Rokni U, Friedland L
Racah Institute of Physics, Hebrew University of Jerusalem, 91904 Jerusalem, Israel.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 May;59(5 Pt A):5242-52. doi: 10.1103/physreve.59.5242.
The phenomenon of double autoresonance in dynamical systems with two degrees of freedom is examined. We analyze the motion of a particle in a two-dimensional centrally symmetric potential, subject to a homogeneous quasiperiodic external field of elliptical polarization. It is shown that if the particle has a sufficiently small initial energy, a double resonance is established when the slowly varying driving frequency approaches the linear resonance frequency. As the driving frequency is changed further, the double resonance is maintained, causing a continuous excitation of the oscillator. When nonlinearity becomes significant, the motion transforms into nearly circular oscillations. The necessary conditions for the persistence of the autoresonance are studied in detail.
研究了具有两个自由度的动力系统中的双自共振现象。我们分析了在二维中心对称势场中，受到均匀椭圆偏振准周期外场作用的粒子的运动。结果表明，如果粒子具有足够小的初始能量，当缓慢变化的驱动频率接近线性共振频率时，会建立双共振。随着驱动频率进一步变化，双共振得以维持，从而导致振荡器的持续激发。当非线性变得显著时，运动转变为近圆周振荡。详细研究了自共振持续存在的必要条件。
