A Basic Approach to the Use of Canonical Variables and Von Zeipel's Method in Perturbation Theory
Abstract
Systematic methods of obtaining approximate solutions to complicated non-linear problems are the subject of perturbation theory, This theory probably reaches its highest development in celestial mechanics where detailed complexities must be taken into account in order to achieve the desired accuracies. Within recent years there has been a considerable revival of interest in the application of classical mechanics theory to practical problems involving satellites and space flight, using the Hamilton-Jacobi theory, canonical variables, and von Zeipel's perturbation method to provide some very elegant solutions to artificial satellite problems. However, many engineers without considerable training or experience in the subject have difficulty in following this work. Probably most of the difficulty arises because of their unfamiliarity with both the mathematical and astronomical jargon involved, and because of the complexity introduced when several degrees of freedom are involved. The von Zeipel perturbation technique at the time of this writing is a specialized tool available principally to astronomers and those trained in celestial mechanics, It is a powerful method which should have wide application to problems involved in other fields. Accordingly, the Memorandum presents the subject from an engineering rather than mathematical point of view, using relatively simple examples to illustrated the method.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1964
- Accession Number
- ADA596202
Entities
People
- J. H. Hutcheson
Organizations
- RAND Corporation