A perturbation method for truly nonlinear oscillator differential equations

Proceedings of Dynamic Systems and Applications

Volumn , Issue , 2003, Pages 302-311

  Mickens, Ronald E ^a,b   Rucker, Sandra A ^a  

^a Department of Physics ^*

^b CLARK ATLANTA UNIVERSITY   (United States)

Author keywords

Linearization; Nonlinear oscillations; Perturbation methods

Indexed keywords

EID: 29244435770     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (9)

1. N. Kryloff and N. Bogoliuboff, Introduction to Nonlinear Mechanics (Princeton University Press; Princeton, NJ; 1943).
2. A. H. Nayfeh, Perturbation Methods (Wiley, New York, 1973).
3. R. E. Mickens, Oscillations in Planar Dynamic Systems (World Scientific, Singapore, 1996).
4. R. E. Mickens, "Fourier representations for periodic solutions of odd-parity systems," Journal of Sound and Vibration 258, 398-401 (2002).
5. R. E. Mickens, "A combined equivalent linearization and averaging perturbation method for nonlinear oscillator equations," Journal of Sound and Vibration 264, 1195-1200 (2003).
6. R. E. Mickens, "A new perturbation method for oscillatory systems," Proceedings of DETC'03 and 2003 19th Biennial ASME Conference on Mechanical Vibration and Noise (September 2-6, 2003; Chicago, IL; American Society of Mechanical Engineers); Paper #DETC2003/VIB-48567.
7. R. Bellman, Perturbation Techniques in Mathematics, Physics and Engineering (Holt, Rinehart and Winston; New York, 1964).
8. D. Zwillinger, Handbook of Differential Equations (Academic Press, Boston, 1989); see Section 110.
9. R. E. Mickens, "Analysis of the simple harmonic oscillator with fractional damping," Journal of Sound and Vibration (in print).