Planar motion of three interacting bodies in a medium with quadratic‐law friction

Abstract A control of planar motion of a system of three interacting bodies (point masses) in a medium with quadratic‐law resistance is considered. The forces of interaction between the bodies are regarded as the control variables. The aim of the control is to drive the system from a given initial state of rest to a given terminal state of rest. It is assumed that at the initial time instant the bodies of the system do not lie on one straight line. No constraints are imposed on the control forces. For the case where the ratios of the squared mass to the resistance coefficient are different for at least one pair of bodies, an algorithm that drives the system exactly into the desired terminal state is constructed. For the case where the ratio of the squared mass to the resistance coefficient is the same for all bodies, an algorithm that drives the system into an arbitrarily small neighborhood of the terminal state is proposed.