An explanation to ``Rolling simplexes and their commensurability'' (field equations in accordance with Tycho Brahe)
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 4, pp. 193-215
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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 $N$ ($N=1,2,3,\dots$). When $N=2$, a quadratic rolling simplex law is proved by purely algebraic means.
@article{FPM_2012_17_4_a11,
author = {Yu. P. Razmyslov},
title = {An explanation to {``Rolling} simplexes and their commensurability'' (field equations in accordance with {Tycho} {Brahe)}},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {193--215},
publisher = {mathdoc},
volume = {17},
number = {4},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2012_17_4_a11/}
}
TY - JOUR AU - Yu. P. Razmyslov TI - An explanation to ``Rolling simplexes and their commensurability'' (field equations in accordance with Tycho Brahe) JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 2012 SP - 193 EP - 215 VL - 17 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_2012_17_4_a11/ LA - ru ID - FPM_2012_17_4_a11 ER -
%0 Journal Article %A Yu. P. Razmyslov %T An explanation to ``Rolling simplexes and their commensurability'' (field equations in accordance with Tycho Brahe) %J Fundamentalʹnaâ i prikladnaâ matematika %D 2012 %P 193-215 %V 17 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/FPM_2012_17_4_a11/ %G ru %F FPM_2012_17_4_a11
Yu. P. Razmyslov. An explanation to ``Rolling simplexes and their commensurability'' (field equations in accordance with Tycho Brahe). Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 4, pp. 193-215. http://geodesic.mathdoc.fr/item/FPM_2012_17_4_a11/