Controllability and decomposition in mechanical systems (Q2761253)

The authors investigate the motion of controlled system whose behavior is described by equations with canonical Hamiltonian variables \(p\) and \(q\): \(\dot q^i = \frac{\partial H}{\partial p_i}\), \(\dot p_i = -\frac{\partial H}{\partial q^i}+Q_i\), \(i=1,\dots,n\), \(H = \frac 12 a^{ij}(q)p_ip_j+\Pi(q)\), \(Q_i = Q_i(q,p,u)\). Here \( H = H(q,p) \) is the Hamiltonian function, \(Q_i\) are generalized nonpotential forces, \(u\in U\) is the \(m\)-dimensional control vector. For this system which is linear with respect to control, the problem on controllability is reduced to the analysis of solvability of a system of partial differential equations of a special form. As example, the authors consider the problem on controllability of angular velocity and orientation of a rigid body by means of a single jet engine.