Hybrid state equations of motion for flexible bodies in terms of quasi-coordinates

This paper is concerned with the general motion of a flexible body in space. Using the extended Hamilton’s principle for distributed systems, standard Lagrange’s equations for hybrid systems are first derived. Then, the equations for the rigid-body motions are transformed into a symbolic vector form of Lagrange’s equations in terms of general quasi-coordinates. The hybrid Lagrange’s equations of motion in terms of general quasi-coordinates are subsequently expressed in terms of quasi-coordinates representing rigid-body motions. Finally, the second-order Lagrange’s equations for hybrid systems are transformed into a set of state equations suitable for control. An illustrative example is presented.