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 way of pals and co-workers of (Late) Professor P. R. "Pat" Sethna of the collage of Minnesota to commemorate his seventieth birthday on could 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 situations might have it, Professor Sethna used to be clinically determined with melanoma within the fall of 1992 and, after a longer conflict with the ailment, he passed on to the great beyond on November four, 1993, quite a few days earlier than the 1st set of contributed papers seemed in print. it really is pleasant to record that the organizers of those vi Foreword commemorative matters in Nonlinear Dynamics have been capable of current to Professor Sethna, at the social gathering of his seventieth birthday, entire 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 basic and critical contributions to either the theoretical and utilized elements of this box. He was once additionally well-known for his amazing management and administrative skills, amply confirmed 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 info for Advances in Nonlinear Dynamics: Methods and Applications
Sethna, P. R. and Schapiro, S. , 'Nonlinear behavior of flutter unstable dynamical systems with gyroscopic and circulatory forces', Journal ofApplied Mechanics 44, 1977,755-762. , Nonlinear Analysis, Vols. 1 and 2, Academic Press, New York, 1970. Coddington, E. A. , Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955. Yakubovich, V. A. and Starzhinski, V. , Linear Differential Equations with Periodic Coefficients, Parts I and II, John Wiley & Sons, New York, 1975. Malkin, I. , 'Some basic theorems of the theory of stability of motion in critical cases', Stability and Dynamics Systems, Translations, American Mathematical Society, Series 1, Vol.
1. CONTINUUM MODEL FOR SMALL SAG An elastic cable suspended between two level supports a distance H apart is shown in Figure 1. The cable, in its equilibrium configuration (dotted curve), has a length of L and a sag at the mid-span, due to gravity, of D. The (non-dimensional) displacement of the cable (solid curve) about equilibrium is u(s, t) = Uj (s, t)~ + U2(S, t)G + U3(S, t)~ where s represents an arc length coordinate measured from the left support (s = 0) along the centerline and t represents time.
And Sinha, S. , 'Optimal control of mechanical systems subjected to periodic loading via Chebyshev polynomials', Optimal Control Applications and Methods 14, 1993,75-90. Sethna, P. R. and Schapiro, S. , 'Nonlinear behavior of flutter unstable dynamical systems with gyroscopic and circulatory forces', Journal ofApplied Mechanics 44, 1977,755-762. , Nonlinear Analysis, Vols. 1 and 2, Academic Press, New York, 1970. Coddington, E. A. , Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.