论文标题

球形CO求和的相对论转化(t,r,θ,ϕ)

Relativistic Transformation of Spherical Co ordinates(t,r,θ,ϕ)

论文作者

Mazumdar, Sarbajit, Parida, Krishna Kant

论文摘要

随着相对论力学的出现,洛伦兹的转化取代了基于牛顿的经典力学在高均匀速度下的惯性框架中的转化,但两种转换都是基于笛卡尔坐标系统,因此可以获得粒子在空间中获得线性速度的位置。如果框架以恒定的角速度旋转,则使用菲利普·富兰克林(Philip Franklin)在1922年提出的富兰克林转换代替了伽利略旋转转化(GRT)。修改后的转换引入了刚体中点旋转运动的概念。两种转换均基于圆柱坐标系。在这里,我们进一步走了一步,用于使用球形坐标系进行相对论转换,以理解穿过对称对象(球体)质量中心的空间中的任何轴的旋转框架的行为。最终,我们了解了如何使用不同的坐标系统发现特殊的相对论理论适用于旋转运动。

With the advent of relativistic mechanics, the Lorentz transformation replaced the Galilean transformation based on classical Newtonian mechanics among inertial frames at high uniform velocities, but both transformations are based on Cartesian coordinate system, hence position of particles obtaining linear velocities in space can be obtained. In case where frames are rotating with constant angular velocity, use of Galilean rotational transformation (GRT) is replaced by Franklin transformation, proposed by Philip Franklin in 1922. The modified transformation introduced the concept of rotational motion of points in a rigid body. Both the transformations are based on cylindrical coordinate system. Here we moved a step further for making a relativistic transformation using spherical coordinate system for understanding the behaviour of rotating frames along any axis in the space passing through the center of mass of a symmetrical object (Sphere). We finally came to an understanding about how Special Theory of relativity is found to be applicable in rotational motion using different co-ordinate system.

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