无阻尼强迫振荡器中的干涉辅助有限共振响应

IF 2 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-07-23 DOI:10.1088/1751-8121/ad6412
Shihabul Haque and Jayanta K Bhattacharjee
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引用次数: 0

摘要

我们将微扰技术应用于共振时的驱动无阻尼正弦振荡器。角位移 θ 遵循动力学原理。线性化近似给出了发散响应(长时间),但非线性项使响应有限。我们通过分别处理短时标和长时标两种方法来解决非线性引起的有限性问题。在长时间尺度上,我们使用传统的扰动技术来提取两种与驱动力相关的行为--一是振荡幅度随时间变化;二是慢模的时间周期随时间变化。另一方面,对于早期时间行为,我们设计了另一种扰动扩展,在这种扩展中,连续项随着求值阶数的增加而增大,但具有交替的符号。这些项之间的交替符号(相位差)会导致破坏性干扰效应。仔细考虑连续项之间的这种破坏性干扰效应,就会得出一个有限响应,它能合理正确地描述响应振幅的初始特性。我们还注意到,当驱动力值较大时,系统似乎会出现一阶过渡行为,最大的李雅普诺夫指数会突然跃升
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Interference aided finite resonant response in an undamped forced oscillator
We apply perturbative techniques to a driven undamped sinusoidal oscillator at resonance. The angular displacement, θ, obeys the dynamics . The linearized approximation gives a divergent response (at long times) but the nonlinear terms make the response finite. We address the nonlinearity-induced finiteness in two ways by separately treating the short and long time scales. At long times, we use the traditional perturbative techniques to extract two drive dependent behaviours—one, the amplitude of oscillation scales as and, two, the time period of the slow mode varies as . For the early time behaviour, on the other hand, we devise an alternate perturbative expansion where the successive terms get larger with the order of evaluation but have alternating signs. The alternating signs (phase differences) between these terms leads to adestructive interference like effect. A careful consideration of this destructive interference like effect between successive terms leads to a finite response which describes the initial behaviour of the amplitude of the response reasonably correctly. We further note that for larger drive values, the system seems to undergo a first order transitional behaviour with a sudden jump in the largest Lyapunov exponent
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来源期刊
CiteScore
4.10
自引率
14.30%
发文量
542
审稿时长
1.9 months
期刊介绍: Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.
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