A phase space investigation of bi-stable systems by means of vectors

An investigation is made to determine the conditions under which a third order system with a bi-stable element will maintain a high frequency oscillation rather than exhibit simple relay switching. A criterion is developed in general terms. The study is made in phase space and vectors are used to determine the direction in which the trajectory intersects the switching plane. The appendix contains an example wherein the criterion is applied to a specific system and the results compared with computer data.