Necessary conditions for subharmonic and superharmonic synchronization in weakly nonlinear systems
Authors:
Richard E. Kronauer and Samuel A. Musa
Journal:
Quart. Appl. Math. 24 (1966), 153-160
MSC:
Primary 34.45
DOI:
https://doi.org/10.1090/qam/203183
MathSciNet review:
203183
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References |
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Additional Information
- Stig Lundquist, Subharmonic oscillations in a nonlinear system with positive damping, Quart. Appl. Math. 13 (1955), 305–310. MR 73027, DOI https://doi.org/10.1090/S0033-569X-1955-73027-3
- M. L. Cartwright, Forced oscillations in nonlinear systems, Contributions to the Theory of Nonlinear Oscillations, Annals of Mathematics Studies, no. 20, Princeton University Press, Princeton, N. J., 1950, pp. 149–241. MR 0035355
- K. Göransson and L. Hansson, An experimental investigation of subharmonic oscillations in a nonlinear system, Kungl. Tekn. Högsk. Handl. Stockholm 1956 (1956), no. 97, 16. MR 82595
H. Poincaré, Les Méthodes nouvelles de la Mécanique Céleste, 1, Gauthier-Villars, Paris (1892) reprint, Dover Publications, Inc., New York (1957)
B. Van der Pol, Forced Oscillations in a Circuit with Nonlinear Resistance (Reception with Reactive Triode), Phil. Mag. and J. Sei., 3, (1927) 65–80; reprint, Selected Papers on Mathematical Trends in Control Theory, Dover Publications, Inc., New York, (1964) 124–140
N. Krylov and N. Bogoliubov, Introduction to Nonlinear Mechanics, Ann. Math. Studies (1947) No. 11, Princeton Univ. Press, Princeton
N. Bogoliubov and Y. Mitropolski, Asymptotic Methods in the Theory of Nonlinear Oscillations (1955) translated by Gordon and Breach, Science Publishers, New York, (1961)
- J. D. Cole and J. Kevorkian, Uniformly valid asymptotic approximations for certain non-linear differential equations, Internat. Sympos. Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, New York, 1963, pp. 113–120. MR 0147701
S. A. Musa, Synchronized Oscillations in Driven Nonlinear Systems, Ph. D. Dissertation, Harvard University, Cambridge, Mass. (1965)
- Robert A. Gambill and Jack K. Hale, Subharmonic and ultraharmonic solutions for weakly non-linear systems, J. Rational Mech. Anal. 5 (1956), 353–394. MR 77741, DOI https://doi.org/10.1512/iumj.1956.5.55014
S. Lundquist, Subharmonic Oscillations in a Nonlinear System with Positive Damping, Quart. Appl. Math. 13 (1955) 305–310
M. L. Cartwright, Forced Oscillations in Nonlinear Systems, Contributions to the theory of Nonlinear Oscillations, 1, Princeton University Press, Princeton (1950) 149–241
L. Hansson and K. Goransson, An Experimental Investigation of Subharmonic Oscillations in a Nonlinear System, Trans. Roy. Inst. Technology, Stockholm (1956)
H. Poincaré, Les Méthodes nouvelles de la Mécanique Céleste, 1, Gauthier-Villars, Paris (1892) reprint, Dover Publications, Inc., New York (1957)
B. Van der Pol, Forced Oscillations in a Circuit with Nonlinear Resistance (Reception with Reactive Triode), Phil. Mag. and J. Sei., 3, (1927) 65–80; reprint, Selected Papers on Mathematical Trends in Control Theory, Dover Publications, Inc., New York, (1964) 124–140
N. Krylov and N. Bogoliubov, Introduction to Nonlinear Mechanics, Ann. Math. Studies (1947) No. 11, Princeton Univ. Press, Princeton
N. Bogoliubov and Y. Mitropolski, Asymptotic Methods in the Theory of Nonlinear Oscillations (1955) translated by Gordon and Breach, Science Publishers, New York, (1961)
J. Cole and J. Kevorkian, Uniformly Valid Asymptotic Approximations for Certain Nonlinear Differential Equations, International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics, Colorado Springs, Academic Press (1963) 113–120
S. A. Musa, Synchronized Oscillations in Driven Nonlinear Systems, Ph. D. Dissertation, Harvard University, Cambridge, Mass. (1965)
R. Gambill and J. Hale, Subharmonic and Ultraharmonic Solutions for Weakly Nonlinear Systems, J. Rati. Mech. Anal. 5 (1956) 353–394.
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Article copyright:
© Copyright 1966
American Mathematical Society
