Some Remarks on the Zero Frequency Modes

Abstract

In the theory of small vibrations the motion of a system can be characterised in terms of either geometrically compatible displacements or dynamically admis-sable impulses ^(1,2,3). However, the number of generalised displacements required to describe the motion of a system need not be the same as the number of generalised impulses required for the same purpose. The reason for this difference is that in either or both formulations certain zero frequency modes may be present. If the co-ordinates which describe such modes are eliminated then the number of displacement and impulse co-ordinates required to describe the oscillatory modes will be equal and one can then transform one formulation to the other by means of Legendre's transformation⁽⁴⁾.