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TY - CONF AU - Sboeva, E. AU - Andrianov, S.N. AU - Ivanov, A.N. AU - Krushinevskii, E. ED - Koscielniak, Shane ED - Satogata, Todd ED - Schaa, Volker RW ED - Thomson, Jana TI - Symbolic Presentation of Nonlinear Dynamic Systems in Terms of Lego-Objects J2 - Proc. of IPAC2018, Vancouver, BC, Canada, April 29-May 4, 2018 C1 - Vancouver, BC, Canada T2 - International Particle Accelerator Conference T3 - 9 LA - english 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. PB - JACoW Publishing CP - Geneva, Switzerland SP - 3441 EP - 3443 KW - quadrupole KW - octupole KW - database KW - controls KW - dipole DA - 2018/06 PY - 2018 SN - 978-3-95450-184-7 DO - 10.18429/JACoW-IPAC2018-THPAK090 UR - http://jacow.org/ipac2018/papers/thpak090.pdf ER -