Free Sinusoidal Oscillations Based on the Mutual Exchange of Kinetic Energy between Three Loads

Abstract

It is noted that free sinusoidal oscillations in a classical mechanical oscillator are due to the mutual transformation of kinetic energy into potential energy. Known is an oscillator, in which free sinusoidal oscillations are accompanied by the transformation of the kinetic energy of an inert element into the same kinetic energy of another inert element. Elements with a different nature of reactivity are absent in such an oscillator. Such an oscillator is essentially monoreactive. The disadvantage of this oscillator is its imbalance due to the asymmetry of the structure, which may require additional vibration protection measures. This drawback can be avoided by using a symmetrical scheme with three loads. For the purposes of this work, it is convenient to use a flat three-coordinate system similar to the three-phase coordinate system used in electrical engineering. For an arbitrary vector R lying in the three-coordinate plane with the origin coinciding with the origin of coordinates, Theorem 1 is true. Coordinates \({{x}_{1}}\), \({{x}_{2}}\), \({{x}_{3}}\) of vector R form a regular triangle, the size of which does not change with an arbitrary rotation of vector R. Theorem 2. The middle of vector R is aligned with the center of the triangle \({{x}_{1}}{{x}_{2}}{{x}_{3}}\). Half of vector R plays the role of a crank, which in real devices is needed to develop angular velocity \(\omega \) and to impart the moment of force to compensate for dissipative losses. In a monoreactive harmonic oscillator with three loads, free sinusoidal oscillations of any given frequency can occur, which is determined solely by the initial conditions.