A BASIC APPROACH TO THE USE OF CANONOCAL VARIABLES AND VON ZEIPEL'S METHOD IN PERTURBATION THEORY,
Abstract
This study was concerned with the von Zeipel perturbation method for finding an approximate solution to differential equations such as occur in non-linear mechanics. The method is illustrated by briefly introducing some fundamental principles of Hamilton-Jacobi mechanics relating to the formation of the Hamiltonian, canonic equations, canonic variables, transformations, etc. The von Zeipel method consists of making successive mathematical transformations of variables of a canonical system of differential equations. The transformations are performed in a methodical way according to established general rules so that the final solution is obtained in a certain desired form. Two examples are worked out in detail, one is for the non-linear spring equation where energy is conserved and the other is for the Van der Pol equation to illustrate how an energy-dissipating system is handled. Also there is a discussion of some basic principles and details regarding the variation of parameters method and finally, a comparison is made of the von Zeipel method with that of Kryloff-Bogoliuboff (which is widely applied in the fields of engineering and physics). (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1964
- Accession Number
- AD0600413
Entities
People
- J. H. Hutcheson
Organizations
- RAND Corporation