On the periodic solutions of the forced oscillator equation
Author:
R. M. Rosenberg
Journal:
Quart. Appl. Math. 15 (1958), 341-354
MSC:
Primary 34.0X
DOI:
https://doi.org/10.1090/qam/92051
MathSciNet review:
92051
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M. L. Cartwright and J. E. Littlewood. Non-linear differential equations of the second order, J. London Math. Soc. 20, 180 (1945)
E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill Book Co., Inc., New York, Toronto, London, 1955
K. O. Friedrichs and J. J. Stoker, Forced vibrations of systems with non-linear restoring force, Quart. Appl. Math. 1, 97 (1943)
C. Hayashi, Forced oscillations in non-linear systems, Nippon Printing and Publishing Co., Ltd., Osaka, 1953
H. Helmholtz, Sensations of tone, English translation Longmans, Green and Co., London, 1895
F. John, On simple harmonic vibrations of a system with non-linear characteristics, Studies in non-linear vibration theory, New York University, New York, 1946, p. 104
F. John, On harmonic vibrations out of phase with the exciting force, Communs. in Appl. Math. 1, 341 (1948)
Th. von Karman, The engineer grapples with non-linear problems, Bull. Am. Math. Soc. 46, 615 (1940)
S. Lefschetz, Existence of periodic solutions for certain differential equations, Proc. Natl. Acad. Sci. 45, 29 (1943)
M. E. Levenson, Harmonic and subharmonic response for the Duffing equation, J. Appl. Phys. 21, 283 (1950)
N. Levinson, Transformation theory of nonlinear differential equations of the second order, Ann. Math. 45, 723 (1944)
C. A. Ludeke, Resonance, J. Appl. Phys. 13, 418 (1942)
N. W. McLachlan, Ordinary non-linear differential equations, Oxford at the Clarendon Press, 1950
F. Melde, Über die Erregung stehender Wellen eines fadenförmigen Körpers, Poggendorff’s Ann. der Physik 109, 193 (1860)
N. Minorski, Introduction to non-linear mechanics, J. W. Edwards, Ann Arbor, 1947
C. Obi, Subharmonic solutions of non-linear differential equations of the second order, J. London Math. Soc. 25, 217 (1950)
Lord Rayleigh, On maintained vibrations, Phil. Mag., 5th Ser. 15, 229 (1883)
G. E. H. Reuter, Subharmonics in non-linear systems with unsymmetrical restoring force, Quart. J. Mech. and Appl. Math. 2, 198 (1949)
R. M. Rosenberg, On the origin of subharmonic vibration of odd orders, Proc., 2nd Midwest Conf. on Solid Mechanics, Purdue University, 1955
J. J. Stoker, Non-linear vibrations, Interscience Publishers, Inc., New York, 1950
E. Trefftz, Zu den Grundlagen der Schwingungstheorie, Math. Ann. 95, 307 (1926)
B. van der Pol and M. J. O. Strutt, On the stability of the solutions of Mathieu’s equation, Phil. Mag. 7th Ser., 5, 18 (1928)
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Article copyright:
© Copyright 1958
American Mathematical Society