World Academy of Science, Engineering and Technology
Published January 23, 2011 | Version 2858
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Lagrangian Geometrical Model of the Rheonomic Mechanical Systems

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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.

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References

  • M. Anastasiei, On the geometry of time-dependent Lagrangians, Mathematical and Computing Modelling, 20, no4/5, Pergamon Press,1994, pp.67-81.
  • I. Bucataru, R. Miron, Finsler-Lagrange Geometry. Applications to dynamical systems, Editura Academiei Romane, Bucures┬©ti, 2007.
  • S. S. Chern, Z. Shen, Riemann-Finsler Geometry, Nankai Tracts in Mathematics, 6, World Scientific, Publishing Co. Pte. Ltd., Hackensack, NJ.
  • M. Crampin, F. A. E. Pirani, Applicable Differential Geometry, London Math. Society, Lectures Notes Series, 59, Cambridge University Press, 1986.
  • C. Frigioiu, C. Gheorghies┬©, Mechanical systems and their associated Lagrange geometries, International Journal of Computer Mathematics, Volume 87 Issue 12, 2010, pp.2846-2856.
  • C. Godbillon, Geometrie Differentielle et Mecanique Analytique, Herman, Paris, 1969.
  • K. Hedrih (Stevanovic), Rheonomic Coordinate method Applid to Nonlinear Vibration Systems with Hereditary Elements, Facta Universitatis, Series "Mechanics, Automatic Control and Robotics", 10(2000), pp.1111-1135.
  • J. Klein, Espaces Variationnels et Mecanique, Ann. Inst Fourier, Grenoble, 12(1962), pp.1-124.
  • O. Krupkova, The geometry of Ordinary Variationel Equations, Springer- Verlag, 1997. [10] M. de Leon, P.R. Rodriguez, Methods of Differential Geometry in Analitical Mechanics, North-Holland, 1989. [11] R. Miron, Dynamical Systems of Lagrangian and Hamiltonian Mechanical Systems, Advanced Studies in Pure Math., 24(2006), pp.165-199. [12] R. Miron, M. Anastasiei, I. Bucataru, The Geometry of Lagrange Spaces, in Handbook of Finsler Geometry, P.L.Antonelli, ed., Kluwer Acad. Publ.FTPH, 2003, pp. 969-1124. [13] R. Miron, C. Frigioiu, Finslerian Mechanical Systems, Algebras, Groups and Geometries, 22(2005), pp.151-168. [14] V. A. Vujicic, K. Hedrih(Stevanovic), The rheonomic constraints change force, Facta Universitatis, Series "Mechanics, Automatic Control and Robotics", 1(1993), pp. 313-322.