The structure of 2-bodies mechanical systems

Under-actuated 2-bodies mechanical systems with 1 actuator are considered. This family of systems includes the double pendulum, the inverted pendulum on a cart, the acrobot, the pendubot... and other systems with two degrees of freedom but only one actuated joint. The maximal linearization problem is investigated and it is shown that these systems may be classified into two subfamilies depending whether or not they have a actuated shape variable or not. In one case, it is possible to solve the maximal linearization problem with internal stability