坐标系的物理基础及其空间性质

PHYSICAL BASIS AND SPATIAL NATURES OF A COORDINATE SYSTEM

在对牛顿经典力学和爱因斯坦相对论对空间时间概念阐述的基础上,指出由于地壳运动是个宏观低速现象,因此完全可采用牛顿力学描述地壳质点在空间的位置以及在外力作用下该位置是如何随时间改变的,决定了必须选择一个不作加速度运动的参照系,才能正确使用牛顿定律对地壳运动进行正确的描述。因此满足牛顿惯性定律的参照系为地壳运动分析使用的坐标系的物理基础。不同坐标系的参照曲面上的虚拟空间具有不同的度量张量,因此具有不同的曲面内蕴几何性质。并对欧几里德三维直角坐标系、平面坐标系、球面坐标系等的空间性质进行了讨论。

By outlining the space-time theory in Newtonian mechanics and Einstein＇ s Relativity, it is pointed out that the crustal movement is a kind of macro-phenomenon of low speed. Thus adopting the Newtonian mechanics to describe position of a crustal particle as well as how it is changed by external forces along with the time are absolutely feasible, and a reference frame without any motion of acceleration is pretty necessary for depicting a crustal movement in a right way by using the Newton Laws. That is, a reference frame in accordance with the Newton inertia Law is one of the physical foundation of coordinate system for the purpose of crustal motion analysis. Considering that different coordinates have their own metric tensors in the respective virtual space on reference surface, they also have different sets of intrinsic geometric properties . Finally, a discussion on the spatial natures of the Cartesian, plane and spherical coordinate systems is made.