论文标题
带有分段多项式函数的弹跳球系统的局部分叉结构
Local bifurcation structure of a bouncing ball system with a piecewise polynomial function for table displacement
论文作者
论文摘要
一个小的刚性球反复在桌子上反复弹跳的系统垂直振动，所谓的弹跳球系统，已广泛研究。假设表以时间的分段多项式函数振动，分叉图在定性上取决于多项式函数的顺序。我们通过关注两期解决方案来阐明分叉图中差异的机理。此外，在表振动的分段立方函数的情况下，我们得出了接近周期双分叉点的分支的近似曲线。我们还进行了数值计算，并证明了近似值很好地重现了数值结果。
The system in which a small rigid ball is bouncing repeatedly on a massive at table vibrating vertically, so-called the bouncing ball system, has been widely studied. Under the assumption that the table is vibrating with a piecewise polynomial function of time, the bifurcation diagram changes qualitatively depending on the order of the polynomial function. We elucidate the mechanism of the difference in the bifurcation diagrams by focusing on the two-period solution. In addition, we derive the approximate curve of the branch close to the period-doubling bifurcation point in the case of the piecewise cubic function of time for the table vibration. We also performed numerical calculation, and we demonstrate that the approximations well reproduce the numerical results.
