Some relations of discrete and wave in dynamical systems
Published: 09.12.2014
Authors: Smirnov V.F.
Published in issue: #12(36)/2014
DOI: 10.18698/2308-6033-2014-12-1352
Category: Basic science
The article presents analysis of the corpuscular and wave properties of discrete dynamical systems, and gives proof of limitations of corpuscular approach in assessing the traveling waves. It is shown that such form of natural vibrations as standing wave allows to obtain a real loading of the dynamic system in all points only at the moment of maximum deflection of the masses. As for any given time it works only in some points of the system (node points of waveforms). On other times the load in the system can be found in accounting of sine of phase angle between the traveling and standing waves.
References
[1] Fok V.A. Teoriya prostranstva, vremeni i tyagoteniya [Theory of Space, Time and Gravitation]. Moscow, Nauka Publ., 1972.
[2] Born M. Einsteins Theory of Relativity. Dover Publications, Inc, New York, 1962.
[3] Sedov L.I. Mekhanika sploshnoi sredy [Continuum Mechanics]. Vol. 1. Moscow, Nauka Publ., 1973, 536 p.
[4] Khaikin S.E. Fizicheskie osnovy mekhaniki [Physical Principles of Mechanics]. Moscow, Nauka Publ., 1971, 752 p.
[5] Landau L.D., Lifshits E.M. Teoriya polya [Field Theory]. Moscow, Nauka Publ., 1973, 504 p.
[6] Jeffreys H., Swirles B. Methods of Mathematical Physics. 3rd revised ed. Cambridge University Press, 1956.
[7] Smirnov V.F., Nazarenko B.P., Zyablikov V.M. Vestnik MGTU im. N.E. Baumana. Seriya Estesnvennye nauki - Herald of the Bauman Moscow State Technical University. Series: Natural Sciences, 2000, no. 1(4), pp. 23-31.
[8] Zyablikov V.M., Smirnov V.F. Spravochnik. Inzhenernyi zhurnal - Handbook. Engineering Journal, 2012, no. 9, pp. 9-13.
[9] Smirnov V.F., Zyablikov V.M. Vestnik mashinostroeniya - Mashinostroenie Bulletin, 1994, no. 10, pp. 7-11.