Virial Approach to the Solution of the Problem of Global Oscillations of the Earth's Atmosphere.

A new formulation of the problem of global oscillations of the earth's atmosphere is proposed. The problem consists in finding a solution which expresses the change in time of a Jacobi function or the potential energy of the atmosphere as the earth's shell. The desired solution should describe the unperturbed virial oscillations of the shell, on which external perturbations are imposed. These perturbations may in the general case be arbitrary given functions of time, the Jacobi function and their first derivatives. To obtain a solution describing the unperturbed virial oscillations of the atmosphere, a scalar virial Jacobi equation is written which within the framework of the earth atmosphere model adopted is reduced to a nonlinear second-order differential equation. A solution of this equation is obtained which represents the periodic variation in time of the Jacobi function or the potential energy.