By D. Quinn, R. Rand, J. Bridge (auth.), Anil K. Bajaj, Steven W. Shaw (eds.)

ISBN-10: 9401041644

ISBN-13: 9789401041645

ISBN-10: 9401103674

ISBN-13: 9789401103671

This is the second one and ultimate factor of the gathering of papers that have been contributed via acquaintances and associates of (Late) Professor P. R. "Pat" Sethna of the college of Minnesota to commemorate his seventieth birthday on could 26, 1993. the 1st set of contributions used to be released in Nonlinear Dynamics because the final factor (no. 6) of Vol. four in 1993. As conditions might have it, Professor Sethna was once clinically determined with melanoma within the fall of 1992 and, after a longer conflict with the affliction, he kicked the bucket on November four, 1993, quite a few days sooner than the 1st set of contributed papers seemed in print. it truly is pleasant to document that the organizers of those vi Foreword commemorative concerns in Nonlinear Dynamics have been in a position to current to Professor Sethna, at the party of his seventieth birthday, whole info of the deliberate commemorative matters. This moment set of contributions is devoted, in memoriam, to Professor P. R. Sethna. As a lot of you're good acutely aware, Professor Sethna was once an energetic researcher within the box of nonlinear vibrations and dynamics for almost 40 years, making many primary and important contributions to either the theoretical and utilized elements of this box. He was once additionally famous for his striking management and administrative talents, amply established via his place because the Head of the dept of Aerospace Engineering and Mechanics on the collage of Minnesota for twenty-six years (1966-1992).

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Since the mean value of the periodic coefficient of the reduced center manifold equation for this case is positive (shown in Figure 6), the fixed point is unstable and hence the corresponding 2T periodic orbits in the original coordinates are unstable. The Poincare points for each of the coordinate set (2 points per set) are plotted in Figure 7. Note that the arrows in Figure 7 indicate the direction of drift of the Poincare points moving away from the periodic orbits confirming their instability.

3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. Arnold, V. , Geometrical Methods in the Theory of Ordinary Differential Equations, Springer-Verlag, New York, 1988. , From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis, Elsevier, New York, 1988. , Bifurcation and Chaos in Simple Dynamical Systems, World Scientific, Singapore, 1989. Sri Namachchivaya, N. and Ariaratnam, S. , 'Periodically perturbed Hopf bifurcation', SIAM Journal of Applied Mathematics 47(1), 1987, 15-39.

Pandiyan and S. C. Sinha where vector W; contains nonlinear monomials which are functions of Yc only. 3. Applications EXAMPLE 1. As an example of a single degree of freedom system, the bifurcations of a parametrically forced simple pendulum is considered. It is assumed that the support of the pendulum is subjected to a sinusoidal motion with frequency w. The general equation of motion for the pendulum is given by [5] x + 8± + (ci - (3 sin WT) sin x =0 (28) where 8, a 2 , (3 and W are the parameters of the system.

### Advances in Nonlinear Dynamics: Methods and Applications by D. Quinn, R. Rand, J. Bridge (auth.), Anil K. Bajaj, Steven W. Shaw (eds.)

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