A trend to design structurally simpler but algorithmically more complex strapdown gyroscopic compasses compared to regular Cardan suspension devices is on the rise. In such devices, on-board computer units take on the functions of orientation and Cardan joints by processing signals from gyroscopes and accelerometers attached to the housing. This report is based on differential equations of motion of single-rotor Cardan assembly gyroscopic compasses with indirect adjustment, as well as on algorithms of strapdown inertial orientation systems (SIOS) [1] in order to build algorithms of strapdown gyroscopic compass operation. Analogy between properties of regular indirect-adjustment gyroscopic devices and analytically designed strapdown computer gyroscopic compasses is shown. Application of adjustments of non-inertial nature to improve the accuracy of gyroscopic compasses is shown.

The report studies the introduction of electromechanical feedback loops to two coordinates of translational equatorial motions of the gyroscopic chamber, which provides tracking of oscillations of the reference computer model. The efficiency of the method is proven theoretically and by using mathematical modeling - the oscillations coincide to a high accuracy. The example shows the error of less than 0.1%.

The main features of the design and circuitry of an ESG-based sensor for measuring three angles of a moving object rotation are discussed. The physical basis of the proposed engineering solution is generation of rotational and single- or two-component translational motion of an electrostatically suspended rotor with the use of a torquer and force transducer. The theoretical justification, algorithms and the results of comparative mathematical simulation are given. It is shown that in the case of single-component rotor oscillations in the equatorial plane, the error in determining the azimuth angle is three times smaller than that in the case of two-component oscillations.

An idea of using computer mechanics for inertial navigation systems is given and examples are presented. The equations, algorithms, and properties of the pendulum-type strapdown inertial navigation system are analyzed. As a result, it has been stated that such a system is analogous to analytical systems. A similar comparison for both semi-analytical and strapdown inertial navigation systems, in which the Schuler's pendulum models are described in a horizontal coordinate system, is carried out. An analogy of their properties is established. By comparing the analytical system, platform axes of which are directed along the axes of the inertial coordinate system (orientation of the Schuler's pendulum is also described in the inertial coordinate system), and the strapdown inertial navigation system with the same orientation of the platform's computer model (the comparison is also made for the operation algorithms of such systems), an analogy of such systems has been established. The degree of use of computer mechanics in all types of strapdown inertial navigation systems is much greater than in platform ones. According to the degree of utilization for principles of computer mechanics, types of inertial navigation systems can be arranged in the following order: strapdown pendulum, other strapdown systems, semi-analytical, analytical, and geometric platform inertial navigation systems. Their accuracy depends on the degree of sophistication of the element base, that is, on sensitive elements and on-board computers. We claim that the smaller the volume and mass of the mechanical part of the system the better its weight-and-dimensional characteristics and cost.

Two schemes of the three-component angular-velocity meter based on the Kovalevsky gyroscope are described: on the electrostatic and mechanical spring suspensions. The gyroscopic degrees of freedom are restricted on the observation coordinates, and there is a rapid rotation around its principal axis. A mathematical model of the device motion along three translational coordinates and two angular coordinates is presented. The formulas for determining the two components of the mobile-object angular velocities lying in the equatorial plane are derived by using the signals in the channels of the radial interaxial correction as well as the algorithm of calculation with the help of an onboard controller of the angular-velocity component of rotation around the object axis, which practically coincides with the principal one. The algorithm includes the coordinates of the relative translational equatorial motions of the rotor and their first and second time derivatives. The algorithms of their determination with the interference filtering based on the Leuenberger observing identification device are given.

The main features of the design and circuitry of an ESG-based sensor intended to measure three angles of moving object (MO) rotations are discussed; also considered is the underlying physical basis, namely, generation of rotational and two-component reciprocating motion of an electrostatically suspended rotor with the use of a gyromotor and force transducer. The design solution is theoretically justified; a numerical example is given to prove its feasibility.

The TGAVM schemes based on the Kovalevskaya gyroscope with both spherical electrostatic and spring suspensions are described. The differential equations of motion of the gyroscope are given, formulae for the output information on the three components of the angular velocity of MO. The formula for determining the third component includes the first and second derivatives on the coordinates of the translational movements of the gyroscope in the equatorial plane. To determine them, an algorithm is used to filter the interference of derivatives, based on the Luenberger identification device. The results of mathematical simulation by the derivation of the three components of the angular velocity, which confirmed the validity of the premises, are given. An analytical approximate solution of the problem is given for the self-centering mode of the gyroscope rotor and for the resonance mode. It is shown that in the second case the sensitivity of the device can be an order of magnitude higher than in the first. The approximate solution is confirmed by calculations of the third component of the angular velocity based on measuring only the coordinates of the translational movement of the gyroscope, without derivatives.

The report focuses on the experience of creating an automatic biaxial rotary test bench for verification of the accuracy characteristics of strapdown inertial navigation systems (SINS). Attention is given to construction solutions adopted in the design process and to the methods of controlling the parameters of SINS. Features of the tracking drive performed on the basis of a stepping motor are considered, the associated controlling algorithms are studied. A mathematical model of the rotary bench is formed, the results of the prototype testing are presented.

The results of studies of the change of the output signal of the angular rate sensor, which occurs as a result of unbalancing of the floating gyro node due to friction in pivoted supports are presented; physical foundations of such a phenomenon are discussed, analytical correlations for calculating the interrelated moments of the unbalancing force, the size of gap in pivoted supports, the gyro node temperature, and the friction forces moment (torque), which cause changes in the output signal, are introduced; a method for evaluating the friction moment and the degree of wear of supports that does not require device disassembly is proposed; analysis of deformations due to load on the pivot and the degree of their influence on friction moments is conducted.

Experimental studies and their results are described for the translation-rotational motion of rolling bodies subjected to forces and elastic deformations of the contact tribological conjunction regions between such bodies and the bases. Most attention is paid to the motion of such bodies outside the contact surfaces in the regions of preliminary displacements and behind these regions. In several experiments, the processes are recorded and analyzed from the very beginning to the termination of the rolling body finite displacements. All displacement stages exhibit oscillations due to variations in the character of motions of the rolling bodies. In the case where the body is only under the action of its weight, the regions of normal strains symmetric with respect to the axis of the weight action are shown as surface indentations outside the region of direct contact between the base and the rolling body. The photographs of the base nonsymmetric deformations due to the additional action of the tangential force on the rolling body are presented. One can see that the indentation slope in the motion or the force action direction is steeper and the indentation depth and length are smaller than those on the opposite side. This suggests that, on the side where the rolling body surface enters the base, the volumes of their deformations and hence the elastic force are greater than on the opposite side. The graphs are constructed for the variation in the values of preliminary and kinematic (in motion) displacements and the arm of rolling friction force for two motor cars, for a solid steel roller, and for a steel roller with two foam rubber wheels. The graphs show that, quantitatively, the displacement values are by one and more orders of magnitude greater than the values of these arms of force. Qualitatively, the arms of rolling friction force, just as the displacements, are characterized by the presence of proportionality and saturation segments of their characteristics. The motion processes of the considered rolling bodies in the directions opposite to those in which each of the bodies moved under the action of the tangential external force are also shown.

A vehicle accommodates as many three-component magnetometers as are enough to identify the location of noise sources and to determine the distribution of magnetic field intensity on a vehicle. The proposed formulas and algorithms provide identification of the Earth’s magnetic field (EMF) parameters and determination of a vehicle’s magnetic heading in case that the information about the yaw and pitch/roll angles from a vertical reference gyro is available. The process of heading determination is simulated, allowing for estimation of procedural errors.

Shimmy is the phenomenon of intensive angular self-excited vibrations of a vehicle wheel. Such self-excited vibrations seriously threaten the safety ofmotion, which explains scientists' profound interest in this phenomenon. This problem is most serious for the front wheels of aircraft. Tyre deformation is usually viewed to be the main cause of shimmy. Without casting doubt on this point, we still note that this is not the only cause. The shimmy phenomenon can also be observed in everyday life and for various hand carts, where any reference to tyre elasticity is most often irrelevant if the wheels are rigid.We show that the polycomponent dry friction theory can completely explain the shimmy phenomenon for absolutely rigidwheels and hence polycomponent dry friction is at least one of its causes in the general case.Dry friction has been neglected by scientists when explaining shimmy because dry friction theory has not been sufficiently well developed until recently; at the same time, shimmy cannot be explained in the framework of earlier conceptions.

A model of sliding and spinning friction forces for a ball in the form of finite relations obtained by integrating the tangential stresses over the contact area whose parameters are determined by Hertz’s theory for the “ball-rough horizontal surface” tribological conjunction pair is supplemented with a model of rolling friction torques. The combined model is peculiar in that the presliding displacement effect in rolling and spinning friction torques is taken into account. It is shown that the ball motions in the presliding displacement zone are of quasilinear character and, under shock perturbations, have the form of damping vibrations in the three orientation angles. The numerical parameters of the rolling and spinning friction model are experimentally determined for the presliding displacement zones, while the sliding friction parameters and partly the spinning friction parameters are calculated. Mathematical modeling permits one to discover new properties of the ball, namely, its deceleration in rolling, the onset of damping vibrations at the beginning and end of motion, and the transient process parameters.

Shimmy is a phenomenon of intense angular self-excited vibrations of the wheels of a carriage. Such self-excited vibrations present a serious threat to traffic safety, which accounts for the great interest of researchers in this phenomenon. The problem is of highest importance for the front wheels of aircraft. Usually, the deformation of pneumatic tires is considered to be the main factor responsible for shimmy. Without challenging this thesis, we nevertheless note that this is not the only factor. The shimmy phenomenon can be observed in everyday life in the case of various carriages that often have nothing to do with pneumatics if the wheels are rigid. Below we will show that the theory of polycomponent dry friction fully explains the shimmy phenomenon for absolutely rigid wheels and, hence, is at least one of the factors responsible for shimmy in the general case. The reason why researchers have not taken dry friction into account when explaining shimmy is that the theory of this kind of friction has not been well developed; at the same time one has failed to explain shimmy in the framework of other existing theories.

Although the exact mechanism is unknown, certain empirical correlations make it possible to predict changes in the position of the free gingival margin. This information is useful in attaining pocket elimination and preserving periodontal health.

Four methods of main pipeline positioning are considered. The most progressive and effective method is the one based on the integration of a satellite navigation system (GPS), a strapdown inertial system of navigation (SINS), and a geoinformation system (GIS). The positioning technology of subsurface pipelines is illustrated by the results from actual pipeline positioning.