On an Application of the Hill Approach to the General Case of the Three-body Problem

Abstract

In this work, we use the energy and angular momentum integrals as a resource for applying Hill’s approach to the general three-body problem. As a result, we obtain theorems on the Lagrange stability and Hill stability in the general three-body problem. Also, specific features of the general and restricted three-body problems are discussed.

Keywords

• N-body problem
• Three-body problem