FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 4, PAGES 193-215

An explanation to "Rolling simplexes and their commensurability" (field equations in accordance with Tycho Brahe)

Yu. P. Razmyslov

Abstract

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Various Cartesian models of central power fields with quadratic dynamics are studied. These examples lead the reader to comprehension of basic aspects of the differential algebraic-geometrical Brahe--Descartes--Wotton theory, which embraces central power fields whose dynamics is composed of flat affine algebraic curves of degree at most $N$ ($N\; =\; 1,2,3,$¼). When $N\; =\; 2$, a quadratic rolling simplex law is proved by purely algebraic means.

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Last modified: July 2, 2012