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

Haşim Çayır

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

Abstract

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.

Keywords

References

[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.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Haşim Çayır This is me
0000-0003-0348-8665
Türkiye

Publication Date

December 1, 2019

Submission Date

August 16, 2019

Acceptance Date

September 19, 2019

Published in Issue

Year 2019 Volume: 37 Number: 4

IZ

https://izlik.org/JA37SU94UP

Cite

RIS / Bibtex

APA

Çayır, H. (2019). EULER-LAGRANGIAN DYNAMICAL SYSTEMS WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS ON TANGENT BUNDLE. Sigma Journal of Engineering and Natural Sciences, 37(4), 1292-1300. https://izlik.org/JA37SU94UP

AMA

1.Çayır H. EULER-LAGRANGIAN DYNAMICAL SYSTEMS WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS ON TANGENT BUNDLE. SIGMA. 2019;37(4):1292-1300. https://izlik.org/JA37SU94UP

Chicago

Çayır, Haşim. 2019. “EULER-LAGRANGIAN DYNAMICAL SYSTEMS WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS ON TANGENT BUNDLE”. Sigma Journal of Engineering and Natural Sciences 37 (4): 1292-1300. https://izlik.org/JA37SU94UP.

EndNote

Çayır H (December 1, 2019) EULER-LAGRANGIAN DYNAMICAL SYSTEMS WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS ON TANGENT BUNDLE. Sigma Journal of Engineering and Natural Sciences 37 4 1292–1300.

IEEE

[1]H. Çayır, “EULER-LAGRANGIAN DYNAMICAL SYSTEMS WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS ON TANGENT BUNDLE”, SIGMA, vol. 37, no. 4, pp. 1292–1300, Dec. 2019, [Online]. Available: https://izlik.org/JA37SU94UP

ISNAD

Çayır, Haşim. “EULER-LAGRANGIAN DYNAMICAL SYSTEMS WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS ON TANGENT BUNDLE”. Sigma Journal of Engineering and Natural Sciences 37/4 (December 1, 2019): 1292-1300. https://izlik.org/JA37SU94UP.

JAMA

1.Çayır H. EULER-LAGRANGIAN DYNAMICAL SYSTEMS WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS ON TANGENT BUNDLE. SIGMA. 2019;37:1292–1300.

MLA

Çayır, Haşim. “EULER-LAGRANGIAN DYNAMICAL SYSTEMS WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS ON TANGENT BUNDLE”. Sigma Journal of Engineering and Natural Sciences, vol. 37, no. 4, Dec. 2019, pp. 1292-00, https://izlik.org/JA37SU94UP.

Vancouver

1.Haşim Çayır. EULER-LAGRANGIAN DYNAMICAL SYSTEMS WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS ON TANGENT BUNDLE. SIGMA [Internet]. 2019 Dec. 1;37(4):1292-300. Available from: https://izlik.org/JA37SU94UP