Some remarks on the separability of damped systems and non-self-adjoint eigenvalue problems

  • Eberhard Brommundt
Part of the International Centre for Mechanical Sciences book series (CISM, volume 1)


We introduce
$$\left. {\begin{array}{*{20}{c}} {{u_1}\left( {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{X} ,t} \right) = u\left( {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{X} ,t} \right)} \\ {{u_2}\left( {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{X} ,t} \right) = \dot u\left( {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{X} ,t} \right)} \end{array}} \right\}\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{u} = \left( {\begin{array}{*{20}{c}} {{u_1}} \\ {{u_2}} \end{array}} \right)$$
into the equation (*) of section 10.1 and obtain
$$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{L} \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{u} = \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{\mu } \dot u,$$
$$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{L} = \left( {\begin{array}{*{20}{c}} 0&1 \\ { - L}&{ - b} \end{array}} \right),\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{\mu } = \left( {\begin{array}{*{20}{c}} 1&0 \\ 0&\mu \end{array}} \right).$$


Boundary Condition Eigenvalue Problem Complex Conjugate Dimensional Case Order System 
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Copyright information

© Springer-Verlag Wien 1969

Authors and Affiliations

  • Eberhard Brommundt
    • 1
  1. 1.Technical University of DarmstadtGermany

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