Chajwa Rahul, Menon Narayanan, Ramaswamy Sriram
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560 089, India.
Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Phys Rev Lett. 2019 Jun 7;122(22):224501. doi: 10.1103/PhysRevLett.122.224501.
We show experimentally that a pair of disks settling at negligible Reynolds number (∼10^{-4}) displays two classes of bound periodic orbits, each with transitions to scattering states. We account for these dynamics, at leading far-field order, through an effective Hamiltonian in which gravitational driving endows orientation with the properties of momentum. This treatment is successfully compared against the measured properties of orbits and critical parameters of transitions between types of orbits. We demonstrate a precise correspondence with the Kepler problem of planetary motion for a wide range of initial conditions, find and account for a family of orbits with no Keplerian analog, and highlight the role of orientation as momentum in the many-disk problem.
我们通过实验表明，一对以可忽略不计的雷诺数（约10⁻⁴）沉降的圆盘呈现出两类束缚周期轨道，每类轨道都有向散射态的转变。我们通过一个有效哈密顿量在远场主导阶上解释了这些动力学，其中引力驱动赋予取向以动量的性质。这种处理方法与测量得到的轨道性质以及不同类型轨道之间转变的临界参数成功进行了比较。我们证明了在广泛的初始条件下与行星运动的开普勒问题存在精确对应，发现并解释了一类没有开普勒类比的轨道，并强调了取向作为动量在多圆盘问题中的作用。
