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Geometric integration of nonlinear dynamical systems. / Andrianov, Serge N.; Edamenko, Nikolai S.

2015 International Conference on "Stability and Control Processes" in Memory of V.I. Zubov, SCP 2015 - Proceedings. ed. / L. A. Petrosyan; A. P. Zhabko. Institute of Electrical and Electronics Engineers Inc., 2015. p. 38-41 7342048 (2015 International Conference on "Stability and Control Processes" in Memory of V.I. Zubov, SCP 2015 - Proceedings).

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Harvard

Andrianov, SN & Edamenko, NS 2015, Geometric integration of nonlinear dynamical systems. in LA Petrosyan & AP Zhabko (eds), 2015 International Conference on "Stability and Control Processes" in Memory of V.I. Zubov, SCP 2015 - Proceedings., 7342048, 2015 International Conference on "Stability and Control Processes" in Memory of V.I. Zubov, SCP 2015 - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 38-41, International Conference on "Stability and Control Processes" in Memory of V.I. Zubov, SCP 2015, St. Petersburg, Russian Federation, 5/10/15. https://doi.org/10.1109/SCP.2015.7342048, https://doi.org/10.1109/SCP.2015.7342048

APA

Andrianov, S. N., & Edamenko, N. S. (2015). Geometric integration of nonlinear dynamical systems. In L. A. Petrosyan, & A. P. Zhabko (Eds.), 2015 International Conference on "Stability and Control Processes" in Memory of V.I. Zubov, SCP 2015 - Proceedings (pp. 38-41). [7342048] (2015 International Conference on "Stability and Control Processes" in Memory of V.I. Zubov, SCP 2015 - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SCP.2015.7342048, https://doi.org/10.1109/SCP.2015.7342048

Vancouver

Andrianov SN, Edamenko NS. Geometric integration of nonlinear dynamical systems. In Petrosyan LA, Zhabko AP, editors, 2015 International Conference on "Stability and Control Processes" in Memory of V.I. Zubov, SCP 2015 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2015. p. 38-41. 7342048. (2015 International Conference on "Stability and Control Processes" in Memory of V.I. Zubov, SCP 2015 - Proceedings). https://doi.org/10.1109/SCP.2015.7342048, https://doi.org/10.1109/SCP.2015.7342048

Author

Andrianov, Serge N. ; Edamenko, Nikolai S. / Geometric integration of nonlinear dynamical systems. 2015 International Conference on "Stability and Control Processes" in Memory of V.I. Zubov, SCP 2015 - Proceedings. editor / L. A. Petrosyan ; A. P. Zhabko. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 38-41 (2015 International Conference on "Stability and Control Processes" in Memory of V.I. Zubov, SCP 2015 - Proceedings).

BibTeX

@inproceedings{7e5bbedc7bba45cdbc176ab6b5d1701f,
title = "Geometric integration of nonlinear dynamical systems",
abstract = "In modern literature, the geometric integration means numerical integration of differential equations that provides an accurate preservation of one or more 'geometric' properties within rounding error. Among these properties we have to mention first conservation of energy, of momentum, of angular momentum, of volume of the phase space, of time-reversal symmetry, of symplectic structure (volume conservation) etc. In this article we consider the concept of geometrical integration using Lie transformations generated by dynamical system on the one hand, and matrix representation for corresponding evolution operators on the other hand. Examples of solutions for some test problems and of practical problems are given.",
keywords = "Computers, Dynamics, Integral equations, Nonlinear control systems, Nonlinear dynamical systems, Trajectory",
author = "Andrianov, {Serge N.} and Edamenko, {Nikolai S.}",
note = "Publisher Copyright: {\textcopyright} 2015 IEEE. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.; International Conference on {"}Stability and Control Processes{"} in Memory of V.I. Zubov, SCP 2015 ; Conference date: 05-10-2015 Through 09-10-2015",
year = "2015",
month = nov,
day = "30",
doi = "10.1109/SCP.2015.7342048",
language = "English",
series = "2015 International Conference on {"}Stability and Control Processes{"} in Memory of V.I. Zubov, SCP 2015 - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "38--41",
editor = "Petrosyan, {L. A.} and Zhabko, {A. P.}",
booktitle = "2015 International Conference on {"}Stability and Control Processes{"} in Memory of V.I. Zubov, SCP 2015 - Proceedings",
address = "United States",
url = "http://www.apmath.spbu.ru/scp2015/openconf.php",

}

RIS

TY - GEN

T1 - Geometric integration of nonlinear dynamical systems

AU - Andrianov, Serge N.

AU - Edamenko, Nikolai S.

N1 - Publisher Copyright: © 2015 IEEE. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2015/11/30

Y1 - 2015/11/30

N2 - In modern literature, the geometric integration means numerical integration of differential equations that provides an accurate preservation of one or more 'geometric' properties within rounding error. Among these properties we have to mention first conservation of energy, of momentum, of angular momentum, of volume of the phase space, of time-reversal symmetry, of symplectic structure (volume conservation) etc. In this article we consider the concept of geometrical integration using Lie transformations generated by dynamical system on the one hand, and matrix representation for corresponding evolution operators on the other hand. Examples of solutions for some test problems and of practical problems are given.

AB - In modern literature, the geometric integration means numerical integration of differential equations that provides an accurate preservation of one or more 'geometric' properties within rounding error. Among these properties we have to mention first conservation of energy, of momentum, of angular momentum, of volume of the phase space, of time-reversal symmetry, of symplectic structure (volume conservation) etc. In this article we consider the concept of geometrical integration using Lie transformations generated by dynamical system on the one hand, and matrix representation for corresponding evolution operators on the other hand. Examples of solutions for some test problems and of practical problems are given.

KW - Computers

KW - Dynamics

KW - Integral equations

KW - Nonlinear control systems

KW - Nonlinear dynamical systems

KW - Trajectory

UR - http://www.scopus.com/inward/record.url?scp=84960122720&partnerID=8YFLogxK

U2 - 10.1109/SCP.2015.7342048

DO - 10.1109/SCP.2015.7342048

M3 - Conference contribution

T3 - 2015 International Conference on "Stability and Control Processes" in Memory of V.I. Zubov, SCP 2015 - Proceedings

SP - 38

EP - 41

BT - 2015 International Conference on "Stability and Control Processes" in Memory of V.I. Zubov, SCP 2015 - Proceedings

A2 - Petrosyan, L. A.

A2 - Zhabko, A. P.

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - International Conference on "Stability and Control Processes" in Memory of V.I. Zubov, SCP 2015

Y2 - 5 October 2015 through 9 October 2015

ER -

ID: 3983423