Yet Another Reincarnation of an Old Problem

Abstract

This essay is devoted to the following problem. Suppose that a particle moves in the Newtonian gravitational field of an attracting center, but, in addition, the particle is subject to a “perturbing acceleration” of constant magnitude and direction Figure 3.1. This problem was considered already by Lagrange, then in the XIXth century by the French mathematicians Charlier and Saint-Germain, and also by I. V. Meshcherskii. They have shown that the problem is integrable by quadratures, but did not carry out the integration to the end, since the form of the quadratures that they obtained was not convenient for inversion. After that the above problem was thrown under the table and apparently saw no further development.

A man of culture gnaws a bone only slightly, and then throws it under the table.

Fafik

(from Thoughts of great and average men, and of Fafik the dog)