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EULER-LAGRANGIAN DYNAMICAL SYSTEMS WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS ON TANGENT BUNDLE

Yıl 2019, Cilt: 37 Sayı: 4, 1292 - 1300, 01.12.2019

Öz

The differential geometry and mahthematical physics has lots of applications. The Euler-Lagrangian mechanics are very important tools for differential geometry, classical and analytical machanics. There are many studies about Euler-Lagrangian dynamics, mechanics, formalisms, systems and equations. The classic mechanics firstly introduced by J. L. Lagrange in 1788. Because of the investigation of tensorial structures on manifolds and extension by using the lifts to the tangent or cotangent bundle, it is possible to generalize to differentiable structures on any space (resp. manifold) to extended spaces (resp. extended manifolds) [5, 6, 9]. In this study, the Euler-Lagrangian theories, which are mathematical models of mechanical systems are structured on the horizontal and the vertical lifts of an almost complex structure in tangent bundle In the end, the geometrical and physical results related to Euler-Lagrangian dynamical systems are concluded.

Kaynakça

  • [1] R. Abraham, J.E. Marsden, T. Ratiu, Manifolds Tensor Analysis and Applications, Springer, 2001.
  • [2] M. de Leon, P.R. Rodrigues, Methods of Differential Geometry in Analytical Mechanics, Elsevier Sc. Pub. Com. Inc., 1989.
  • [3] Z. Kasap, Weyl-mechanical systems on tangent manifolds of constant W-sectional curvature, IJGMMP, 10 (2013), no.10, 1-13.
  • [4] J. Klein, Escapes Varialionnels et Mécanique, Ann. Inst. Fourier, Gronoble, 12 (1962).
  • [5] A. A. Salimov, Tensor Operators and Their applications, Nova Science Publ., New York, 2013.
  • [6] S. Sasaki, On the diferential geometry of tangent bundles of Riemannian manifolds, Tohoku Math J, 10 (1958), 338-358.
  • [7] M. Tekkoyun, On para-Euler-Lagrange and para-Hamilton equations, Phys. Lett. A, 340 (2005), 7-11.
  • [8] M. Tekkoyun, Mechanical Systems on Manifolds, Geometry Balkan Press, Bucharest, Romania, 2014.
  • [9] K. Yano, S .Ishihara, Tangent and Cotangent Bundles Differential geometry. Pure and Applied Mathematics. Mercel Dekker, Inc, New York, 1973.
Yıl 2019, Cilt: 37 Sayı: 4, 1292 - 1300, 01.12.2019

Öz

Kaynakça

  • [1] R. Abraham, J.E. Marsden, T. Ratiu, Manifolds Tensor Analysis and Applications, Springer, 2001.
  • [2] M. de Leon, P.R. Rodrigues, Methods of Differential Geometry in Analytical Mechanics, Elsevier Sc. Pub. Com. Inc., 1989.
  • [3] Z. Kasap, Weyl-mechanical systems on tangent manifolds of constant W-sectional curvature, IJGMMP, 10 (2013), no.10, 1-13.
  • [4] J. Klein, Escapes Varialionnels et Mécanique, Ann. Inst. Fourier, Gronoble, 12 (1962).
  • [5] A. A. Salimov, Tensor Operators and Their applications, Nova Science Publ., New York, 2013.
  • [6] S. Sasaki, On the diferential geometry of tangent bundles of Riemannian manifolds, Tohoku Math J, 10 (1958), 338-358.
  • [7] M. Tekkoyun, On para-Euler-Lagrange and para-Hamilton equations, Phys. Lett. A, 340 (2005), 7-11.
  • [8] M. Tekkoyun, Mechanical Systems on Manifolds, Geometry Balkan Press, Bucharest, Romania, 2014.
  • [9] K. Yano, S .Ishihara, Tangent and Cotangent Bundles Differential geometry. Pure and Applied Mathematics. Mercel Dekker, Inc, New York, 1973.
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Articles
Yazarlar

Haşim Çayır Bu kişi benim 0000-0003-0348-8665

Yayımlanma Tarihi 1 Aralık 2019
Gönderilme Tarihi 16 Ağustos 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 37 Sayı: 4

Kaynak Göster

Vancouver Çayır H. EULER-LAGRANGIAN DYNAMICAL SYSTEMS WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS ON TANGENT BUNDLE. SIGMA. 2019;37(4):1292-300.

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