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To Problem of the Rewinding of the Tape with Automatically Adjustable Influences
Bukhara Engineering-Technological Institute, Bukhara, Republic of Uzbekistan
- 1 Bukhara Engineering-Technological Institute, Bukhara, Republic of Uzbekistan
Applied Mathematics·Volume 05 (2014)·Pages 2235–2242·Published 5 August 2014·DOI10.4236/am.2014.515217
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Abstract
In this work the problem of rewinding of a tape with constant speed is considered. Considering that drums represent bodies of variable weight, the equations of motion of system are formulated. Taking into account parametrical clearing of system of servo-constraints, the structure of force of reaction of servo-constraints which provides steady realization of servo-constraints (a constancy of linear speed of a tape) is defined. For realization of servo-constraints, it is offered to build digital watching system (DWS) and the full system of equations of DWS is formed. Laws of change of the operating influences, systems providing stability under the relation of the variety defined of servo-constraints are defined.
KeywordsRewinding of TapeServo-ConstraintSpeedForce of Reaction of Servo-ConstraintsParametrical ClearingStabilityThe Digital Watching SystemFull System of the Equations
- Beghin, H. (1967) The Theory of Hygroscopic Compasses. Nauka Press, Moscow, 5-31.
- Appel, P. (1925) Sur les une forme generale des equations de la dynamique (memorial des Sciences Mathematique, fasccule 1). Paris, 1-50.
- Przeborski, A. (1902) Die allgemeinsten Gleichunden der Klassischen Dunamik. Mathematische Zeitschrift, 36, 184-194. http://dx.doi.org/10.1007/BF01188619
- Novoselov, V.S. (1969) New Settlers Nonlinear Nonholonomic Co-Ordinates in the Analytical Mechanics. Leningrad State University, 217, 50-83.
- Shulgin, M.F. (1958) About Some Differential Equations of Analytical Dynamics and Their Integration. The Central Asian State University Press, Tashkent, 73-94.
- Rumyantsev, V.V. (1961) About Motion of Some Systems with Nonideal Constraints. The Moscow State University bulletin, Series, Маthematics and Меchаnics, 61-66.
- Rumyantsev, V.V. (1976) About Motion of Operated Mechanical Systems. The Journal of Applied Mathematics and Mechanics, 5, 771-781.
- Kirgetov, V.I. (1967) About Motion of Operated Mechanical Systems with Conditional Constrains (Servo-Constraints). The Journal of Applied Mathematics and Mechanics, 3, 433-446.
- Azizov, А.G. (1975) About the Equations of Dynamics of Systems with Servo-Constraints. Proceedings of Tashkent State University, 476, 67-75.
- Azizov, A.G. (1980) Applied Problems of Dynamics of Operated Systems. Tashkent State University, Tashkent, 1-28.
- Nugmanova, Sh.S. (1953) About the Equations of Motions of Adjustable Systems. The Kazan Aviation Institute, 27, 26-35.
- Chetaev, N.G. (1962) About a Principle of House. In: Chetaev, N.G., Ed., Stability of Motion. Works on the Analytical Mechanics, Academy of Science of the USSR, 329-334.
- Chetaev, N.G. (1962) On the Compelled Motions. In: Chetaev, N.G., Ed., Stability of Motion. Works on the Analytical Mechanics, Academy of Science of the USSR, 311-316.
- Krasovsky, N.N. (1959) Some of Problems of Theories of Stability of Motion. Fizmatgiz, Moscow, 17-139.
- Lure, A.I. (1961) Analytical Mechanics. Fizmatgiz, Moscow, 13-430.
- Teshaev, M.Kh. (1999) About Stabilization of the Mechanical Systems Constrained by Geometrical Constriets. The Uzbek Magazine “Problems of Mechanics”, 1, 7-20.