Volume 6, 2001
|Page(s)||333 - 360|
|Published online||15 August 2002|
Controllability of a slowly rotating Timoshenko beam
Technische Universität Darmstadt, Fachbereich Mathematik,
Arbeitsgruppe 10, Schlossgartenstr. 7, 64289 Darmstadt, Germany; email@example.com.
Received: January 2001
Consider a Timoshenko beam that is clamped to an axis perpendicular to the axis of the beam. We study the problem to move the beam from a given initial state to a position of rest, where the movement is controlled by the angular acceleration of the axis to which the beam is clamped. We show that this problem of controllability is solvable if the time of rotation is long enough and a certain parameter that describes the material of the beam is a rational number that has an even numerator and an odd denominator or vice versa.
Mathematics Subject Classification: 93C20 / 93B05 / 93B60
Key words: Rotating Timoshenko beam / exact controllability / eigenvalues / moment problem.
© EDP Sciences, SMAI, 2001
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