Routh reducibility and controllability of unstable mechanical systems

Abstract Routh reduction presents the minimum number of differential equations that uniquely describe state nonlinear mechanical systems where variables can be separated into essential ones and cyclic ones. This work extends reducibility for a relevant set controlled systems. A chain theorems is presented identifying conditions when reduced order rank applied determining Kalman controllability reducible actuation takes place along coordinates only, while some their derivatives are observed. Four examples represent advantages using to check and/or exclude linear in such