ON STABILIZATION OF UNSTABLE ROTATION IN THE RESISTING MEDIUM OF THE LAGRANGE GYROSCOPE USING THE SECOND GYROSCOPE AND ELASTIC HINGES

The possibility of stabilizing an unstable uniform rotation in a resisting medium of a "sleeping" Lagrange gyroscope using a rotating second gyroscope and elastic spherical hinges is considered. The "sleeping" gyroscope rotates around a fixed point with an elastic recovery spherical hinge, and the second gyroscope is located above it. The gyroscopes are also connected by an elastic spherical restorative hinge and their rotation is supported by constant moments directed along their axes of rotation. It is shown that stabilization will be impossible in the absence of elasticity in the common joint and the coincidence of the center of mass of the second gyroscope with its center. With the help of the kinetic moment of the second gyroscope and the elasticity coefficients of the hinges, on the basis of an alternative approach, the stabilization conditions obtained in the form of a system of three inequalities and the conditions found on the elasticity coefficients at which the leading coefficients of these inequalities are positive. It is shown that stabilization will always be possible at a sufficiently large angular velocity of rotation of the second gyroscope under the assumption that the center of mass of the second gyroscope and the mechanical system are below the fixed point. The possibility of stabilizing the unstable uniform rotation of the "sleeping" Lagrange gyroscope using the second gyroscope and elastic spherical joints in the absence of dissipation is also considered. The "sleeping" gyroscope rotates at an angular velocity that does not meet the Mayevsky criterion. It is shown that stabilization will be impossible in the absence of elasticity in the common joint and the coincidence of the center of mass of the second gyroscope with its center. On the basis of the innovation approach, stabilization conditions were obtained in the form of a system of three irregularities using the kinetic moment of the second gyroscope and the elastic coefficients of the hinges. The condition for the angular momentum of the first gyroscope and the elastic coefficients at which the leading coefficients of these inequalities are positive are found. It is shown that if the condition for the angular momentum of the first gyroscope is fulfilled, stabilization will always be possible at a sufficiently large angular velocity of rotation of the second gyroscope, and in this case the center of mass of the second gyroscope can be located above the fixed point.

Determination of meridian position by a two-step ground gyrocompass in eesthetical rotor positioning

Contradiction between accuracy and time of definition of a plane of a geographical meridian has significantly weakened with appearance of automatic gyrocompasses and algorithmic methods of processing of the information from them. These methods allow us to expand the range of possible modes of gyrocompasses, including non-traditional. The article considers an automatic two-stage ground gyro compass operating in the mode of natural stopping of the rotor after its pulse acceleration by non-electrical means (squib , compressed air, etc.). The specified mode is attractive because it allows to identify uncontrolled harmful moment around the axis of suspension in one start and significantly reduce the measurement time. In order to further improve the device, it is proposed to abandon the measurement of the current value of the kinetic moment, and to identify the decay coefficient of the exponential function by observing the azimuthal motion of the sensitive element of the device. Moreover, the paper shows that it is possible not to measure the initial value of the kinetic momentum, replacing the measurement with identification of this parameter by observing the same azimuthal motion of the sensitive element. In this case there is no need to have on the sensitive element any nodes associated with the transmission of power and electrical signals, the sensitive element can be made as a purely mechanical element, carrying on itself a rotating rotor. For all considered variants of measurement (or identification) of parameters the machine simulation was carried out, which confirmed the performance of the proposed methodology.

Mathematical models of the gyrostabilizer in different modes of its operation

The article considers the development of a mathematical model of the stabilization and rotation system in the modes of stabilization, targeting, auto-tracking of the target and electrical arrest. The output signals shall be signals proportional to the components of the angular velocities of the line of sight, the angles of pitch and dash of deviation around the axes of the gyrosystem and the angles of inconsistency of the line of sight relative to the optical axis of the homing head. The system of cardan suspension of the stabilization and rotation system is considered, where the actuators are located on the axes of rotation of the outer and inner frames of the cardan suspension. The homing head is mounted on the inner frame. The inner frame is a gyrostabilized platform. Depending on the mode of operation of the stabilization and rotation system: in the stabilization mode, the coordinate system that is stabilized is assumed to be stationary in inertial space; in the auto-tracking mode of the target, the coordinate system that is stabilized by Oxyz is returned according to the change of direction to the target; in the mode of electrical locking, the axes of the coordinate system which is stabilized by Oxyz coincide with the axes of Oxoyozo connected to the body of the main product. To obtain differential equations, the projections of the total vector of the kinetic moment of the inner and outer frames on the axis of the outer frame are taken and written according to the theorem on the change of the kinetic moment of the considered system relative to the axes of suspensions. The total moments of external forces applied to the outer and inner frames around their axes of rotation, which have the following components: moments of actuators, moments of viscous and dry friction, imbalance and other unaccounted for factors around the axes of the outer and inner frames . The moments of the forces of viscous and dry friction are presented in the classical form, taking into account the signs when changing the direction of movement. The mass of the inner frame with all devices mounted on it, and the mass of the entire movable system (outer and inner frames), as well as the radius vector characterizing the displacement of the center of mass, give a static imbalance of the movable system relative to the suspension axis of the i-th frame are components imbalance. The scientific novelty of the work is to obtain a mathematical model for a particular product, as well as the practical feasibility of their application. The result is a differential equation that fully describes this system of stabilization and rotation, takes into account the parameters of actuators, turbulent moments, as well as random effects and can be used depending on the tasks.

The concept of creating thrust based on angular momentum change

The change in the kinetic moment of a material body is considered regarding to classical and quantum mechanics. The possibility of creating the propulsion system in terms of energy efficiency exceeding the photon engine has been theoretically proved. The proposed new principle of motion is based on the law of conservation of angular momentum and is fully consistent with the basic fundamental laws of physics. It is proposed to use the radiation/absorption of streams of low-energy particles with spin in the direction perpendicular to the movement of the material body. The practical implementation of this idea is confirmed by the presence of promising approaches to solving the problem of quantizing gravity (string theory, loop quantum gravity, etc.) recognized by the world scientific community and by the successful results of experiments conducted by the authors with the motion of bodies in a vacuum chamber. The proposed idea, the examples and experiments has given grounds for the formation of new physical concepts of the speed, mass and inertia of bodies. The obtained results can be used in experiments to search for elementary particles with low energy, to explain a number of physics phenomena and to develop transport of objects based on new physical principles.

The concept of creating thrust based on angular momentum change

The change in the kinetic moment of a material body is considered regarding to classical and quantum mechanics. The possibility of creating the propulsion system in terms of energy efficiency exceeding the photon engine has been theoretically proved. The proposed new principle of motion is based on the law of conservation of angular momentum and is fully consistent with the basic fundamental laws of physics. It is proposed to use the emission/absorption of streams of low-energy particles with spin in the direction perpendicular to the movement of the material body. The practical implementation of this idea is confirmed by the presence of promising approaches to solving the problem of quantizing gravity (string theory, loop quantum gravity, etc.) recognized by the world scientific community and by the successful results of experiments conducted by the authors with the motion of bodies in a vacuum chamber. The proposed idea, the examples and experiments has given grounds for the formation of new physical concepts of the speed, mass and inertia of bodies. The obtained results can be used in experiments to search for elementary particles with low energy, to explain a number of physics phenomena and to develop transport of objects based on new physical principles.

The concept of creating thrust based on angular momentum change

The change in the kinetic moment of a material body is considered regarding to classical and quantum mechanics. The possibility of creating the propulsion system in terms of energy efficiency exceeding the photon engine has been theoretically proved. The proposed new principle of motion is based on the law of conservation of angular momentum and is fully consistent with the basic fundamental laws of physics. It is proposed to use the emission/absorption of streams of low-energy particles with spin in the direction perpendicular to the movement of the material body. The practical implementation of this idea is confirmed by the presence of promising approaches to solving the problem of quantizing gravity (string theory, loop quantum gravity, etc.) recognized by the world scientific community and by the successful results of experiments conducted by the authors with the motion of bodies in a vacuum chamber. The proposed idea, the examples and experiments has given grounds for the formation of new physical concepts of the speed, mass and inertia of bodies. The obtained results can be used in experiments to search for elementary particles with low energy, to explain a number of physics phenomena and to develop transport of objects based on new physical principles.

Kinetic energy at collision of two automobiles

At collision of two automobiles under the influence of shock pulses the change of their speed occurs. The dynamic characteristic of movement of mechanical system consisting of two automobiles includes traffic, kinetic moment regarding motionless centre and kinetic energy. On the basis of dynamics theorems the author has determined a loss of kinetic energy of central-straight collision of two automobiles. The paper considers specific cases — elastic and absolutely inelastic collisions. It is established that at elastic collision the kinetic energy decreases by the amount of kinetic energy of lost velocities with amendment that includes a coefficient of recovery at collision.

Steady-state rotational motion of the Photon M-2 satellite

At the end of the flight, the attitude motion of the Photon M-2 satellite (it was in orbit 2005.05.31-2005.06.16) can be described by a generalized conservative system of differential equations. The secular change in the own kinetic moment of this satellite is described by the so-called evolutionary equations of Beletsky, which also form a generalized conservative system. The preprint examines the relationship between these systems. The satellite motion equations are reduced to equations of the 4th order describing the motion of the satellite axis of symmetry. Beletsky's equations are of the second order and describe the secular motion of the ort of the satellite's own kinetic moment. The solutions of these systems of equations corresponding to the real movements of the satellite are, respectively, conditionally periodic and periodic. The solutions of the 4th-order system are dominated by two frequencies – high and low ones. The spectral analysis showed that the low frequency coincides with the frequency of solutions of Beletsky’s equations. And the solutions of these equations coincide with the low-frequency component in the solution of the 4th-order system with respect to the variables that determine the direction of the axis of symmetry of the satellite.

DETERMINING THE BALANCE CONFIGURATION, IN CASE OF THE OSCILLATING MOVEMENT OF THE MAIN SPINDLE AT CNC LATHE

In the paper we present a mathematical model through which are determined the balance conditions, needed for the stability analysis of the oscillating movement of the main spindle at CNC lathe. We take into account Hamilton's variation principle, the axiom of impulse derivative and the axiom of kinetic moment derivative. We present the general movement equations that generate the oscillations based on the calculus hypotheses, performing the introduction of the external solicitations. Establishment of the balance configuration is done by imposing the conditions that the system of forces that act upon the ensemble spindle – bearings - tool causes a deformation of the spindle, without producing spindle vibration. We obtain the new differential equations of the movement, in which the forces and moments are determined from the static case, based on which we can determine the integration constants in the characteristic points of the main spindle.

DETERMINING THE BALANCE CONFIGURATION, IN CASE OF THE OSCILLATING MOVEMENT OF THE MAIN SPINDLE AT CNC LATHE

In the paper we present a mathematical model through which are determined the balance conditions, needed for the stability analysis of the oscillating movement of the main spindle at CNC lathe. We take into account Hamilton's variation principle, the axiom of impulse derivative and the axiom of kinetic moment derivative. We present the general movement equations that generate the oscillations based on the calculus hypotheses, performing the introduction of the external solicitations. Establishment of the balance configuration is done by imposing the conditions that the system of forces that act upon the ensemble spindle – bearings - tool causes a deformation of the spindle, without producing spindle vibration. We obtain the new differential equations of the movement, in which the forces and moments are determined from the static case, based on which we can determine the integration constants in the characteristic points of the main spindle.