Ferguson M. L., Miller B. N., Thompson M. A.
Department of Physics, Texas Christian University, Fort Worth, Texas 76129.
Chaos. 1999 Dec;9(4):841-848. doi: 10.1063/1.166467.
Gravitational billiards provide a simple method for the illustration of the dynamics of Hamiltonian systems. Here we examine a new billiard system with two parameters, which exhibits, in two limiting cases, the behaviors of two previously studied one-parameter systems, namely the wedge and parabolic billiard. The billiard consists of a point mass moving in two dimensions under the influence of a constant gravitational field with a hyperbolic lower boundary. An iterative mapping between successive collisions with the lower boundary is derived analytically. The behavior of the system during transformation from the wedge to the parabola is investigated for a few specific cases. It is surprising that the nature of the transformation depends strongly on the parameter values. (c) 1999 American Institute of Physics.
引力台球为说明哈密顿系统的动力学提供了一种简单方法。在此，我们研究一个具有两个参数的新台球系统，该系统在两种极限情况下呈现出两个先前研究过的单参数系统的行为，即楔形台球和抛物线台球。这个台球系统由一个在恒定引力场影响下在二维空间中运动的质点组成，其下边界为双曲线。通过解析方法推导出质点与下边界连续碰撞之间的迭代映射。针对一些特定情况研究了系统从楔形转变为抛物线形过程中的行为。令人惊讶的是，转变的性质强烈依赖于参数值。（c）1999美国物理研究所。
