指南车广义运动方程的创建  

PERFORMS THE GENERAL MOTION EQUATIONS OF THE SOUTH POINTING CHARIOT

作　　者：邓崇林 TENG Chunglin

机构地区：[1]不详

出　　处：《物理与工程》2019年第4期7-16,34,共11页Physics and Engineering

摘　　要：在平面上行进的指南车遥指向南,本文的关注点是如果将其推广至曲面上时,将有哪些运动规律。本研究承接前人给出微型指南车是一台能遂行向量平行移动之机器的功能属性的观点,将此做为定量基础,深入探索其运动现象,从而创建微型指南车之广义运动方程,能够描述其指向器在曲面上的随行偏转运动与原地补转运动,以及一般指南车在平面上的自由运动等物理图像。当作用曲面退化成平面时,其广义运动方程会简化成自由平移方程,正是这个运动规律,使得在平面上的指南车指向器遵循着方向上的守恒律。相较于广义运动方程的微分形式,其另有对封闭路径积分形式的相位方程。This study performs the general motion equations for revealing kinematics of the South-Pointing Chariot(SPC)that rolls without slipping or jumping on the surface.When the micro-SPC(limit of zero size)travels along an arbitrary path on curved surface,the author derive the path-following the equation of motion for describing the effect of rolling of micro-SPC is therefore to rotate the direction of pointer by geodesic curvature.When the micro-SPC turn at the corner of the curve on curved surface,the author derives the rotate equation of motion for describing the rate of rotation of pointer occur with the opposite of the rate of rotation of the chariot.No matter how the ordinary SPC travels or rotates on plane surface,set of equations of motion on curved surface will degenerate into one called the free equation of motion,which tells us why the SPC always preserves the direction of its pointer.Compared with the differential form of the generalized equation of motion,there is another phase equation in the integral form of the closed path.

关 键 词：平行移动 向量平移 指南车 傅科摆 高斯博内公式 几何相位 测地曲率 

分 类 号：G63[文化科学—教育学]