Abstract

In this paper we propose a symbolic representation of the solutions of the equations of evolution of dynamical systems in the framework of matrix formalism and Lie algebra for a number of elements of the accelerator (in particular, dipole, quadrupole and octupole) up to the 4th order. The considered solutions are Lego-objects*, which are include into the general scheme of the representation beam dynamics. It allows modeling of schemes of various accelerators and thereby to increasing performance of parametrical optimization. Let us note that the symbolic approach to solving such problems is more preferable than the numerical one, which is widely used. This leads to a reduction in the time and resources spent on solving optimization problems, as well as the ability to create universal Lego objects. The paper considers the verification of the obtained formulas from the experimental data. The corresponding Lego objects are the main components of the special software for both symbolic and numerical dynamics analysis. This software is planned to be used for modeling within the framework of the NICA accelerator project.
Original languageEnglish
Title of host publicationProceedings of the 9th International Particle Accelerator Conference
EditorsShane Koscielniak, Todd Satogata, Volker RW Schaa, Jana Thomson
Place of PublicationGeneva, Switzerland
PublisherJACoW
Pages3441-3443
Number of pages3
ISBN (Print)978-3-95450-184-7
DOIs
Publication statusPublished - Jun 2018

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accelerators
computer programs
optimization
problem solving
dynamical systems
resources
algebra
quadrupoles
dipoles
formalism
matrices

Cite this

Sboeva, E., Andrianov, S., Ivanov, A., & Krushinevskii, E. (2018). Symbolic Presentation of Nonlinear Dynamic Systems in Terms of Lego-Objects. In S. Koscielniak, T. Satogata, V. RW. Schaa, & J. Thomson (Eds.), Proceedings of the 9th International Particle Accelerator Conference (pp. 3441-3443). Geneva, Switzerland: JACoW. https://doi.org/10.18429/JACoW-IPAC2018-THPAK090
Sboeva, E. ; Andrianov, S. ; Ivanov, A. ; Krushinevskii, E. . / Symbolic Presentation of Nonlinear Dynamic Systems in Terms of Lego-Objects. Proceedings of the 9th International Particle Accelerator Conference. editor / Shane Koscielniak ; Todd Satogata ; Volker RW Schaa ; Jana Thomson. Geneva, Switzerland : JACoW, 2018. pp. 3441-3443
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title = "Symbolic Presentation of Nonlinear Dynamic Systems in Terms of Lego-Objects",
abstract = "In this paper we propose a symbolic representation of the solutions of the equations of evolution of dynamical systems in the framework of matrix formalism and Lie algebra for a number of elements of the accelerator (in particular, dipole, quadrupole and octupole) up to the 4th order. The considered solutions are Lego-objects*, which are include into the general scheme of the representation beam dynamics. It allows modeling of schemes of various accelerators and thereby to increasing performance of parametrical optimization. Let us note that the symbolic approach to solving such problems is more preferable than the numerical one, which is widely used. This leads to a reduction in the time and resources spent on solving optimization problems, as well as the ability to create universal Lego objects. The paper considers the verification of the obtained formulas from the experimental data. The corresponding Lego objects are the main components of the special software for both symbolic and numerical dynamics analysis. This software is planned to be used for modeling within the framework of the NICA accelerator project.",
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author = "E. Sboeva and S. Andrianov and A. Ivanov and E. Krushinevskii",
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Sboeva, E, Andrianov, S, Ivanov, A & Krushinevskii, E 2018, Symbolic Presentation of Nonlinear Dynamic Systems in Terms of Lego-Objects. in S Koscielniak, T Satogata, VRW Schaa & J Thomson (eds), Proceedings of the 9th International Particle Accelerator Conference. JACoW, Geneva, Switzerland, pp. 3441-3443. https://doi.org/10.18429/JACoW-IPAC2018-THPAK090

Symbolic Presentation of Nonlinear Dynamic Systems in Terms of Lego-Objects. / Sboeva, E. ; Andrianov, S. ; Ivanov, A. ; Krushinevskii, E. .

Proceedings of the 9th International Particle Accelerator Conference. ed. / Shane Koscielniak; Todd Satogata; Volker RW Schaa; Jana Thomson. Geneva, Switzerland : JACoW, 2018. p. 3441-3443.

Research output

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N2 - In this paper we propose a symbolic representation of the solutions of the equations of evolution of dynamical systems in the framework of matrix formalism and Lie algebra for a number of elements of the accelerator (in particular, dipole, quadrupole and octupole) up to the 4th order. The considered solutions are Lego-objects*, which are include into the general scheme of the representation beam dynamics. It allows modeling of schemes of various accelerators and thereby to increasing performance of parametrical optimization. Let us note that the symbolic approach to solving such problems is more preferable than the numerical one, which is widely used. This leads to a reduction in the time and resources spent on solving optimization problems, as well as the ability to create universal Lego objects. The paper considers the verification of the obtained formulas from the experimental data. The corresponding Lego objects are the main components of the special software for both symbolic and numerical dynamics analysis. This software is planned to be used for modeling within the framework of the NICA accelerator project.

AB - In this paper we propose a symbolic representation of the solutions of the equations of evolution of dynamical systems in the framework of matrix formalism and Lie algebra for a number of elements of the accelerator (in particular, dipole, quadrupole and octupole) up to the 4th order. The considered solutions are Lego-objects*, which are include into the general scheme of the representation beam dynamics. It allows modeling of schemes of various accelerators and thereby to increasing performance of parametrical optimization. Let us note that the symbolic approach to solving such problems is more preferable than the numerical one, which is widely used. This leads to a reduction in the time and resources spent on solving optimization problems, as well as the ability to create universal Lego objects. The paper considers the verification of the obtained formulas from the experimental data. The corresponding Lego objects are the main components of the special software for both symbolic and numerical dynamics analysis. This software is planned to be used for modeling within the framework of the NICA accelerator project.

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Sboeva E, Andrianov S, Ivanov A, Krushinevskii E. Symbolic Presentation of Nonlinear Dynamic Systems in Terms of Lego-Objects. In Koscielniak S, Satogata T, Schaa VRW, Thomson J, editors, Proceedings of the 9th International Particle Accelerator Conference. Geneva, Switzerland: JACoW. 2018. p. 3441-3443 https://doi.org/10.18429/JACoW-IPAC2018-THPAK090