On a lower bound for the instability range of Beck's rod (Q1063459)
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scientific article; zbMATH DE number 3917856
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a lower bound for the instability range of Beck's rod |
scientific article; zbMATH DE number 3917856 |
Statements
On a lower bound for the instability range of Beck's rod (English)
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1984
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A lower bound for the critical values of \(q\) in the boundary eigenvalue problem \(\mu\ddot v(x,t) + \alpha v''''(x,t) + qv''(x,t) = 0\), \(v(0,t) = v'(0,t) = v''(\ell,t) = v''''(\ell,t) = 0\), in which \(\mu\) is the mass per unit length, \(\alpha\) the bending stiffness, and \(q\) a constant factor (magnitude of the control force) in the control law of a slender antenna arm whose lateral vibrational deflections are given by \(v(x,t)\), and which is mounted on a satellite, is derived as to provide a safe datum for the design of an unconditionally stable control for the antenna arm.
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instability range of Beck's rod
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stable without spillover
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Lyapunov-like functional
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lower bound
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critical values
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boundary eigenvalue problem
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slender antenna arm
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lateral vibrational deflections
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mounted on a satellite
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safe datum
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design
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unconditionally stable control
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