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TY - UNPB AU - Vorontsov, V.A. ED - Kuzin, Maksim V. ED - Schaa, Volker RW TI - About One Way of the Solution of the Hill Equation J2 - Proc. of RUPAC2018, Protvino, Russia, 01-05 October 2018 C1 - Protvino, Russia T2 - Russian Particle Accelerator Conference T3 - 26 LA - english AB - The equation of Hill finds application in the different fields of science and technology, including accelerating technique. The known approaches assume the analysis of stability of the decision after definition of eigenvalues of a matrix of transition from initial values of couple of fundamental decisions to their values through the period of the function defining an oscillation frequency of amplitudes of decisions. Fundamental decisions are defined by the numerical solution of differential equations for amplitude and a phase received immediately from the equation of Hill. The different way of analytical submission of fundamental solutions of the equation of Hill and numerical approach to its decision is given in work. In it matrix approach to a task and the simplified algorithm of its decision corresponding to it is used. The received results are compared to results of the solution of the equation of Hill in the traditional way. On some plane the solution of the equation of Hill will be displayed in the form of closed curves with the repeating sites. At the same time curves will be not periodic if a change of a phase is incommensurable with 2Pi. If the solution of the equation of Hill is not limited, it will be displayed in the form of two spirals. Zero of some integral can judge stability of the decision on equality Thus, the specified technique of the solution of the equation of Hill allows along with finding of couple of fundamental decisions to define their stability. PB - JACoW Publishing CP - Geneva, Switzerland ER -