High-Frequency Diffraction of a Point Source Field by a Strongly Elongated Elliptic Cylinder

The problem of diffraction of a high-frequency point source acoustic field by an infinite elliptic cylinder with a strongly elongated cross-section is studied. At every direction of propagation, the solution is shown to be similar to those of a linear source field diffraction by a cylinder with correspondingly enlarged major semiaxis.

Least-action Principle Applied to the Kepler Problem

The least-action principle is examined for the two-body Kepler problem. This examination allows one to couple the eccentricity parameter of the Kepler orbit with the size of the major semiaxis of that orbit. The obtained formula is applied to an estimate of eccentricities characteristic for a set of the planetary and satellitary tracks.