vector fields, quaternions, kinematics and projective geometry, and i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2003
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/36/25/305