Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
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 proceeding › Conference contribution › Research › peer-review
}
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