Periodic bouncing modes for two uniformly magnetized spheres. I. Trajectories.
Periodic bouncing modes for two uniformly magnetized spheres. I. Trajectories.
复制标题
两个均匀磁化球体的周期性弹跳模式。
作者：
Boyd F. Edwards;B. Johnson;J. Edwards
我们考虑一个均匀磁化的球体，在一个平面内无摩擦地运动，以响应第二个相同的固定球体的场，使弹性硬球与这个球体碰撞。我们寻求相关的非线性运动方程的周期解。我们找到了小振幅模式的封闭形式的数学解，并使用这些来表征和验证我们的大振幅模式，我们发现数值。我们的龙格-库塔积分方法使我们能够找到1243个不同的周期模式与自由球最初位于其稳定的平衡位置。这些模式中的每一个从具有无限小幅度角运动的有限幅度径向弹跳模式分叉，并且支持具有增加的角运动量的状态族。这些状态提供了丰富多样的行为和美丽的对称轨迹，包括每个周期多达157次碰撞和580次角振荡的状态。
We consider a uniformly magnetized sphere that moves without friction in a plane in response to the field of a second, identical, fixed sphere, making elastic hard-sphere collisions with this sphere. We seek periodic solutions to the associated nonlinear equations of motion. We find closed-form mathematical solutions for small-amplitude modes and use these to characterize and validate our large-amplitude modes, which we find numerically. Our Runge-Kutta integration approach allows us to find 1243 distinct periodic modes with the free sphere located initially at its stable equilibrium position. Each of these modes bifurcates from the finite-amplitude radial bouncing mode with infinitesimal-amplitude angular motion and supports a family of states with increasing amounts of angular motion. These states offer a rich variety of behaviors and beautiful, symmetric trajectories, including states with up to 157 collisions and 580 angular oscillations per period.
影响因子：
1.9
作者：
Hall C
通讯作者：
Hall C