M. : Science, 1976. — 672 c. The monograph outlines the theoretical foundations of inertial navigation - determining the orientation and location of moving objects without any information from the outside, based solely on the readings of sensitive elements of mechanical nature located on the object itself. These include free gyroscopes, gyromayatniks, gyrostobilizators, gyrocompasses, gyroscopic and other measures of apparent accelerations (newtonometers). The description of the theory of behavior of these devices under relative motion conditions, mainly applied to problems of inertial navigation, is one of the central points of the monograph. The use of gyroscopic stabilization on board mobile objects in the conditions of their spatial angular motion leads to the need to consider complex geometric and kinematic problems. The monograph provides general methods and examples of solving such problems by various methods, including through matrices, Rodrig Hamilton and Cayley Klein parameters and quaternion algebra. Inertial navigation proper refers to the consideration of the theory of behavior of specific schemes, Combining gyroscopes, Newtonometers and Computational-Solution Devices , and the study of differential equations, the solution of which ultimately determines the location of the object and its course on the earth's sphere (the spatial inertial navigation system is unstable). The monograph is intended for a wide range of researchers, engineers, postgraduates and senior students engaged in the study of special sections of theoretical and applied mechanics and inertial navigation. It can also be useful for specialists developing theoretical and especially practical problems of stabilization and management of mobile objects for various purposes up to and including space applications.