By D. Quinn, R. Rand, J. Bridge (auth.), Anil K. Bajaj, Steven W. Shaw (eds.)
This is the second one and ultimate factor of the gathering of papers that have been contributed by means of acquaintances and co-workers of (Late) Professor P. R. "Pat" Sethna of the collage of Minnesota to commemorate his seventieth birthday on may perhaps 26, 1993. the 1st set of contributions was once released in Nonlinear Dynamics because the final factor (no. 6) of Vol. four in 1993. As conditions may have it, Professor Sethna used to be clinically determined with melanoma within the fall of 1992 and, after a longer conflict with the sickness, he passed on to the great beyond on November four, 1993, quite a few days sooner than the 1st set of contributed papers seemed in print. it truly is pleasing to record that the organizers of those vi Foreword commemorative matters in Nonlinear Dynamics have been in a position to current to Professor Sethna, at the get together of his seventieth birthday, entire info of the deliberate commemorative concerns. 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 facets of this box. He used to be additionally famous for his awesome management and administrative talents, amply established via his place because the Head of the dept of Aerospace Engineering and Mechanics on the college of Minnesota for twenty-six years (1966-1992).
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Additional resources for Advances in Nonlinear Dynamics: Methods and Applications
The idea was introduced by Poincare  and later developed by Birkoff , Bernoussou  and Arnold . In this approach the continuous-time periodic system is reformulated as discrete-time events by defining a point mapping called the Poincare map. Thus the original non-autonomous differential system is replaced by a set of difference equations which do not explicitly depend on time. However, in order to obtain the corresponding difference equations, one must construct an exact or an approximate solution of a system of nonlinear differential equations.
Separatrix crossing: Time-invariant potentials with dissipation', SIAM Journal of Applied Mathematics 50, 1990, 1716--1744. 5. D. Thesis, Cornell University, 1992. 6. Bridge, J. , 'Chaos and symbol sequences in systems with a periodically-disappearing figureeight separatrix', in Bifurcation Phenomena and Chaos in Thermal Convection, Bau, H. , and Korpela, S. A. ), American Society of Mechanical Engineering, HTD, Vol. 124,1992, pp. 47-55. 7. Cary, J. R. and Skodje, R. , 'Phase change between separatrix crossings', Physica D 36, 1989,287-316.
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  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.)