Controllability and decomposition in mechanical systems

• Published in: Journal of applied mathematics and mechanics Vol. 64; no. 1; pp. 25 - 34
• Main Authors: Vujičič, V.A., Kovalev, A.M.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 2000
• DOI: 10.1016/S0021-8928(00)00022-8
• ISSN: 0021-8928

The method of oriented manifolds [1] is used to obtain criteria for the controllability of non-linear mechanical systems of general form. For systems that are linear in control, the question of controllability is reduced to an analysis of the solvability of a system of partial differential equations of special form typical of the invariant relations method and the Lyapunov function method. When the number of controls is equal to the number degrees of freedom, using the example of specific systems with two degrees of freedom the case of confluence of the matrix of coefficients for the control vector in the equations of motion is considered. In the context of a discussion of the property [2] of complete controllability of classes of mechanical systems, problem formulations are proposed in which weakening of the property of control robustness (only variation of the constant parameters is allowed) enables new classes of controllable systems to be obtained. The important case, for mechanics, of the decomposability of the equations of motion into kinematic and dynamic equations is investigated and a theorem establishing the relation between the controllability of the linear system and its dynamical subsystem is proved. Examples are given. The problem of controlling the angular velocity and orientation of a rigid body by means of a single jet engine is considered, for the solution of which the method of oriented manifolds and the decomposition method are used.