Investigation in Nonlinear Mechanics.

Abstract

The first phase of this work was the completion of the project on stability regions for Hill's equation. The main result was a description of the asymptotic behavior of the stability regions for large values of the parameters in the equation. Equations for asymptotic curves for the stability boundaries were obtained in a number of cases. The principal thrust of the work on this project has been the study of branching phenomena associated with general boundary-value problems for ordinary differential equations. The problem considered has been: (1) x' = F(t,x,mu) Ax(a) + Bx(b) = k where it is further assumed that there is a solution x sub 0(t) of the problem when mu = 0. Results have included a qualitative description of the simpler cases of branching for both the vector case and the scalar case. A further phase of the project has had to do with the group inverse of a differential operator and its application to branching problems for nonlinear systems. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1977
Accession Number
ADA046299

Entities

People

  • W. S. Loud

Organizations

  • University of Minnesota

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Classification
  • Differential Equations
  • Equations
  • Mathematical Analysis
  • Mathematics
  • Mechanics
  • Military Research
  • Minnesota
  • Nonlinear Systems
  • Partial Differential Equations
  • Physics
  • Real Variables
  • Students

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Linear Algebra
  • Technical Research and Report Writing.