The paper presents a spatial model of the satellite antenna with an arbitrary number of flexible arms. Such a system is an example of an open kinematic chain with a tree-like structure. The modification of the rigid finite element method is used to discretise flexible links. The equations of motion are derived from the Lagrange equations and the motion of the system is described using joint coordinates and homogenous transformations. Numerical simulations have been carried out to analyse how the method of extending the arms influences the dynamics of the system.

The paper presents its contribution to tracking control design of mechanical systems in underactuated mode conditions, i.e. when the number of actuators is less than the number of possible control inputs. Fully actuated mechanical systems are quite well-researched and controller designs are well-developed for them as well. However, due to costs, weight, design, and performance regimes or due to an actuator failure, the underactuated control mode is required in applications. With the aid of the computational procedure for constrained dynamics (CoPCoD), the constrained dynamics, i.e. the reference motion dynamics, and tracking control in an underactuated mode are designed for an example of a three-link planar manipulator model with rigid and flexible links. A dynamic optimization problem is formulated in the paper to obtain optimal time courses of manipulator joint coordinates in underactuated mode conditions in order to apply them to a manipulator driving links controller.