Boundary control by displacements at one endpoint of an inhomogeneous rod for fixed other endpoint in the case of coinciding times of passage of the wave through either of the inhomogeneity parts (Q608950)
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scientific article; zbMATH DE number 5820365
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Boundary control by displacements at one endpoint of an inhomogeneous rod for fixed other endpoint in the case of coinciding times of passage of the wave through either of the inhomogeneity parts |
scientific article; zbMATH DE number 5820365 |
Statements
Boundary control by displacements at one endpoint of an inhomogeneous rod for fixed other endpoint in the case of coinciding times of passage of the wave through either of the inhomogeneity parts (English)
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29 November 2010
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The author considers the process of longitudinal vibrations of an inhomogeneous rod with end points \(x= 0\) and \(x= l\), which are described in the general case by the wave equation \(u_{tt}(x,t)- a^2u_{xx}(x,t)= 0\) and take place on the time interval \(0\leq t\leq T\). He find a closed analytic form of the boundary control by displacements bring the stick from the original rest state into a given terminal state specified by given terminal displacement and velocity.
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analytic form of the boundary control
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0.8995610475540161
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0.8990734815597534
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0.8694102168083191
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