ANALYTICAL SOLUTION OF SOME PROBLEMS OF APPLIED THEORY OF GYROSCOPES | ||
| The International Conference on Applied Mechanics and Mechanical Engineering | ||
| Article 99, Volume 15, 15th International Conference on Applied Mechanics and Mechanical Engineering., May 2012, Pages 1-15 PDF (317.67 K) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/amme.2012.37257 | ||
| Author | ||
| A. N. Tyurehodzhayev | ||
| Professor, Department of Applied Mechanics and Machinery Engineering Principles, the Kazakh National Technical University named after K. I. Satpayev, Almaty, Kazakhstan. | ||
| Abstract | ||
| ABSTRACT Motion of solid body with a fixed point is described by a system of nonlinear differential equations of motion of L. Euler. Gyroscopic instruments represent an axisymmetric solid body with a fixed point. The first partial solutions of the problem were obtained in works [1-4]. The subsequent development of Mechanics and Mathematics demonstrated that a nonlinear system of motion of L. Euler equations may describe a wide class of motions of celestial bodies, stability of motion of spacecrafts, Earth satellites, ships, aircrafts, monorail trains, etc. The great interest to the problems with a fixed point is due to the gyroscopic effects, which became widespread in the modern technology, navigation and in many other areas. More than 250 years have passed since the origination of nonlinear equations of motion of L. Euler, however, the interest in obtaining the solutions of these equations do not weaken. The world holds a huge amount of publications, for example, [5-14]. The analytical solutions of some problems characterizing the functioning of gyroscopes have been obtained based on the method of partial discretization of nonlinear differential equations, formed by the author of the report. This paper demonstrates an analytical solution of the nonlinear problem on the motion of an axisymmetric solid body with a fixed point at a high velocity rate of selfrotation n. New analytical results have been obtained based on the method of partial discretization of nonlinear differential equations. | ||
| Keywords | ||
| Gyroscope; Motion of solid body fixed at a point; Angular velocity of self-rotation; Nonlinear equations of motion; Unloading | ||
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