ON THE STABILITY OF THE EQUILIBRIUM SOLUTIONS OF THE PLANE RESTRICTED THREE BODY PROBLEM IN THE SENSE OF LIAPOUNOV.
Abstract
The stability of the five equilibrium solutions of the plane restjicted three body problems is investigated in a topological sense of Liapounov. This aspect of motion has always been a subject of considerable interest primarily because the stability criteria were derived from linearizing the dynamical equations. It is shown that the question cannot be resolved by means of existing theorems governing the first approximation since these cases belong to an exceptional class which Liapounov had termed critical. The stability of the equidistant positions and instability of the collinear solutions are established however in accordance with a less restrictive definition by using surfaces which are formed from the Jacobi integral. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1964
- Accession Number
- AD0438857
Entities
People
- Samuel E. Moskowitz
Organizations
- General Electric