On stability diagrams for damped Hill equations

Pedersen, Pauli

doi:10.1090/qam/766884

Author: Pauli Pedersen
Journal: Quart. Appl. Math. 42 (1985), 477-495
MSC: Primary 34B30; Secondary 65L07
DOI: https://doi.org/10.1090/qam/766884
MathSciNet review: 766884
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In previous works, the Galerkin approach is shown to be most efficient for quantitative stability analysis of the solutions to Hill equations. This approach, furthermore, should be recognized to be a theoretical tool as well, which enables us in a most simple way to prove a number of theorems on decoupling, symmetry and other similarities related to the stability diagrams.

P. Pedersen, Stability of the solutions to Mathieu-Hill equations with damping, Ingenieur-Archiv, Vol. 49, 1980, pp. 15–29

Ali Hasan Nayfeh and Dean T. Mook, Nonlinear oscillations, Wiley-Interscience [John Wiley & Sons], New York, 1979. Pure and Applied Mathematics. MR 549322

P. Pedersen, A quantitative stability analysis of the solutions to the Carson-Cambi equation, J. Franklin Institute, 39, 359–367 (1980)

R. Tobey et al.: PL/1 FORMAC symbolic mathematics interpreter, IBM, 360D-03.3.004, 1969, p. 164

Jarl Jensen, Tensor formac, interaktivt formac (in Danish), Solid Mechanics, Technical Univ. of Denmark, 1978

SYSTEM/360 Continuous System Modeling Program, IBM, GH20-0367-4, 1972

F. R. Gantmacher, The theory of matrices. Vol. 1, AMS Chelsea Publishing, Providence, RI, 1998. Translated from the Russian by K. A. Hirsch; Reprint of the 1959 translation. MR 1657129
Thomas Muir, A treatise on the theory of determinants, Dover Publications, Inc., New York, 1960. Revised and enlarged by William H. Metzler. MR 0114826