Kinematics and Dynamics of a Particle in Gravitation Field

Abstract

It is accepted that three-dimensional physical space is a hypersurface with a Riemannian metric in four-dimensional space. The metric tensor of this three-dimensional space is defined by Einstein's equations. Another coordinate of four-dimensional space is time. In this space, the equations of the world line of a particle with a mass m are defined under certain initial conditions: the starting point of the space and the vector of the particle's initial velocity. This approach removes all the problems and contradictions noted in the monograph [1], and the resulting equations adequately describe, for example, the curvilinear motion of planets without energy change.