Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

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
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  • [1] 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
  • [2] 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) MR 0201732
  • [3] Ta-Lun Yang, and R. M. Rosenberg, On the vibrations of a particle in the plane, Internat. J. Nonlinear Mech., 2, 1-25 (1967) MR 0230499
  • [4] G. A. Bliss, Lectures on the calculus of variations, 7th Impr., Univ. of Chicago Press, Chicago, Ill., 1963 MR 0017881
  • [5] R. M. Rosenberg, On normal mode vibrations, Proc. Camb. Philos. Soc. 60, 595-611 (1964) MR 0163464
  • [6] J. K. Kuo, On nonsimilar normal mode vibrations of nonlinear systems having many degrees of freedom, Ph.D. thesis, Univ. of Calif., Berkeley, 1964
  • [7] Sir William Thomson and P. G. Tait, Treatise on natural philosophy, vol. 1, p't. 1, new ed., Cambridge Univ. Press, 1879 MR 1254662
  • [8] P. Hartman, Ordinary differential equations, Wiley, New York, 1964 MR 0171038
  • [9] J. Mawhin, Oscillations en modes normaux des systémes dynamiques nonlinéaires á plusieurs degrés de liberté, Bull. Soc. Royale Sciences Liége 9, 540-557 (1964)
  • [10] H. Busemann, The geometry of geodesics, Academic Press, New York, 1955, p. 25 MR 0075623

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DOI: https://doi.org/10.1090/qam/235209
Article copyright: © Copyright 1968 American Mathematical Society

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