On the stability boundaries of linear periodic Hamiltonian or reversible differential equations

Brief Reports
  • 34 Downloads

Abstract

Two-parameter families of time periodic reversible or Hamiltonian differential equations are considered. The goal is to describe conditions such that the stability boundary is a smooth curve, at least locally. This is done by transforming the monodromy matrix of the system to a suitable normal form.

Keywords

Differential Equation Normal Form Mathematical Method Smooth Curve Stability Boundary 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    F. Meyre,Stability Analysis of Large Parametrically Excited Linear Vibration Systems, Ph.D. Thesis, ETH, 1984.Google Scholar
  2. [2]
    U. Kirchgraber, F. Meyer and G. Schweitzer,Stability of Two-Parameter Families of Linear Periodic Systems, in H. Neunzert (ed.),The Road Vehicle System and Related Mathematics. Teubner, Stuttgart 1985, pp. 92–101.Google Scholar
  3. [3]
    R. Broucke,Stability of periodic orbits in the elliptic, restricted three-body problem, AIAA J.7, no. 6, June 1969.Google Scholar
  4. [4]
    V. A. Yakubovich and V. M. Starzhinskii,Linear Differential Equations with Periodic Coefficients, Wiley, New York 1975.Google Scholar
  5. [5]
    A. Vanderbauwhede,Normal forms and versal unfolding of symplectic linear mappings, World Scientific Series in Applicable Analysis, Vol. IV, 1995.Google Scholar

Copyright information

© Birkhäuser Verlag 1996

Authors and Affiliations

  • U. Manz
    • 1
  1. 1.MathematikETH Zurich

Personalised recommendations