非完整系统中的类费米加速和幂律能量增长
Fermi-like acceleration and power-law energy growth in nonholonomic systems
摘要：
本文研究了具有参数激励的非完整系统--时变质量分布的Chaubergin雪橇。一个详细的分析是由无限增长的能量（费米的加速度的模拟）的情况下，激励是通过一个转子具有可变的角动量的存在的制度的问题。证明了雪橇的平移速度无限增加且渐近性为$τ^{\frac{1}{3}}$的轨迹的存在性。此外，它表明，当粘性摩擦与非退化的Rayleigh函数，无界加速消失，减少系统的轨迹渐近趋于极限环。
英文摘要：
This paper is concerned with a nonholonomic system with parametric excitation - the Chaplygin sleigh with time-varying mass distribution. A detailed analysis is made of the problem of the existence of regimes with unbounded growth of energy (an analogue of Fermi's acceleration) in the case where excitation is achieved by means of a rotor with variable angular momentum. The existence of trajectories for which the translational velocity of the sleigh increases indefinitely and has the asymptotics $τ^{\frac{1}{3}}$ is proved. In addition, it is shown that, when viscous friction with a nondegenerate Rayleigh function is added, unbounded speed-up disappears and the trajectories of the reduced system asymptotically tend to a limit cycle.
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