Section of Stability Theory and Mechanics of Controlled Systems
Division of Complex Physical and Technical Systems Modeling
Federal Research Center “Informatics and Control”
Russian Academy of Sciences
Several Fundamental Publications
- On Rubik's Cube (written in Russian and retrieved from the past millenium).
- An analytic unifying formula of oscillatory and rotary motion of a simple pendulum (dedicated to the 70th birthday of Jan Jerzy Slawianowski, written in 2013 and updated in 2014) // Proceedings of International Conference “Geometry, Integrability, Mechanics and Quantization”, Varna, Bulgaria, 2014, June 6-11. Printed by “Avangard Prima”, Sofia, Bulgaria, 2015: 160-171.
- Multiplication and division on elliptic curves, torsion points and roots of modular equations. An article written in 2014 (with references updated in 2019) // Zapiski Nauchnykh Seminarov POMI (485). An highly amusing blog cites it here 5次方程式の解の公式を求める. It was also cited in an article by Stefan Schmid.
- An arithmetic-geometric mean of a third kind! A paper, written in 2015, with references updated in 2019, containing “perfect” formulae for calculating three kinds of complete Elliptic Integrals // Lecture Notes in Computer Science, volume 11661: 37-56. Presented on August 30, 2019 at the 21st International Workshop on Computer Algebra in Scientific Computing, yet it was earlier cited in an article by Hea Kejing, Zhoua Xiaoqiang and Lin Qian. See also their footnote at the bottom of page 123.
- Torque free motion of a rigid body: from Feynman wobbling plate to Dzhanibekov flipping wingnut. A 15-page paper, written in 2017 (with references updated in 2019), where a symmetric (in the moments of inertia) expression for the rate of precession is obtained, as well as, the relevance of constructing the Galois critical axis, for describing the motion of both “Burke's twisting tennis racket” and “Dzhanibekov's flipping wingnut”, is shown.
Few little known papers (in Russian)