Advertisement

Oscillations of Linear Systems

  • Frank C. Hoppensteadt
Chapter
Part of the Applied Mathematical Sciences book series (AMS, volume 94)

Abstract

A linear system of ordinary differential equations has the form
$$dx/dt = A\left( t \right)x + f\left( t \right)$$
Given an N-dimensional vector f and an N × N-dimensional matrix A(t) of functions of t, we seek a solution vector x(t). We write x, fE N and AE N × N and sometimes x′ = dx/dt or = dx/dt.

Keywords

Linear System Support Point Stability Diagram Periodic Coefficient Constant Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.1.
    P. Horowitz, W. Hill, The Art of Electronics, 2nd ed., Cambridge University Press, New York, 1989.Google Scholar
  2. 1.2.
    R.I. Higgins, Electronics with Digital and Analog Integrated Circuits, Prentice-Hall, Englewood Cliffs, New Jersey, 1983.Google Scholar
  3. 1.3.
    R. Courant, D. Hilbert, Methods of Mathematical Physics, Vol I, WileyInterscience, New York, 1968.Google Scholar
  4. 1.4.
    J.S. Frame, Applications of Matrices in Engineering, MSU Lecture Notes, 1965.Google Scholar
  5. 1.5.
    D.K. Fadeev, V.N. Fadeeva, Computational Methods in Linear Algebra, W.H. Freeman, San Francisco, 1963.Google Scholar
  6. 1.6.
    F.R. Gantmacher, Applications of the Theory of Matrices, Wiley-Interscience, New York, 1959.zbMATHGoogle Scholar
  7. 1.7.
    E.A. Coddington, N. Levinson, The Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.Google Scholar
  8. 1.8.
    W. Magnus, S. Winkler, Hill’s Equation, Wiley-Interscience, New York, 1966.Google Scholar
  9. 1.9.
    A.S. Besicovitch, Almost Periodic Functions, Dover, New York, 1954.Google Scholar
  10. 1.10.
    N. Wiener, The Fourier Integral and Certain of its Applications, Dover, New York, 1958.Google Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Frank C. Hoppensteadt
    • 1
  1. 1.College of Natural SciencesMichigan State UniversityEast LansingUSA

Personalised recommendations