Abstract
In this paper we show that the rotating elastic beam model proposed by Baillieul and Levi has an inertial manifold which is linear. We emphasize that the spectrum of the linear dissipative part of the model equations does not satisfy the gap condition.
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Supported in part by grants from the National Science Foundation and Air Force Office of Scientific Research and by a Seed Grant from Ohio State University.
Supported in part by AFOSR and NSF Grant DMS 8915672, and by the University of California-Irvine Graduate Council Funds.
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References
J. Baillieul and M. Levi, Rotational Elastic Dynamics ,Physica 27D, 1987,43–62.
A. M. Bloch, Analysis of a Rotating Flexible System ,Acta Applicandae Mathematicae15 No. 3,1989,211–234.
A. M. Bloch and R.R. Ryan, Approximate Models of Rotating Beams ,Proc. ofthe 27th IEEE Conference on Decision and Control, IEEE, 1988,1230–1235.
A. M. Bloch and R. R. Ryan, Stability and Stiffening of Driven and Free Planar Rotating beams ,Com. Math AMS 97,1989,11–25.
P. Constantin, C. Foias, B. Nicolaenko and R. Temam, Integral Manifoldsand Inertial Manifold for Dissipative Partial Differential Equations, Springer-Verlag,1989.
C. Foias, G. R. Sell and R. Temam, Inertial Manifolds for Evolutionary Equations,J. Differential Equations, 73,1988, 309–353.
C. Foias, G. R. Sell and E. S. Titi, Exponential Tracking and Approximation of Inertial Manifolds for Dissipative Equations ,J. Dynamics and DifferentialEquations 1,1989,199–224.
D. B. Henry, Geometric Theory of Semilinear Parabolic Equations, LectureNotes in mathematics No. 840, Springer-Verlag, 1981, New York.
P. S. Krishnaprasad and J. E. Marsden, Hamiltonian Structures and Stability for Rigid Bodies with Flexible Attachments ,Arch, for Rat. Mech. andAnalysis 98 No. 1,1987,73–93.
B. Nicolaenko, Inertial Manifolds for Models of Compressible Gas Dynam icsCont. Math AMS 99,1987,165–179.
J. C. Simo, D. Lewis and J. E. Marsden, Stability of Relative Equilibria Part1: The Reduced Energy-Momentum Method1989, to appear.
R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics,Springer-Verlag, 1988.
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© 1991 Springer Science+Business Media New York
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Bloch, A.M., Titi, E.S. (1991). On The Dynamics of Rotating Elastic Beams. In: New Trends in Systems Theory. Progress in Systems and Control Theory, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0439-8_15
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DOI: https://doi.org/10.1007/978-1-4612-0439-8_15
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6760-7
Online ISBN: 978-1-4612-0439-8
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