Eberhard Brommundt

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

We introduce

Lyapunov’s definition of stability

\left. {\begin{array}{*{20}{c}} {{u_1}\left( {\underset{\raise0.3em\hbox{

Kinetic stability of non-autonomous systems

\smash{\scriptscriptstyle\thicksim}

Investigation of bifurcation points

}}{X} ,t} \right) = u\left( {\underset{\raise0.3em\hbox{

Equations of motion for (nonlinear) nonconservative systems

\smash{\scriptscriptstyle\thicksim}

Kinetic stability of autonomous systems

}}{X} ,t} \right)} \\ {{u_2}\left( {\underset{\raise0.3em\hbox{

Separation of variables; boundary value problem; eigenvalue problem

\smash{\scriptscriptstyle\thicksim}

Relations between stability and vibrations of conservative systems (Example: Compressed bar)

}}{X} ,t} \right) = \dot u\left( {\underset{\raise0.3em\hbox{

Nonlinear vibrations of nonautonomous systems

\smash{\scriptscriptstyle\thicksim}