Tracking a target in a three-dimensional space by a nonholonomic constraint

Document Type : Original Article


Department of Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.


The constrained mechanical systems in velocity component are known as nonholonomic constraints which are significantly important in engineering and robotics. A number of applicable theoretical studies have been performed on such systems among which the geometrical approach for mechanical systems has received extensive consideration. The movement direction, dynamical stability, and system control are among the topics geometrically related to mechanical (nonholonomic) systems. In this paper, a review of the geometrical point of view of mechanical systems constrained by
nonholonomic constraints is represented. Moreover, we aim to find the motion equation of a ballistic missile moving towards a given target in a three-dimensional space. Initially, we calculate the motion equation of a ballistic missile which is launched towards an object moving along the z-axis with a constant velocity c. Finally, a general condition is assumed and the motion equation of the missile chasing a moving object in a R3 space along a certain curve defined by the parametrical equations x =ξ(t), y = η(t) and z = ζ(t) is calculated.