To Problem of the Rewinding of the Tape with Automatically Adjustable Influences

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.

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.

KEYWORDS

Rewinding of Tape, Servo-Constraint, Speed, Force of Reaction of Servo-Constraints, Parametrical Clearing, Stability, The Digital Watching System, Full System of the Equations

Rewinding of Tape, Servo-Constraint, Speed, Force of Reaction of Servo-Constraints, Parametrical Clearing, Stability, The Digital Watching System, Full System of the Equations

Cite this paper

Teshaev, M. (2014) To Problem of the Rewinding of the Tape with Automatically Adjustable Influences.*Applied Mathematics*, **5**, 2235-2242. doi: 10.4236/am.2014.515217.

Teshaev, M. (2014) To Problem of the Rewinding of the Tape with Automatically Adjustable Influences.

References

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[2] Appel, P. (1925) Sur les une forme generale des equations de la dynamique (memorial des Sciences Mathematique, fasccule 1). Paris, 1-50.

[3] Przeborski, A. (1902) Die allgemeinsten Gleichunden der Klassischen Dunamik. Mathematische Zeitschrift, 36, 184-194. http://dx.doi.org/10.1007/BF01188619

[4] Novoselov, V.S. (1969) New Settlers Nonlinear Nonholonomic Co-Ordinates in the Analytical Mechanics. Leningrad State University, 217, 50-83.

[5] Shulgin, M.F. (1958) About Some Differential Equations of Analytical Dynamics and Their Integration. The Central Asian State University Press, Tashkent, 73-94.

[6] Rumyantsev, V.V. (1961) About Motion of Some Systems with Nonideal Constraints. The Moscow State University bulletin, Series, Маthematics and Меchаnics, 61-66.

[7] Rumyantsev, V.V. (1976) About Motion of Operated Mechanical Systems. The Journal of Applied Mathematics and Mechanics, 5, 771-781.

[8] 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.

[9] Azizov, А.G. (1975) About the Equations of Dynamics of Systems with Servo-Constraints. Proceedings of Tashkent State University, 476, 67-75.

[10] Azizov, A.G. (1980) Applied Problems of Dynamics of Operated Systems. Tashkent State University, Tashkent, 1-28.

[11] Nugmanova, Sh.S. (1953) About the Equations of Motions of Adjustable Systems. The Kazan Aviation Institute, 27, 26-35.

[12] 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.

[13] 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.

[14] Krasovsky, N.N. (1959) Some of Problems of Theories of Stability of Motion. Fizmatgiz, Moscow, 17-139.

[15] Lure, A.I. (1961) Analytical Mechanics. Fizmatgiz, Moscow, 13-430.

[16] Teshaev, M.Kh. (1999) About Stabilization of the Mechanical Systems Constrained by Geometrical Constriets. The Uzbek Magazine “Problems of Mechanics”, 1, 7-20.

[17] Teshaev, M.Kh. (2005) About Designing of Reactions of Servo-Constraints the Systems Constrained by Kinematical Constraints. The Uzbek Magazine “Problems of Mechanics”, 1, 3-7.

[18] Ziyatdinov, R.M. (1980) Dynamic of Machine Units with Automatically Adjustable Variators. Tashkent, 1-23.

[19] Bessonov, A.P. (1967) Bas of Dynamics of Mechanisms with Variable Weight of Links. The Nauka, Moscow, 84-102.

[20] Medvedev, V.S. (1979) Designing of Watching Drives by Means of the COMPUTER. Mechanical Engineering, Moscow, 47-62.

[21] Merkin, G.D. (1987) Introduction to Theory of Stability. The Nauka, Moscow, 1-304.

[1] Beghin, H. (1967) The Theory of Hygroscopic Compasses. Nauka Press, Moscow, 5-31.

[2] Appel, P. (1925) Sur les une forme generale des equations de la dynamique (memorial des Sciences Mathematique, fasccule 1). Paris, 1-50.

[3] Przeborski, A. (1902) Die allgemeinsten Gleichunden der Klassischen Dunamik. Mathematische Zeitschrift, 36, 184-194. http://dx.doi.org/10.1007/BF01188619

[4] Novoselov, V.S. (1969) New Settlers Nonlinear Nonholonomic Co-Ordinates in the Analytical Mechanics. Leningrad State University, 217, 50-83.

[5] Shulgin, M.F. (1958) About Some Differential Equations of Analytical Dynamics and Their Integration. The Central Asian State University Press, Tashkent, 73-94.

[6] Rumyantsev, V.V. (1961) About Motion of Some Systems with Nonideal Constraints. The Moscow State University bulletin, Series, Маthematics and Меchаnics, 61-66.

[7] Rumyantsev, V.V. (1976) About Motion of Operated Mechanical Systems. The Journal of Applied Mathematics and Mechanics, 5, 771-781.

[8] 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.

[9] Azizov, А.G. (1975) About the Equations of Dynamics of Systems with Servo-Constraints. Proceedings of Tashkent State University, 476, 67-75.

[10] Azizov, A.G. (1980) Applied Problems of Dynamics of Operated Systems. Tashkent State University, Tashkent, 1-28.

[11] Nugmanova, Sh.S. (1953) About the Equations of Motions of Adjustable Systems. The Kazan Aviation Institute, 27, 26-35.

[12] 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.

[13] 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.

[14] Krasovsky, N.N. (1959) Some of Problems of Theories of Stability of Motion. Fizmatgiz, Moscow, 17-139.

[15] Lure, A.I. (1961) Analytical Mechanics. Fizmatgiz, Moscow, 13-430.

[16] Teshaev, M.Kh. (1999) About Stabilization of the Mechanical Systems Constrained by Geometrical Constriets. The Uzbek Magazine “Problems of Mechanics”, 1, 7-20.

[17] Teshaev, M.Kh. (2005) About Designing of Reactions of Servo-Constraints the Systems Constrained by Kinematical Constraints. The Uzbek Magazine “Problems of Mechanics”, 1, 3-7.

[18] Ziyatdinov, R.M. (1980) Dynamic of Machine Units with Automatically Adjustable Variators. Tashkent, 1-23.

[19] Bessonov, A.P. (1967) Bas of Dynamics of Mechanisms with Variable Weight of Links. The Nauka, Moscow, 84-102.

[20] Medvedev, V.S. (1979) Designing of Watching Drives by Means of the COMPUTER. Mechanical Engineering, Moscow, 47-62.

[21] Merkin, G.D. (1987) Introduction to Theory of Stability. The Nauka, Moscow, 1-304.