The Nature of Oscillation and Rotation of the Earth

Abstract

We have presented the physical and theoretical fundamentals of the virial theory of dynamical equilibrium for study of the unperturbed and perturbed motion of a self-gravitating body. As it was noted, the condition of dynamical (oscillating) equilibrium of the body, which is determined by a functional relationship between the polar moment of inertia and the potential (kinetic) energy of any natural conservative and dissipative system in the form of the generalized virial theorem or Jacobi’s virial equation, serve as the bases of the presented theory. It was shown in Chap. 3 that the outstanding property of Jacobi’s virial equation is its ability to be both the equation of dynamical equilibrium and equation of motion simultaneously. Moreover, it is valid for all the known models of the dynamics of natural systems. The secret of universality of the equation is in its ability to describe the motion of a material system as a whole in its fundamental integral characteristics which are the energy and polar moment of inertia. It was shown in Chap. 2 that the functional relationship between the potential energy and the polar moment of inertia was revealed by means of analyzing the orbits of the artificial satellites. The potential energy, which is generated by interaction of the mass particles, is the force function of the body, i.e. the active component of its motion. The potential energy creates the inner and outer force field of the body. The kinetic energy is the reactive (inertial) constituent of the force field and is developed in the form of motion of the body’s mass particles and its shells. In the equations of motion written, for instance, for continuous media in coordinates and velocities under the mass force ρF one understands the gravity force induced by the outer force field. As a result, formulation and solution of any geophysical problems including dynamics of the body and change in its form and structure appears to be physically incorrect. As to the problem of the orbital motion of the body in the central force field, then the dynamical effects of the interacting bodies are ignored because of their smallness.