LAUSR

This contribution deals with Mikota’s oscillator, a linear vibration chain with arbitrary n degrees of freedom. Of special interest are both the left- and right-eigenvectors of the undamped system. Investigating the first two right-eigenvectors leads to a conjecture concerning the general structure of the remaining $$n-2$$n-2 right-eigenvectors. This general structure is proven, and an analytical expression is found which provides an efficient possibility to calculate all left- and right-eigenvectors in a successive manner. Additionally, it is revealed that the mode shapes of this special vibration chain are (partly) orthogonal to each other with respect to the standard scalar product.