Research Article
BibTex RIS Cite

Geodesics on the Momentum Phase Space with metric $^{{C}}{g}$

Year 2018, , 61 - 67, 11.03.2018
https://doi.org/10.32323/ujma.396109

Abstract

In this paper, a system of the differential equations giving geodesics on the momentum phase space with pseudo Riemann metric $^{C}g$ of a Hamilton space is found by using the Euler Lagrange equations. Then, space like geodesics on pseudo hyperbolic 2-space $H_{1}^{2}$ are obtained. Finally, a system of the differential equations giving geodesics on the cotangent bundle with pseudo Riemann metric $^{C}g$ of $H_{1}^{2}$  is get.

References

  • [1] R. Abraham and J. E. Marsden, Foundations of mechanics, W. A. Benjamin Inc.,New York, 1967.
  • [2] I. Ayhan, On the tangent sphere bundle of the pseudo hyperbolic two space, Global Journal of Advanced Research on Classical and Modern Geometries, vol. 3, no. 2, pp 76-90, 2014.
  • [3] I. Ayhan, On the sphere bundle with the Sasaki semi Riemann metric of a space form, Global Journal of Advanced Research on Classical and Modern Geometries, vol. 3, no. 1, pp 25-35, 2014.
  • [4] I. Ayhan, Geodesics on the tangent sphere bundle of 3-Sphere, International Electronic Journal of Geometry, vol. 6, no. 2, pp 100-109, 2013.
  • [5] A. C. Coken, I Ayhan, On the geometry of the movements of the particles in a Hamilton space, Abstract and Applied Analysis, DOI:10.1155/2013/830147, 2013.
  • [6] P. Free, Introduction to general relativity, Lecture Notes, Virgo site, 2003.
  • [7] R. Miron, H. Hrimiuc, H. Shimada, and V. S. Sabau, The geometry of Hamilton and Lagrange spaces, Kluwer Academic, New York, USA, 2001.
  • [8] A. Polnarev, Motion of a test particle in a gravitational field and Hamilton Jacobi equations, relativity and gravitation, Lectures Notes 5, 2011.
  • [9] S. Waner, G. C. Levine, Introduction to differential geometry and general relativity, Lectures Notes, 2005.
  • [10] C. K. Wonk, Classical physics in Galilean and Minkowski space-times, Lecture Notes 3, 2009.
  • [11] K. Yano and S. Ishihara, Tangent and cotangent bundles, Marcel Decker Inc., New York, 1973.
Year 2018, , 61 - 67, 11.03.2018
https://doi.org/10.32323/ujma.396109

Abstract

References

  • [1] R. Abraham and J. E. Marsden, Foundations of mechanics, W. A. Benjamin Inc.,New York, 1967.
  • [2] I. Ayhan, On the tangent sphere bundle of the pseudo hyperbolic two space, Global Journal of Advanced Research on Classical and Modern Geometries, vol. 3, no. 2, pp 76-90, 2014.
  • [3] I. Ayhan, On the sphere bundle with the Sasaki semi Riemann metric of a space form, Global Journal of Advanced Research on Classical and Modern Geometries, vol. 3, no. 1, pp 25-35, 2014.
  • [4] I. Ayhan, Geodesics on the tangent sphere bundle of 3-Sphere, International Electronic Journal of Geometry, vol. 6, no. 2, pp 100-109, 2013.
  • [5] A. C. Coken, I Ayhan, On the geometry of the movements of the particles in a Hamilton space, Abstract and Applied Analysis, DOI:10.1155/2013/830147, 2013.
  • [6] P. Free, Introduction to general relativity, Lecture Notes, Virgo site, 2003.
  • [7] R. Miron, H. Hrimiuc, H. Shimada, and V. S. Sabau, The geometry of Hamilton and Lagrange spaces, Kluwer Academic, New York, USA, 2001.
  • [8] A. Polnarev, Motion of a test particle in a gravitational field and Hamilton Jacobi equations, relativity and gravitation, Lectures Notes 5, 2011.
  • [9] S. Waner, G. C. Levine, Introduction to differential geometry and general relativity, Lectures Notes, 2005.
  • [10] C. K. Wonk, Classical physics in Galilean and Minkowski space-times, Lecture Notes 3, 2009.
  • [11] K. Yano and S. Ishihara, Tangent and cotangent bundles, Marcel Decker Inc., New York, 1973.
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

İsmet Ayhan 0000-0002-4131-8168

Publication Date March 11, 2018
Submission Date February 16, 2018
Acceptance Date March 7, 2018
Published in Issue Year 2018

Cite

APA Ayhan, İ. (2018). Geodesics on the Momentum Phase Space with metric $^{{C}}{g}$. Universal Journal of Mathematics and Applications, 1(1), 61-67. https://doi.org/10.32323/ujma.396109
AMA Ayhan İ. Geodesics on the Momentum Phase Space with metric $^{{C}}{g}$. Univ. J. Math. Appl. March 2018;1(1):61-67. doi:10.32323/ujma.396109
Chicago Ayhan, İsmet. “Geodesics on the Momentum Phase Space With Metric $^{{C}}{g}$”. Universal Journal of Mathematics and Applications 1, no. 1 (March 2018): 61-67. https://doi.org/10.32323/ujma.396109.
EndNote Ayhan İ (March 1, 2018) Geodesics on the Momentum Phase Space with metric $^{{C}}{g}$. Universal Journal of Mathematics and Applications 1 1 61–67.
IEEE İ. Ayhan, “Geodesics on the Momentum Phase Space with metric $^{{C}}{g}$”, Univ. J. Math. Appl., vol. 1, no. 1, pp. 61–67, 2018, doi: 10.32323/ujma.396109.
ISNAD Ayhan, İsmet. “Geodesics on the Momentum Phase Space With Metric $^{{C}}{g}$”. Universal Journal of Mathematics and Applications 1/1 (March 2018), 61-67. https://doi.org/10.32323/ujma.396109.
JAMA Ayhan İ. Geodesics on the Momentum Phase Space with metric $^{{C}}{g}$. Univ. J. Math. Appl. 2018;1:61–67.
MLA Ayhan, İsmet. “Geodesics on the Momentum Phase Space With Metric $^{{C}}{g}$”. Universal Journal of Mathematics and Applications, vol. 1, no. 1, 2018, pp. 61-67, doi:10.32323/ujma.396109.
Vancouver Ayhan İ. Geodesics on the Momentum Phase Space with metric $^{{C}}{g}$. Univ. J. Math. Appl. 2018;1(1):61-7.

 23181

Universal Journal of Mathematics and Applications 

29207              

Creative Commons License  The published articles in UJMA are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.