Accession Number : ADA130213

Title :   On Perturbation Theory.

Descriptive Note : Technical rept.,


Personal Author(s) : Taff,Laurence G

PDF Url : ADA130213

Report Date : 01 Jun 1983

Pagination or Media Count : 48

Abstract : Perturbation theory in celestial mechanics has a long, rich history of failure stretching back to Newton. I believe that the causes of this are two-fold. One problem is the difficulty of dealing with the mathematical structure used in celestial mechanics to express perturbation theory as opposed to the constructs used in field theories (eg. trajectory equations vs. linear second order partial differential equations). The second flows directly from this and relates to the misapplications of certain mathematical techniques (averaging, series expansions) within the context of perturbation theory. These incorrect analyses usually appear in second-order theories such as Kozai's (1959) artificial satellite theory. Ideally this report would clearly illustrate the nature of these difficulties utilizing a complex (but exactly soluble) physical model intimately tied to the two-body problem and then go on to lay the foundations for a new perturbation theory. I believe that that's exactly what is accomplished herein except that the hints of the base of this new mathematical formalism are severely limited. The exactly soluble physical model is the three dimensional harmonic oscillator complicated by anisotropic terms, anharmonic terms, and air resistance. The deep connection is provided by Bertrand's theorem which is also proved. (Author)

Descriptors :   *Perturbation theory, *Mathematical models, *Celestial mechanics, Orbits, Numerical methods and procedures, Failure, Three dimensional, Harmonic generators, Anharmonic oscillators, Time dependence, Equations, Trajectories, Anisotropy, Air resistance

Subject Categories : Celestial Mechanics
      Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE