On the existence of normal mode vibrations in nonlinear systems
Authors:
C. H. Pak and R. M. Rosenberg
Journal:
Quart. Appl. Math. 26 (1968), 403-416
MSC:
Primary 34.45; Secondary 70.00
DOI:
https://doi.org/10.1090/qam/235209
MathSciNet review:
235209
Full-text PDF Free Access
References |
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Additional Information
R. M. Rosenberg, On nonlinear vibrations of systems with many degrees of freedom, Adv. Appl. Mech., vol. 9. Academic Press, New York, 1966, pp. 156–243
- C. H. Cooke and R. A. Struble, On the existence of periodic solutions and normal mode vibrations of nonlinear systems, Quart. Appl. Math. 24 (1966), 177–193. MR 201732, DOI https://doi.org/10.1090/S0033-569X-1966-0201732-4
- Ta-lun Yang and R. M. Rosenberg, On the vibrations of a particle in the plane, Internat. J. Non-Linear Mech. 2 (1967), 1–25 (English, with French, German and Russian summaries). MR 230499, DOI https://doi.org/10.1016/0020-7462%2867%2990015-7
- Gilbert A. Bliss, Lectures on the Calculus of Variations, University of Chicago Press, Chicago, Ill., 1946. MR 0017881
- R. M. Rosenberg, On normal mode vibrations, Proc. Cambridge Philos. Soc. 60 (1964), 595–611. MR 163464
J. K. Kuo, On nonsimilar normal mode vibrations of nonlinear systems having many degrees of freedom, Ph.D. thesis, Univ. of Calif., Berkeley, 1964
- The correspondence between Sir George Gabriel Stokes and Sir William Thomson, Baron Kelvin of Largs, Cambridge University Press, Cambridge, 1990. Vol. I, 1846–1869. Vol. II, 1870–1901; Edited with an introduction by David B. Wilson. MR 1254662
- Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171038
J. Mawhin, Oscillations en modes normaux des systémes dynamiques nonlinéaires á plusieurs degrés de liberté, Bull. Soc. Royale Sciences Liége 9, 540–557 (1964)
- Herbert Busemann, The geometry of geodesics, Academic Press Inc., New York, N. Y., 1955. MR 0075623
R. M. Rosenberg, On nonlinear vibrations of systems with many degrees of freedom, Adv. Appl. Mech., vol. 9. Academic Press, New York, 1966, pp. 156–243
C. H. Cooke and R. A. Struble, The existence of periodic solutions and normal mode vibrations in nonlinear systems, Quart. Appl. Math. 24, 177–193 (1966)
Ta-Lun Yang, and R. M. Rosenberg, On the vibrations of a particle in the plane, Internat. J. Nonlinear Mech., 2, 1–25 (1967)
G. A. Bliss, Lectures on the calculus of variations, 7th Impr., Univ. of Chicago Press, Chicago, Ill., 1963
R. M. Rosenberg, On normal mode vibrations, Proc. Camb. Philos. Soc. 60, 595–611 (1964)
J. K. Kuo, On nonsimilar normal mode vibrations of nonlinear systems having many degrees of freedom, Ph.D. thesis, Univ. of Calif., Berkeley, 1964
Sir William Thomson and P. G. Tait, Treatise on natural philosophy, vol. 1, p’t. 1, new ed., Cambridge Univ. Press, 1879
P. Hartman, Ordinary differential equations, Wiley, New York, 1964
J. Mawhin, Oscillations en modes normaux des systémes dynamiques nonlinéaires á plusieurs degrés de liberté, Bull. Soc. Royale Sciences Liége 9, 540–557 (1964)
H. Busemann, The geometry of geodesics, Academic Press, New York, 1955, p. 25
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Article copyright:
© Copyright 1968
American Mathematical Society
