Выделение гироскопических инерционных сил из центробежных и кориолисовых инерционных сил

Abstract

The purpose of the study is to identify in the equations of dynamics of mechanical systems generalized gyroscopic inertial forces, consisting of a part of centrifugal and Coriolis inertial forces, indica¬ting the bodies whose movements form these forces. The methods of research refer to mechanics of body systems, systems analysis and robotics. The results of the study allow us to write out general formulas for calculating generalized centrifugal, Coriolis and gyroscopic inertial forces through partial derivatives on generalized coordinates from elements of the matrix of inertial coefficients in the expression of kinetic energy of arbitrary mechanical system. In the process of analyzing these formulas for systems of bodies with an open tree structure, such as orbital stations with manipulators on board or walking vehicles in the single-supported walking phase, the bodies whose movements affect the occurrence of the listed inertial forces are highlighted. For robot manipulation systems we present examples of the equations of dynamics, in which all possible inertial forces are highlighted and the bodies that form them are indicated. Conclusion. Singling out the gyroscopic forces allows you to simplify the formula for calculating the power consumption of drives, because the power of these forces is zero. This fact, in particular, allows to simplify the expression of the minimizing functional in the problem of energy optimal control. The isolated centrifugal forces can be used to realize program motions of some bodies of manipulators with polar, cylindrical, spherical and angular coordinate systems without expenditure of power consumed by their drives.