Kleine Schwingungen dynamischer Systeme

Summary

The Hamiltonian differential equations for small displacements of a dynamical system with a finite number of degrees of freedom are solved by use of the methods of linear algebra. In this way the stability of the equilibrium configuration or uniform motion in the case of positive definite total energy is demonstrated. Especially gyroscopic terms may appear in the hamiltonian, making impossible the usual proof of stability by means of transformation to normal coordinates. This method is then applied to the Weierstrass procedure of solution.

For use in the above integration, the spectral representation of a matrix with linear elementary divisors is given through the adjoint of its characteristic matrix.