| Aleksandr Kotelnikov | |
| Birth Name: | Aleksandr Petrovich Kotelnikov |
| Birth Date: | 20 October 1865 |
| Birth Place: | Kazan, Russian Empire |
| Death Place: | Moscow, Soviet Union |
| Alma Mater: | Kazan University |
| Thesis Title: | The Cross-Product Calculus and Certain of its Applications in Geometry and Mechanics |
| Thesis Year: | 1884 |
| Academic Advisors: | Ippolit S. Gromeka |
| Awards: | Stalin Prize (1943) |
Aleksandr Petrovich Kotelnikov (Russian: Алекса́ндр Петро́вич Коте́льников; October 20, 1865 – March 6, 1944) was a Russian and Soviet mathematician specializing in geometry and kinematics.
Aleksandr was the son of, a colleague of Nikolai Lobachevsky. The subject of hyperbolic geometry was non-Euclidean geometry, a departure from tradition. The early exposure to Lobachevsky's work eventually led to Aleksandr undertaking the job of editing Lobachevsky's works.
Kotelnikov studied at Kazan University, graduating in 1884. He began teaching at a gymnasium. Having an interest in mechanics, he did graduate study. His thesis was The Cross-Product Calculus and Certain of its Applications in Geometry and Mechanics. His work contributed to the development of screw theory and kinematics.[1] Kotelnikov began instructing at the university in 1893. His habilitation thesis was The Projective Theory of Vectors (1899).
In Kiev, Kotelnikov was professor and head of the department of pure mathematics until 1904. Returning to Kazan, he headed the mathematics department until 1914. He was at the Kyiv Polytechnic Institute directing the department of Theoretical Mechanics until 1924, when he moved to Moscow and took up teaching at Bauman Technical University.
In addition to the Works of Lobachevsky, Kotelnikov was also the editor of the collected works of Nikolay Zhukovsky, the father of Russian aerodynamics.
One reviewer put Kotelnikov at the head of a chain of investigations of Spaces over Algebras.[2] Successive researchers included D.N. Zeiliger, A.P. Norden, and B. A. Rosenfel'd.
See main article: Dual quaternion. Kotelnikov advanced an algebraic method of representing Euclidean motions that had been introduced by William Kingdon Clifford. Though developed to render motions in three-dimensional space, an eight-dimensional algebra of doubled quaternions
H
R3
If r is one of the square roots of minus one in
H
\underline{r}
H
<\underline{r}, \underline{s}> = 0
<r, s> = 0 and <r,s*>+<r*,s> = 0,
\underline{r} and \underline{s}
q = Q*pQ where Q = \cos(\underline{\omega})+\underline{u} \sin(\underline{\omega})
\underline{u}