Absolutely New, Simple and Effective Theory of Movement Steadiness

Smol’yakov Eduard Rimovich

doi:doi:10.11648/j.ijtam.20180404.11

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Absolutely New, Simple and Effective Theory of Movement Steadiness

Smol’yakov Eduard Rimovich

Published in International Journal of Theoretical and Applied Mathematics (Volume 4, Issue 4)

Received: 3 December 2018 Accepted: 20 December 2018 Published: 14 January 2019

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Abstract

The absolutely new, simple and effective theory is proposed which differs from the classical Liapunov's theory of the movement steadiness. This theory permits to simplify and to speed up the search for the stable movement many times. The classical theory is very complex for using in the engineer practice and one does not bring success in many cases. It was necessary to create a theory that would be devoid of all shortcomings of the classical theory. In this work, it is proposed exactly such theory. Instead of the very complex Liapunov’s function we propose to use the variations calculation. This gives the invaluable winner in the speed and simplicity while searching for the stable movement.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 4, Issue 4)
DOI	10.11648/j.ijtam.20180404.11
Page(s)	35-39
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Dynamical Systems, Movement Steadiness, New Theory

References

[1]	Merkin D. A. Introduction into theory of movement stability. Moscow: Nauka, 1987.
[2]	Routh E. J. The advanced part of a treatise on the dynamics of a system of rigid bodies. London, 1884.
[3]	Ziegler H. Linear Elastic Stability. A. Critical Analysis of Methods // ZAMP. Basel – Zurich, IV, F – 2. 1953.
[4]	Hagedorn P. Uber die instabilitat konservativer systeme mit girosropischen Kraften // RationalMech and Anal. 1975, Bd. 58, № 1.
[5]	Herrman G. Stability of Equilibrium of Elastic Systems Subjested to Nonconservative Fordes // Applied Mechanics Reviews. 1967. V.20. № 2.
[6]	Karapetyan A. V. Stability of Stational movemnts. Moscow : URSS, 1998.
[7]	Chetaev N. G. Stability of movement. The works on the analytical mechanics. Moscow: RAN SSSR, 1962.
[8]	Krasovskii N. N. Some problems of the movement stability theory. Moscow: Fizmatgis, 1959.
[9]	Demidovich B. P. Lecture on mathematical theory of stability. Moscow.: MGU, 1998.
[10]	Bliss G. A. Lecture on the variational calculation.. Moscow.: IL, 1950.

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APA Style

Smol’yakov Eduard Rimovich. (2019). Absolutely New, Simple and Effective Theory of Movement Steadiness. International Journal of Theoretical and Applied Mathematics, 4(4), 35-39. https://doi.org/10.11648/j.ijtam.20180404.11

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ACS Style

Smol’yakov Eduard Rimovich. Absolutely New, Simple and Effective Theory of Movement Steadiness. Int. J. Theor. Appl. Math. 2019, 4(4), 35-39. doi: 10.11648/j.ijtam.20180404.11

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AMA Style

Smol’yakov Eduard Rimovich. Absolutely New, Simple and Effective Theory of Movement Steadiness. Int J Theor Appl Math. 2019;4(4):35-39. doi: 10.11648/j.ijtam.20180404.11

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@article{10.11648/j.ijtam.20180404.11,
  author = {Smol’yakov Eduard Rimovich},
  title = {Absolutely New, Simple and Effective Theory of Movement Steadiness},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {4},
  number = {4},
  pages = {35-39},
  doi = {10.11648/j.ijtam.20180404.11},
  url = {https://doi.org/10.11648/j.ijtam.20180404.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20180404.11},
  abstract = {The absolutely new, simple and effective theory is proposed which differs from the classical Liapunov's theory of the movement steadiness. This theory permits to simplify and to speed up the search for the stable movement many times. The classical theory is very complex for using in the engineer practice and one does not bring success in many cases. It was necessary to create a theory that would be devoid of all shortcomings of the classical theory. In this work, it is proposed exactly such theory. Instead of the very complex Liapunov’s function we propose to use the variations calculation. This gives the invaluable winner in the speed and simplicity while searching for the stable movement.},
 year = {2019}
}

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TY  - JOUR
T1  - Absolutely New, Simple and Effective Theory of Movement Steadiness
AU  - Smol’yakov Eduard Rimovich
Y1  - 2019/01/14
PY  - 2019
N1  - https://doi.org/10.11648/j.ijtam.20180404.11
DO  - 10.11648/j.ijtam.20180404.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 35
EP  - 39
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20180404.11
AB  - The absolutely new, simple and effective theory is proposed which differs from the classical Liapunov's theory of the movement steadiness. This theory permits to simplify and to speed up the search for the stable movement many times. The classical theory is very complex for using in the engineer practice and one does not bring success in many cases. It was necessary to create a theory that would be devoid of all shortcomings of the classical theory. In this work, it is proposed exactly such theory. Instead of the very complex Liapunov’s function we propose to use the variations calculation. This gives the invaluable winner in the speed and simplicity while searching for the stable movement.
VL  - 4
IS  - 4
ER  -

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Author Information

Smol’yakov Eduard Rimovich

Department of Mathematics, Lomonosov Moscow State University, Moscow, Russia

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Plain Text BibTeX RIS

APA Style

Smol’yakov Eduard Rimovich. (2019). Absolutely New, Simple and Effective Theory of Movement Steadiness. International Journal of Theoretical and Applied Mathematics, 4(4), 35-39. https://doi.org/10.11648/j.ijtam.20180404.11

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ACS Style

Smol’yakov Eduard Rimovich. Absolutely New, Simple and Effective Theory of Movement Steadiness. Int. J. Theor. Appl. Math. 2019, 4(4), 35-39. doi: 10.11648/j.ijtam.20180404.11

Copy | Download

AMA Style

Smol’yakov Eduard Rimovich. Absolutely New, Simple and Effective Theory of Movement Steadiness. Int J Theor Appl Math. 2019;4(4):35-39. doi: 10.11648/j.ijtam.20180404.11

Copy | Download

@article{10.11648/j.ijtam.20180404.11,
  author = {Smol’yakov Eduard Rimovich},
  title = {Absolutely New, Simple and Effective Theory of Movement Steadiness},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {4},
  number = {4},
  pages = {35-39},
  doi = {10.11648/j.ijtam.20180404.11},
  url = {https://doi.org/10.11648/j.ijtam.20180404.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20180404.11},
  abstract = {The absolutely new, simple and effective theory is proposed which differs from the classical Liapunov's theory of the movement steadiness. This theory permits to simplify and to speed up the search for the stable movement many times. The classical theory is very complex for using in the engineer practice and one does not bring success in many cases. It was necessary to create a theory that would be devoid of all shortcomings of the classical theory. In this work, it is proposed exactly such theory. Instead of the very complex Liapunov’s function we propose to use the variations calculation. This gives the invaluable winner in the speed and simplicity while searching for the stable movement.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Absolutely New, Simple and Effective Theory of Movement Steadiness
AU  - Smol’yakov Eduard Rimovich
Y1  - 2019/01/14
PY  - 2019
N1  - https://doi.org/10.11648/j.ijtam.20180404.11
DO  - 10.11648/j.ijtam.20180404.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 35
EP  - 39
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20180404.11
AB  - The absolutely new, simple and effective theory is proposed which differs from the classical Liapunov's theory of the movement steadiness. This theory permits to simplify and to speed up the search for the stable movement many times. The classical theory is very complex for using in the engineer practice and one does not bring success in many cases. It was necessary to create a theory that would be devoid of all shortcomings of the classical theory. In this work, it is proposed exactly such theory. Instead of the very complex Liapunov’s function we propose to use the variations calculation. This gives the invaluable winner in the speed and simplicity while searching for the stable movement.
VL  - 4
IS  - 4
ER  -

Copy | Download