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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1977
- Accession Number
- ADA046299
Entities
People
- W. S. Loud
Organizations
- University of Minnesota