Normal modes, uncoupling, and stability for a class of nonlinear oscillators
Authors:
G. Pecelli and E. S. Thomas
Journal:
Quart. Appl. Math. 37 (1979), 281-301
MSC:
Primary 34C15; Secondary 58F14, 58F22, 58F30, 70K20
DOI:
https://doi.org/10.1090/qam/548988
MathSciNet review:
548988
Full-text PDF Free Access
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G. Pecelli and E. S. Thomas, On a class of modes defined by Rosenberg, to appear
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F. M. Arscott, Periodic differential equations, Pergamon, 1964
R. Churchill, H. Jurenka and E. Thomas, A note on iso-energentic stability, Int. J. Nonlinear Mech., 12, 37–43 (1977)
R. Churchill, G. Pecelli, and D. Rod, Stability transitions for periodic orbits in Hamiltonian systems, to appear
R. Churchill, G. Pecelli, D. Rod and S. Sackolic, Coexistence of stable and random motion, Rocky Mountain J. Math. 7, 445–456 (1977)
C. H. Cooke and R. A. Struble, On the existence of periodic solutions and normal mode vibrations of nonlinear systems, Quart. Appl. Math. 24, 177–193 (1966)
W. B. Gordon, A theorem on the existence of periodic solutions to Hamiltonian systems with convex potential, J. Diff. Eq. 10, 324–334 (1971)
P. Hartman, Ordinary differential equations, John Wiley, 1964
C. S. Hsu, On a restricted class of Hill’s equations and some applications, J. Appl. Mech. 28e, 551–556 (1961).
C. S. Hsu, On the parametric excitations of a dynamic system having multiple degrees of freedom, J. Appl. Mech. 30E, 367–372 (1963)
N. W. McLachlan, Ordinary non-linear differential equations in engineering and physical sciences (2nd ed.), Clarendon Press, 1956
W. Magnus and S. Winkler, Hill’s equation, Interscience Publishers, 1966
J. K. Moser, On invariant curves of area-preserving mappings of an annulus, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II, Nr. 1 (1962)
C. H. Pak and R. M. Rosenberg, On the existence of normal mode vibrations in nonlinear systems, Quart. Appl. Math. 26, 403–416 (1968)
G. Pecelli and E. Thomas, An example of elliptic stability with large parameters: Lamé’s equation and the Arnold-Moser-Rüssmann criterion, Quart. Appl. Math. 36, 129–140 (1978)
G. Pecelli and E. S. Thomas, On a class of modes defined by Rosenberg, to appear
R. M. Rosenberg, On the existence of normal mode vibrations of nonlinear systems with two degrees of freedom, Quart. Appl. Math. 22, 217–234 (1964)
R. M. Rosenberg and C. P. Atkinson, On the natural modes and their stability of non-linear two-degree-of-freedom systems, J. Appl. Mech. 26, 377–385, (1959)
R. M. Rosenberg and J. K. Kuo, Nonsimilar normal mode vibrations of nonlinear systems having two degrees of freedom, J. Appl. Mech. 31E, 283–290 (1964)
H. Rüssmann, Über die Normalform analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung, Math. Annalen 19, 55–72 (1967)
H. D. Seifert, Periodische Bewegungen mechanischer Systeme, Math. Zeit. 51, 197–216 (1947)
C. L. Siegel and J. K. Moser, Lectures on celestial mechanics, Springer, Grundlehren Bd. 187 (1971)
A. Weinstein, Normal modes for nonlinear Hamiltonian systems, Inv. Math. 20, 47–57 (1973)
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Article copyright:
© Copyright 1979
American Mathematical Society