Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India.
Chaos. 2012 Mar;22(1):013131. doi: 10.1063/1.3692970.
The dynamics of a classical system driven by a rapidly oscillating field (with frequency ω) in the presence of friction has been investigated using the multiple scale perturbation theory (MSPT). By exploiting the idea of separation of time scales, the slow motion has been computed in a systematic expansion in the inverse of ω to the order ω(-3). This perturbation series can be viewed as a generalization of the calculation presented by Landau and Lifshitz for Kapitza's pendulum (where the point of suspension is moved periodically) in the presence of friction. The radiation induced dynamics of the system is found to be described by an effective time-independent potential with friction that controls the slow motion. The explicit appearance of friction in our computed effective potential is a manifestation of the dynamical effect due to the fast motion. The present study demonstrates that MSPT can be used to understand and predict the classical dynamics of a driven system in the presence of friction.
利用多尺度微扰理论(MSPT)研究了在摩擦存在的情况下,由快速振荡场(频率为 ω)驱动的经典系统的动力学。通过利用时间尺度分离的思想,在ω的倒数的ω(-3)阶次上对慢运动进行了系统的展开计算。该微扰级数可以看作是 Landau 和 Lifshitz 为 Kapitza 摆(悬挂点周期性移动)在摩擦存在下的计算的推广。发现系统的辐射诱导动力学由具有摩擦的有效时不变势描述,该势控制着慢运动。我们计算的有效势中摩擦的显式出现是快速运动引起的动力学效应的表现。本研究表明,MSPT 可用于理解和预测存在摩擦的驱动系统的经典动力学。