Advertisement

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)

Abstract

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

Keywords

Boundary Condition Eigenvalue Problem Complex Conjugate Dimensional Case Order System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Wien 1969

Authors and Affiliations

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

Personalised recommendations