Accession Number:

AD0669630

Title:

STABILITY OF SOME NONLINEAR SYSTEMS,

Descriptive Note:

Corporate Author:

CALIFORNIA UNIV BERKELEY STRUCTURAL ENGINEERING LAB

Personal Author(s):

Report Date:

1968-02-01

Pagination or Media Count:

75.0

Abstract:

The stability of systems governed by x double dot fx qx, x dotx dot - phit rx Sxt is studied. Liapunovs Direct Method and a linearization approach have been used in the study of stability of the above system for phit L sub 1 integrable, and periodic, respectively. In the former case a sufficiency region of stability is constructed through the use of a Liapunov function. In the latter case, which is investigated by means of a linearization process, a Hill equation is obtained, whose stability is studied by a method suggested by Malkin. Malkins method is then modified to obtain, by use of a first approximation, the first stability region in parameter space. A second approximation is also worked out. When the approximations obtained herein for general periodic function are reduced to the special cases of the Mathieu equation and the Hill-3-term equation, the results compare very well with the available numerical results based on the exact solution of each of those equations. Author

Subject Categories:

  • Theoretical Mathematics
  • Construction Equipment, Materials and Supplies

Distribution Statement:

APPROVED FOR PUBLIC RELEASE