运动的复平面坐标描述及其应用几例
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摘要
复平面坐标系在描述某些运动时具有独特的优点,在处理诸如显含速度的法向力(洛伦兹力、转动参考系中的科里奥利力等)作用下的圆周运动、旋轮线运动,以及某些情况下刚体的转动与滚动等运动时,采用此类坐标系都很方便。在该系中可以便捷地得出圆周运动的切向与法向加速度表达式,能够使一些在其他坐标系中解决起来比较复杂的问题得到简洁的处理。本文介绍运动的复平面坐标表示,并以正交电磁场中带电粒子的运动、水平转台上的小球滚动(来源于IYPT2015)等例子对其应用进行讨论。
The complex plane coordinate system has some unique advantages to describe some motions,such as circular motion and wheel line motion under the normal forces(Lorentz force,Coriolis force in the rotating frame)and the rotation or rolling of the rigid body,and so on.The tangential and normal acceleration of the circular motion can be obtained easily,and some problems which are difficult to solve in other coordinate system can be solved by simple processing in this coordinate system.In this paper,the description in complex plane coordinate system is introduced and discussed through several examples including the motion of a charged particle in orthogonal electromagnetic field and the rolling of a ball on the horizontal turntable.
The complex plane coordinate system has some unique advantages to describe some motions,such as circular motion and wheel line motion under the normal forces(Lorentz force,Coriolis force in the rotating frame)and the rotation or rolling of the rigid body,and so on.The tangential and normal acceleration of the circular motion can be obtained easily,and some problems which are difficult to solve in other coordinate system can be solved by simple processing in this coordinate system.In this paper,the description in complex plane coordinate system is introduced and discussed through several examples including the motion of a charged particle in orthogonal electromagnetic field and the rolling of a ball on the horizontal turntable.
引文
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[4]赵凯华,罗蔚茵.力学[M].北京:高等教育出版社,2004.07:28-29.
[5]黄祝明,吴锋.大学物理学[M].北京:化学工业出版社,2002.09:28,9-14.
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[7]毛骏健,顾牡.大学物理学[M].北京:高等教育出版社,1999.11:14-15.
[8]唐海燕,王丽梅,宋士贤.工科物理教程(上册)[M].北京:国防工业出版社,2007.01:39-40.
[9]王思聪.复平面上的圆的方程[J].遵义师专学报,1995(1):54-62.WANG Sicong.The equation of a circle in a complex plane[J].Journal of Zunyi Teachers College,1995(1):54-62.(in Chinese)
[10]胡建新.带电粒子在正交恒定电磁场中运动状态的分析[J].大学物理.2004(4):8-10.HU Jianxin.The motion of a charged particle in electric and magnetic fields perpendicular to each other[J].College Physics,2004(4):8-10.(in Chinese)
[2]康颖.大学物理(上册)[M].北京:科学出版社,2015.12:7-20.
[3]程守洙,江之永.普通物理学上册[M].北京:高等教育出版社,2006.12:5,14.
[4]赵凯华,罗蔚茵.力学[M].北京:高等教育出版社,2004.07:28-29.
[5]黄祝明,吴锋.大学物理学[M].北京:化学工业出版社,2002.09:28,9-14.
[6]FEYNMAN R P,LEIGHTON R B,SANDS M.费恩曼物理学讲义(第一卷)[M].郑永令,华宏鸣,吴子仪,等译.上海:上海科学技术出版社,2005.06:117-120.
[7]毛骏健,顾牡.大学物理学[M].北京:高等教育出版社,1999.11:14-15.
[8]唐海燕,王丽梅,宋士贤.工科物理教程(上册)[M].北京:国防工业出版社,2007.01:39-40.
[9]王思聪.复平面上的圆的方程[J].遵义师专学报,1995(1):54-62.WANG Sicong.The equation of a circle in a complex plane[J].Journal of Zunyi Teachers College,1995(1):54-62.(in Chinese)
[10]胡建新.带电粒子在正交恒定电磁场中运动状态的分析[J].大学物理.2004(4):8-10.HU Jianxin.The motion of a charged particle in electric and magnetic fields perpendicular to each other[J].College Physics,2004(4):8-10.(in Chinese)