从李萨如图形到黑洞背景下质点的周期运动轨道  

From the Lissajous figure to the periodic orbits of particles in the background of black holes

作　　者：魏少文 付春娥 WEI Shao-wen;FU Chun-e(School of Physical Science and Technology,Lanzhou University,Lanzhou,Gansu 730000,China;Institute of Theoretical Physics,School of Physics,Xi’an Jiaotong University,Xi’an,Shaanxi 710049,China)

机构地区：[1]兰州大学物理科学与技术学院基础物理1教研室,甘肃兰州730000 [2]西安交通大学物理学院应用物理系,陕西西安710049

出　　处：《大学物理》2024年第5期6-8,28,共4页College Physics

基　　金：兰州大学教育教学改革研究项目资助;国家自然科学基金(12075103);陕西省自然科学基金(2022JQ-037)资助。

摘　　要：从笛卡儿坐标系下横纵坐标方向简谐振动所形成的经典李萨如图形出发,考虑了极坐标参考系下沿径向和角向两个方向振动所形成的李萨如图形.分析了平衡点位于极坐标系原点和做匀速圆周运动时所对应李萨如图形的特征.进一步将这一结果推广到了黑洞背景下质点做束缚运动所形成的周期轨道.这些结果丰富和扩展了对李萨如图形的认识和理解.Starting from the classical Lissajous figures formed by the simple harmonic vibrations in the transverse and longitudinal directions under the classical Cartesian coordinate system,we study the Lissajous figures formed by the vibrations in the radial and angular directions under the polar coordinates.The features of the Lissajous figures are analyzed when the equilibrium point is located at the origin of polar coordinates and the equilibrium point moves in a circular motion.These results are further extended to the periodic orbits formed by the bound motion of particles in the background of black holes.This further enriches and expands our knowledge and understanding of the Lissajous figures.

关 键 词：李萨如图形 周期轨道 黑洞 

分 类 号：O442[理学—电磁学]