Modeling and Analysis of a Multidimensional Planar Monoreactive Oscillator

Abstract

The work belongs to the field of mechanical engineering, namely: to oscillating mechanical systems. The relevance of the study is determined by the fact that fluctuations of inertial masses are found everywhere. In the field of construction and use of aviation and rocket technology, this topic is of particular importance. Like a three-dimensional plane coordinate system in the coordinate plane Z, a multidimensional system with n axes shifted relative to each other by angles can be considered. There is an arbitrary vector emanating from the origin. It is proved that the points which are the coordinates of the end of the vector in the coordinate system are the vertices of a regular polygon. The shape and dimensions of the polygon are not related to the coordinates of the vector i.e. are unchanged. The center of a regular polygon in all cases coincides with the middle of the vector. In the considered (idealized) case, the polygon, at the vertices of which there are oscillating weights of masses m, lies in the Z plane multi-piston mechanism. In the considered multidimensional plane monoreactive oscillator, free harmonic linear oscillations of loads can occur. In this case, only kinetic energy is involved in the energy exchange. There is no need for elastic elements. The oscillator does not have a fixed natural oscillation frequency. The frequency depends on the initial speeds and positions of the weights. A regular polygon makes a double rotation - around the point 0 and around the point r. At the same time, the loads carry out linear harmonic oscillations with amplitude R. The use of a crank-slider or crank-and-rod mechanism will allow organizing the parallel movement of goods.