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IssuesArchive of Issues2008-1pp.153-164

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M. A. Chuev, "Differential equations of program motions of a mechanical system," Mech. Solids. 43 (1), 153-164 (2008)
Year 2008 Volume 43 Number 1 Pages 153-164
DOI 10.3103/S0025654408010160
Title Differential equations of program motions of a mechanical system
Author(s) M. A. Chuev (Kaluga Branch of Bauman Moscow State Technical University, Bazhenova 2, Kaluga, 2486000, Russia)
Abstract We obtain all types and forms of differential equations describing the program motions of a mechanical system both for ideal and nonideal primary constraints. We find the forms of differential equations of motion that significantly simplify the mathematical transformations required to obtain them in explicit form.
References
1.  M. A. Chuev, "Programmed Motions of a Mechanical System," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 34-41 (2002) [Mech. Solids (Engl. Transl.) 37 (3), 28-35 (2002)].
2.  I. V. Meshcherskii, Differential Constraints in the Case of a Single Material Point (Kharkov Univ. Typography, Kharkov, 1887) [in Russian].
3.  M. A. Chuev, "Differential Equations of Program Motions of a Mechanical System (Second Type)," Vestnik RUDN. Ser. Prikl. Mat. i Inform, No. 1, 45-52 (2001).
4.  M. A. Chuev, "Differential Equations of Program Motions of Mechanical System," in Theses of 37th All-Russia Scientific Conference in Problems of Mathematics, Informatics, Physics, Chemistry, and Methodology of Teaching in Natural Sciences. Math. Section (Izd-vo RUDN, Moscow, 2001), pp. 50-51 [in Russian].
5.  M. A. Chuev, "Differential Equations of Program Motions of Mechanical System," in Stability and Vibrations of Nonlinear Systems of Control: Theses of 7th Intern. Seminar (Inst. for Problems of Control, Moscow, 2002), pp. 140-142 [in Russian].
6.  M. A. Chuev, "Differential Equations of Program Motions of Mechanical System," in All-Russia Sci. Tech. Conf.: Progressive Technologies, Constructions, and Systems in Instrumental and Mechanical Engineering. Materials, Vol. 1 (Izd-vo MGTU im. Baumana, Moscow, 2003), p. 372 [in Russian].
7.  M. A. Chuev, "To the Problem of Analytic Method for Mechanism Synthesizing," Izv. Vyssh. Uchebn. Zaved. Mashinostr., No. 8, 165-167 (1974).
8.  M. A. Chuev, "Method of Incomplete Integral in Mechanics of Nonholonomic Systems," in Foundations of Analytic Mechanics, Ed. by V. V. Dobronravov (Bysshaya Shkola, Moscow, 1976) [in Russian].
9.  N. N. Polyakhov, S. A. Zegzhda, and M. P. Yushkov, "A Generalization of the Gauss Principle to the Case of Nonholonomic Systems of Higher Order," Dokl. Akad. Nauk SSSR 269(6), 1329-1330 (1983) [Sov. Math. Dokl. (Engl. Transl.)].
10.  Sh. Kh. Soltakhanov, "On a Modification of the Polyakhov-Zegzhda-Yushkov Principle," Vestn. Leningrad. Univ. Mat. Mekh. Astronom., No. 4, 58-61 (1990) [Vestnik Leningrad Univ. Math. (Engl. Transl.)].
11.  I. A. Kaplan, Practical Tasks in Higher Mathematics, Part 3 (Vishch. Shk., Kharkov, 1974) [in Russian].
12.  G. Korn and T. Korn, Mathematical handbook for Scientists and Engineers (McGraw-Hill, New York, 1968; Nauka, Moscow, 1970).
13.  M. M. Gokhberg (Editor), Reference Book in Cranes, Vol. 2 (Mashinostroenie, Moscow, 1988) [in Russian].
Received 16 May 2005
Link to Fulltext http://www.springerlink.com/content/m2553n860tm0521n
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