Amplitude Isolines and Invariants of Motion of Non-Linear Oscillatory Systems Operating in the First and Higher Zones of Parametrical Instability
N.G. Zuyev, A.M. Titarenko, and O.I. Podgaiko
Kharkiv National University of Radio Engineering and Electronics,
14, Lenin Ave, Kharkiv, 61166, Ukraine
Abstract
The equations for amplitude isolines are obtained for the non-linear parametric system described by the Mathieu equation with cubic right-hand side part. For the linear case those equations are in line with the Mathieu zone boundaries The invariants of motion relating the amplitude and the phase of oscillations are obtained for the non-linear Mathieu equation and the dependence between the square of the amplitude and the phase is found in an explicit form for the first zone of instability as well as the dependence between the eigen time of the system and the oscillations phase is found in squiring.
References
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