EULER-LAGRANGE EQUATIONS ON THREE-DIMENSIONAL SPACE

In this article, it is aimed to introduce the Euler-Lagrange equations using a three-dimensional space for mechanical systems. In addition to, the geometrical-physical results related to three-dimensional space formechanical systems are also given. 

EULER-LAGRANGE EQUATIONS ON THREE-DIMENSIONAL SPACE - ÜÇ BOYUTLU UZAYDA EULER-LAGRANGE DENKLEMLERİ

EULER-LAGRANGE EQUATIONS ON THREE-DIMENSIONAL SPACEIn this article, it is aimed to introduce the Euler-Lagrange equations using a three-dimensional space for mechanical systems. In addition to, the geometrical-physical results related to three-dimensional space formechanical systems are also given. ÜÇ BOYUTLU UZAYDA EULER-LAGRANGE DENKLEMLERİBu makale ile üç boyutlu uzay kullanılarak mekanik sistemler için Euler-Lagrange denklemlerini tanıtmak amaçlanmıştır. Ek olarak, üç boyutlu uzaydaki mekanik sistemler için geometrik ve fiziksel sonuçlar da verilmiştir. 

___

  • J. Klein, Escapes Variationnels et Mécanique, Ann. Inst. Fourier, Grenoble, 12 (1962), 1-124.
  • M. De Leon, P.R. Rodrigues, Methods of Differential Geometry in Analytical Mechanics, North-Holland Mathematics Studies, 152 (1989).
  • R. Abraham, J. E. Marsden, T. Ratiu, Manifolds, Tensor Analysis and Applications, Springer, (2001), 483-542.
  • H. de Vries, Understanding Relativistic Quantum Field Theory, The Hamiltonian and Lagrangian http://www.physics- quest.org/Book_Chapter_Lagrangian.pdf), (2009).
  • M. Tekkoyun, On Para-Euler Lagrange and Para-Hamiltonian Equations, Physics Letters A, 34 (2005), 7-11. W.K.
  • Nanomechanics of Materials, American Scientific Publishers, Stevenson Ranch, CA, (2005).
  • M. Tekkoyun, M. Sari., Bi-para-Mechanical Systems on tThe Bi-Lagrangian Manifold, Physica B-Condensed Matter, 405 (2010), Issue 10, 2390- 23
  • M. Tekkoyun, Y. Yayli, Mechanical Systems on Generalized-Quaternionic IJGMMP, 8 (2011), No. 7, 1-13. Kähler Manifolds,
  • Z. Kasap and M. Tekkoyun, Mechanical Systems on Almost Para/Pseudo-Kähler.Weyl Manifolds, IJGMMP, 10 (2013). No.5, 1-8
  • O. Enge, P. Maiber, Multibody System Dynamics, Modelling Eelectromechanical Systems with Electrical Switching Components Using the Linear Complementarity System Dynamics, 13 (2005), No.4, 21-445. Problem, Multibody
  • D. McDu and D. Salamon, J-Holomorphic Curves http://www.math.sunysb.edu/~dusa/jholsm.pdf. Cohomology, A. Newlander and L. Nirenberg, Complex Analytic Manifolds. Ann. of Math. 65 (1957), 391-404. in Almost Complex