Dynamics modeling and scientific development directions of mechanics and applied mathematics
DOI:
https://doi.org/10.21638/spbu01.2021.112Abstract
The development of scientific areas of mechanics as a result of the research of the Honorary Professor of St.Petersburg State University, Honored Worker of Science and Technology of the Russian Federation, Doctor of Physics and Mathematics Viktor Sergeevich Novoselov, the founder of the scientific school on analytical mechanics, space dynamics and applied mathematics is considered. The main theorems of analytic dynamics were extended to mechanical systems of variable composition. Using a variational technique, a number of remarkable results were obtained on the dynamics of controlled systems. In particular, a general scheme for constructing analytical approximations was proposed and repeatedly applied to solve equations.Keywords:
analytical dynamics, celestial mechanics, control systems, robotics, biomechanics, quantum mechanics and statistical physics
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References
Литература
1. Новоселов В.С. Аналитическая механика систем с переменными массами. Ленинград, Изд-во Ленингр. ун-та (1969).
2. Новоселов В.C. Траектория перехода точки переменной массы в центральном поле. Вестник Ленинградского университета. Серия 1. Математика. Механика. Астрономия, вып. 19 (1965).
3. Новоселов В.С. Вариационные методы в механике. Ленинград, Изд-во Ленингр. ун-та (1966).
4. Новоселов В.С. Голономные системы в лагранжевых координатах. Ленинград, Изд-во Ленингр. ун-та (1967).
5. Новоселов В.С. Варьирование динамических моделей движения. Ленинград, Изд-во Ленингр. ун-та (1983).
6. Новоселов В.С. Аналитическая теория оптимизации в гравитационных полях. Ленинград, Изд-во Ленингр. ун-та (1972).
7. Новоселов В.С., Королев В.С. Аналитическая механика управляемой системы, учеб. пособие. Санкт-Петербург, Изд-во С.-Петерб. ун-та (2005).
8. Новоселов В.С. Статистические модели механики, учеб. пособие. Санкт-Петербург, Изд- во С.-Петерб. ун-та (1999).
9. Новоселов В.С. Статистическая динамика, учеб. пособие. Санкт-Петербург, Изд-во С.-Петерб. ун-та (2009).
10. Новоселов В.С., Кирпичников С.Н., Королев В.С., Поляхова Е.Н., Шмыров А.С. Аналитические и качественные методы исследования вырожденных случаев возмущенных и управ- ляемых гамильтоновых систем. Отчет НИР 96-01-00609, Российский фонд фундаментальных ис- следований (1996).
11. Новоселов В.С. Интегральные инварианты и солитонные решения длинноволновых уравнений. Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Ин- форматика. Процессы управления, вып. 3, 69–75 (2010).
12. Новоселов В.С. К имитационному моделированию нервного импульса. Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Информатика. Процессы управления, вып. 4, 73–83 (2011).
13. Новоселов В.С. К математической модели пейсмекера. Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Информатика. Процессы управления, вып. 4, 58–64 (2012).
14. Novoselov V. S., Korolev V. S. Stochastic model of the universe matter. 2017 Constructive Nonsmooth Analysis and Related Topics (dedicated to the memory of V. F. Demyanov) (CNSA), St. Petersburg, 1–4 (2017). https://doi.org/10.1109/CNSA.2017.7973974
References
1. Novoselov V. S. Analytical mechanics of systems with variable masses. Leningrad, Leningrad University Press (1969). (In Russian)
2. Novoselov V. S. The trajectory of the transition point of variable mass in the central field. Vestnik of Leningrad University. Series 1. Mathematics. Mechanics. Astronomy, iss. 19 (1965). (In Russian)
3. Novoselov V. S. Variational methods in mechanics. Leningrad, Leningrad University Press (1966). (In Russian)
4. Novoselov V. S. Holonomic systems in Lagrangian coordinates. Leningrad, Leningrad University Press (1967). (In Russian)
5. Novoselov V. S. Variation of dynamic motion patterns. Leningrad, Leningrad University Press (1983). (In Russian)
6. Novoselov V. S. Analytical theory of optimization in gravitational fields. Leningrad, Leningrad University Press (1972). (In Russian)
7. Novoselov V. S., Korolev V. S. Analytical mechanics of a controlled system, St. Petersburg, St. Petersburg University Press (2005). (In Russian)
8. Novoselov V. S. Statistical models of mechanics, St. Petersburg, St. Petersburg University Press (1999). (In Russian)
9. Novoselov V. S. Statistical dynamics, St. Petersburg, St. Petersburg University Press (2009). (In Russian)
10. Novoselov V. S., Kirpichnikov S.N., Korolev V. S., Polyakhova E.N., Shmyrov A. S. Analytical and qualitative methods for the study of degenerate cases of excited and controlled Hamiltonian systems, Research Report 96-01-00609, Russian Foundation for Basic Research (1996). (In Russian)
11. Novoselov V. S. Integral invariants and soliton solutions of long-wave equations. Vestnik Sankt- Peterburgskogo universiteta. Seria 10. Prikladnaa matematika. Informatika. Processy upravlenia, iss. 3, 69–75 (2010). (In Russian)
12. Novoselov V. S. To simulation of nerve impulses. Vestnik Sankt-Peterburgskogo universiteta. Seria 10. Prikladnaa matematika. Informatika. Processy upravlenia, iss. 4, 73–83 (2011). (In Russian)
13. Novoselov V. S. To the mathematical model of pacemaker. Vestnik Sankt-Peterburgskogo universiteta. Seria 10. Prikladnaa matematika. Informatika. Processy upravlenia, iss. 4, 58–64 (2012). (In Russian)
14. Novoselov V. S., Korolev V. S. Stochastic model of the universe matter. 2017 Constructive Nonsmooth Analysis and Related Topics (dedicated to the memory of V. F. Demyanov) (CNSA), St. Petersburg, 1–4 (2017). https://doi.org/10.1109/CNSA.2017.7973974
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Published
2021-05-29
How to Cite
Alferov, G. V., Korolev, V. S., Polyakhova, E. N., & Kholshevnikov, K. V. (2021). Dynamics modeling and scientific development directions of mechanics and applied mathematics. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8(1), 138–149. https://doi.org/10.21638/spbu01.2021.112
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Section
Mechanics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
