Естественные науки УДК 519.3: 65.011 A.I. BOKHONSKY, N.I. VARMINSKA OPTIMAL TRANSLATIONAL MOTION OF THE ELASTIC OBJECTS WITH RESISTANCE Using control of translational motion of an elastic object (moving in the minimal acceptable time) with linear–viscous resistance due to the selection of the type and parameters of control the absolute quiescence of the object at the end of movement is provided. <...> Solution of the inverse task of dynamics is illustrated by a numerical example. <...> Keywords: elastic object, translational optimal movement, linear–viscous resistance, inverse task of dynamics. 1. <...> INTRODUCTION There are studies on the control of oscillations of linear and nonlinear mechanical systems in absolute motion [1, 2]. <...> Control tasks of elastically deformable systems fluctuations are relevant in using manipulators of finite stiffness (manipulators of minimal mass), transportation and assembly of elastically deformable objects under terrestrial conditions and in outer space. <...> There is a need to use such special movement controls, in which fluctuations of transported objects are significantly reduced or completely eliminated, i.e. in an acceptable minimum possible time of translational motion the relative or absolute quiescence at the end of the movement is achieved [5, 6]. <...> For practical implementation of the translational movement controls of elastic objects we must consider not only the actual dynamic characteristics of the transported object (e.g., internal friction and linear–viscous friction), but also the properties of engines, which implement this movement. <...> The purpose of the research is the accounting of the linear–viscous resistance in relative motion with optimal translational motion of an elastic object. <...> Here, the optimal (purposeful) movement means the existence of a functional–criterion that receives a stationary value in the actual movement [3, 4]. 2. <...> TRANSLATIONAL MOTION OF AN ELASTIC OBJECT WITH ACCELERATION U t a sin( pt ) e ( ) The task of optimal translational motion of an elastic object with one degree of freedom from the initial state of absolute quiescence to the final state of absolute quiescence (figure 1) in such reasonable minimal time that is consistent with the object natural period of fluctuations is solved. <...> Figure 1 – Scheme of the movement of an object with one degree of freedom that are transcendental equations. <...> It is assumed that the acceleration of the base is <...>