{"title":"Lagrangian Geometrical Model of the Rheonomic Mechanical Systems","authors":"Camelia Frigioiu, Katica (Stevanovic) Hedrih, Iulian Gabriel Birsan","volume":49,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":24,"pagesEnd":31,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/2858","abstract":"
In this paper we study the rheonomic mechanical systems from the point of view of Lagrange geometry, by means of its canonical semispray. We present an example of the constraint motion of a material point, in the rheonomic case.<\/p>\r\n","references":"[1] M. Anastasiei, On the geometry of time-dependent Lagrangians, Mathematical\r\nand Computing Modelling, 20, no4\/5, Pergamon Press,1994,\r\npp.67-81.\r\n[2] I. Bucataru, R. Miron, Finsler-Lagrange Geometry. Applications to\r\ndynamical systems, Editura Academiei Romane, Bucures\u252c\u00a9ti, 2007.\r\n[3] S. S. Chern, Z. Shen, Riemann-Finsler Geometry, Nankai Tracts in\r\nMathematics, 6, World Scientific, Publishing Co. Pte. Ltd., Hackensack,\r\nNJ.\r\n[4] M. Crampin, F. A. E. Pirani, Applicable Differential Geometry, London\r\nMath. Society, Lectures Notes Series, 59, Cambridge University Press,\r\n1986.\r\n[5] C. Frigioiu, C. Gheorghies\u252c\u00a9, Mechanical systems and their associated\r\nLagrange geometries, International Journal of Computer Mathematics,\r\nVolume 87 Issue 12, 2010, pp.2846-2856.\r\n[6] C. Godbillon, Geometrie Differentielle et Mecanique Analytique, Herman,\r\nParis, 1969.\r\n[7] K. Hedrih (Stevanovic), Rheonomic Coordinate method Applid to Nonlinear\r\nVibration Systems with Hereditary Elements, Facta Universitatis,\r\nSeries \"Mechanics, Automatic Control and Robotics\", 10(2000),\r\npp.1111-1135.\r\n[8] J. Klein, Espaces Variationnels et Mecanique, Ann. Inst Fourier, Grenoble,\r\n12(1962), pp.1-124.\r\n[9] O. Krupkova, The geometry of Ordinary Variationel Equations, Springer-\r\nVerlag, 1997.\r\n[10] M. de Leon, P.R. Rodriguez, Methods of Differential Geometry in\r\nAnalitical Mechanics, North-Holland, 1989.\r\n[11] R. Miron, Dynamical Systems of Lagrangian and Hamiltonian Mechanical\r\nSystems, Advanced Studies in Pure Math., 24(2006), pp.165-199.\r\n[12] R. Miron, M. Anastasiei, I. Bucataru, The Geometry of Lagrange Spaces,\r\nin Handbook of Finsler Geometry, P.L.Antonelli, ed., Kluwer Acad.\r\nPubl.FTPH, 2003, pp. 969-1124.\r\n[13] R. Miron, C. Frigioiu, Finslerian Mechanical Systems, Algebras, Groups\r\nand Geometries, 22(2005), pp.151-168.\r\n[14] V. A. Vujicic, K. Hedrih(Stevanovic), The rheonomic constraints change\r\nforce, Facta Universitatis, Series \"Mechanics, Automatic Control and\r\nRobotics\", 1(1993), pp. 313-322.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 49, 2011"}