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.

Original languageEnglish
Title of host publication2015 International Conference on "Stability and Control Processes" in Memory of V.I. Zubov, SCP 2015 - Proceedings
EditorsL. A. Petrosyan, A. P. Zhabko
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages38-41
Number of pages4
ISBN (Electronic)9781467376983
DOIs
StatePublished - 30 Nov 2015
EventInternational Conference on "Stability and Control Processes" in Memory of V.I. Zubov, SCP 2015 - Петергоф, St. Petersburg, Russian Federation
Duration: 5 Oct 20159 Oct 2015
http://www.apmath.spbu.ru/scp2015/openconf.php

Publication series

Name2015 International Conference on "Stability and Control Processes" in Memory of V.I. Zubov, SCP 2015 - Proceedings

Conference

ConferenceInternational Conference on "Stability and Control Processes" in Memory of V.I. Zubov, SCP 2015
Abbreviated titleSCP 2015
Country/TerritoryRussian Federation
CitySt. Petersburg
Period5/10/159/10/15
Internet address

    Research areas

  • Computers, Dynamics, Integral equations, Nonlinear control systems, Nonlinear dynamical systems, Trajectory

    Scopus subject areas

  • Computational Mechanics
  • Control and Systems Engineering

ID: 3983423