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Contact Hamiltonian Description of 1D Frictional Systems

Year 2021, Volume: 4 Issue: 2, 100 - 107, 30.06.2021
https://doi.org/10.33434/cams.937807

Abstract

In this paper, we consider contact Hamiltonian description of 1D frictional dynamics with no conserved force. Friction forces that are monomials of velocity, and sum of two monomials are considered. For that purpose, quite general forms of contact Hamiltonians are taken into account. We conjecture that it is impossible to give a contact Hamiltonian description dissipative systems where the friction force is not in the form considered in this paper.

Thanks

We would like to thank anonymous referees whose comments improved the paper.

References

  • [1] A. McInerney, A. First Steps in Differential Geometry. Springer, New York, 2013.
  • [2] S. Lie, Geometrie der Beru ̈hrungstransformationen (dargestellt von S. Lie und G. Scheffers), B. G. Teubner, Leipzig, 1896
  • [3] J.W. Gibbs, Part 1,”Graphical methods in the thermodynamics of fluids” and Part 2, ”A method of geometrical representation of the thermodynamic properties of substances by means of surfaces”, Trans. Connecticut Acad., Part 1,309–342 and Part 2,382–404, 1873.
  • [4] H. Geiges. Christiaan huygens and contact geometry, Nieuw Arch. Wiskd, 6(2) (2005), 117–123.
  • [5] H. Geiges. A brief history of contact geometry and topology, Expositiones Math., 19(1) (2001), 25–53.
  • [6] V.I. Arnold, Mathematical Methods of Classical Mechanics, Springer, New York, 1989.
  • [7] A. Bravetti, H. Cruz, D. Tapias, Contact Hamiltonian mechanics, Ann. Phys., 376 (2017), 17–39.
  • [8] Q. Liu, P.J. Torres, C. Wang. Contact hamiltonian dynamics: Variational principles, invariants, completeness and periodic behavior, Ann. Phys., 395 (2018), 26–44.
  • [9] F.S. Dündar. Contact hamiltonian description of systems with exponentially decreasing force and friction that is quadratic in velocity, Fundam. J. Math. Appl., 3 (2020), 29–32.
Year 2021, Volume: 4 Issue: 2, 100 - 107, 30.06.2021
https://doi.org/10.33434/cams.937807

Abstract

References

  • [1] A. McInerney, A. First Steps in Differential Geometry. Springer, New York, 2013.
  • [2] S. Lie, Geometrie der Beru ̈hrungstransformationen (dargestellt von S. Lie und G. Scheffers), B. G. Teubner, Leipzig, 1896
  • [3] J.W. Gibbs, Part 1,”Graphical methods in the thermodynamics of fluids” and Part 2, ”A method of geometrical representation of the thermodynamic properties of substances by means of surfaces”, Trans. Connecticut Acad., Part 1,309–342 and Part 2,382–404, 1873.
  • [4] H. Geiges. Christiaan huygens and contact geometry, Nieuw Arch. Wiskd, 6(2) (2005), 117–123.
  • [5] H. Geiges. A brief history of contact geometry and topology, Expositiones Math., 19(1) (2001), 25–53.
  • [6] V.I. Arnold, Mathematical Methods of Classical Mechanics, Springer, New York, 1989.
  • [7] A. Bravetti, H. Cruz, D. Tapias, Contact Hamiltonian mechanics, Ann. Phys., 376 (2017), 17–39.
  • [8] Q. Liu, P.J. Torres, C. Wang. Contact hamiltonian dynamics: Variational principles, invariants, completeness and periodic behavior, Ann. Phys., 395 (2018), 26–44.
  • [9] F.S. Dündar. Contact hamiltonian description of systems with exponentially decreasing force and friction that is quadratic in velocity, Fundam. J. Math. Appl., 3 (2020), 29–32.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Furkan Semih Dündar 0000-0001-5184-5749

Gülhan Ayar 0000-0002-1018-4590

Publication Date June 30, 2021
Submission Date May 16, 2021
Acceptance Date June 9, 2021
Published in Issue Year 2021 Volume: 4 Issue: 2

Cite

APA Dündar, F. S., & Ayar, G. (2021). Contact Hamiltonian Description of 1D Frictional Systems. Communications in Advanced Mathematical Sciences, 4(2), 100-107. https://doi.org/10.33434/cams.937807
AMA Dündar FS, Ayar G. Contact Hamiltonian Description of 1D Frictional Systems. Communications in Advanced Mathematical Sciences. June 2021;4(2):100-107. doi:10.33434/cams.937807
Chicago Dündar, Furkan Semih, and Gülhan Ayar. “Contact Hamiltonian Description of 1D Frictional Systems”. Communications in Advanced Mathematical Sciences 4, no. 2 (June 2021): 100-107. https://doi.org/10.33434/cams.937807.
EndNote Dündar FS, Ayar G (June 1, 2021) Contact Hamiltonian Description of 1D Frictional Systems. Communications in Advanced Mathematical Sciences 4 2 100–107.
IEEE F. S. Dündar and G. Ayar, “Contact Hamiltonian Description of 1D Frictional Systems”, Communications in Advanced Mathematical Sciences, vol. 4, no. 2, pp. 100–107, 2021, doi: 10.33434/cams.937807.
ISNAD Dündar, Furkan Semih - Ayar, Gülhan. “Contact Hamiltonian Description of 1D Frictional Systems”. Communications in Advanced Mathematical Sciences 4/2 (June 2021), 100-107. https://doi.org/10.33434/cams.937807.
JAMA Dündar FS, Ayar G. Contact Hamiltonian Description of 1D Frictional Systems. Communications in Advanced Mathematical Sciences. 2021;4:100–107.
MLA Dündar, Furkan Semih and Gülhan Ayar. “Contact Hamiltonian Description of 1D Frictional Systems”. Communications in Advanced Mathematical Sciences, vol. 4, no. 2, 2021, pp. 100-7, doi:10.33434/cams.937807.
Vancouver Dündar FS, Ayar G. Contact Hamiltonian Description of 1D Frictional Systems. Communications in Advanced Mathematical Sciences. 2021;4(2):100-7.

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