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Contact Hamiltonian Description of Systems with Exponentially Decreasing Force and Friction that is Quadratic in Velocity

Yıl 2020, Cilt: 3 Sayı: 1, 29 - 32, 10.06.2020
https://doi.org/10.33401/fujma.716406

Öz

We have given a simple contact Hamiltonian description of a system with exponentially vanishing (or zero) potential under a friction term that is quadratic in velocity. We have given two applications: to cavity solitons and to a free body under air friction.

Teşekkür

We would like to thank Metin Arık and Bayram Tekin for useful discussions. We also would like to Gülhan Ayar for bringing contact geometry to our attention.

Kaynakça

  • [1] H. Geiges, A brief history of contact geometry and topology, Expo. Math., 19(1) (2001), 25–53.
  • [2] H. Geiges, Christiaan huygens and contact geometry, (2005) arXiv:math/0501255.
  • [3] A. Bravetti, H. Cruz, D. Tapias, Contact Hamiltonian mechanics, Ann. Phys.-New York, 376 (2017), 17–39.
  • [4] Q. Liu, P. J. Torres, C. Wang, Contact Hamiltonian dynamics: Variational principles, invariants, completeness and periodic behavior, Ann. Phys.-New York, 395 (2018), 26–44.
  • [5] D. Sloan, Dynamical similarity. Phys. Rev. D, 97(12) (2018), 123541.
  • [6] E. Anderson, J. Barbour, B. Foster, N. O Murchadha, Scale-invariant gravity: Geometrodynamics. Classical Quant. Grav., 20 (2003), 1571–1604.
  • [7] E. Anderson, J. Barbour, B. Z. Foster, B. Kelleher, N. O. Murchadha, The physical gravitational degrees of freedom, Classical Quant. Grav., 22 (2005), 1795–1802.
  • [8] J. Barbour, N. O Murchadha, Classical and Quantum Gravity on Conformal Superspace, (1999), arXiv:gr-qc/9911071.
  • [9] F. Mercati, A Shape Dynamics Tutorial, (2014), arXiv:1409.0105.
  • [10] S. R. Anbardan, C. Rimoldi, R. Kheradmand, G. Tissoni, F. Prati, Exponentially decaying interaction potential of cavity solitons, Phys. Rev. E, 97(3) (2018), 032208.
  • [11] L. A. Lugiato, F. Prati, M. Brambilla, L. Columbo, S. Barland, G. Tissoni, K. M. Aghdami, R. Kheradmand, H. Tajalli, H. Vahed, Cavity solitons, In Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics, Springer, 2013, 395–404.
Yıl 2020, Cilt: 3 Sayı: 1, 29 - 32, 10.06.2020
https://doi.org/10.33401/fujma.716406

Öz

Kaynakça

  • [1] H. Geiges, A brief history of contact geometry and topology, Expo. Math., 19(1) (2001), 25–53.
  • [2] H. Geiges, Christiaan huygens and contact geometry, (2005) arXiv:math/0501255.
  • [3] A. Bravetti, H. Cruz, D. Tapias, Contact Hamiltonian mechanics, Ann. Phys.-New York, 376 (2017), 17–39.
  • [4] Q. Liu, P. J. Torres, C. Wang, Contact Hamiltonian dynamics: Variational principles, invariants, completeness and periodic behavior, Ann. Phys.-New York, 395 (2018), 26–44.
  • [5] D. Sloan, Dynamical similarity. Phys. Rev. D, 97(12) (2018), 123541.
  • [6] E. Anderson, J. Barbour, B. Foster, N. O Murchadha, Scale-invariant gravity: Geometrodynamics. Classical Quant. Grav., 20 (2003), 1571–1604.
  • [7] E. Anderson, J. Barbour, B. Z. Foster, B. Kelleher, N. O. Murchadha, The physical gravitational degrees of freedom, Classical Quant. Grav., 22 (2005), 1795–1802.
  • [8] J. Barbour, N. O Murchadha, Classical and Quantum Gravity on Conformal Superspace, (1999), arXiv:gr-qc/9911071.
  • [9] F. Mercati, A Shape Dynamics Tutorial, (2014), arXiv:1409.0105.
  • [10] S. R. Anbardan, C. Rimoldi, R. Kheradmand, G. Tissoni, F. Prati, Exponentially decaying interaction potential of cavity solitons, Phys. Rev. E, 97(3) (2018), 032208.
  • [11] L. A. Lugiato, F. Prati, M. Brambilla, L. Columbo, S. Barland, G. Tissoni, K. M. Aghdami, R. Kheradmand, H. Tajalli, H. Vahed, Cavity solitons, In Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics, Springer, 2013, 395–404.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Furkan Semih Dündar 0000-0001-5184-5749

Yayımlanma Tarihi 10 Haziran 2020
Gönderilme Tarihi 8 Ocak 2020
Kabul Tarihi 21 Ocak 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 1

Kaynak Göster

APA Dündar, F. S. (2020). Contact Hamiltonian Description of Systems with Exponentially Decreasing Force and Friction that is Quadratic in Velocity. Fundamental Journal of Mathematics and Applications, 3(1), 29-32. https://doi.org/10.33401/fujma.716406
AMA Dündar FS. Contact Hamiltonian Description of Systems with Exponentially Decreasing Force and Friction that is Quadratic in Velocity. FUJMA. Haziran 2020;3(1):29-32. doi:10.33401/fujma.716406
Chicago Dündar, Furkan Semih. “Contact Hamiltonian Description of Systems With Exponentially Decreasing Force and Friction That Is Quadratic in Velocity”. Fundamental Journal of Mathematics and Applications 3, sy. 1 (Haziran 2020): 29-32. https://doi.org/10.33401/fujma.716406.
EndNote Dündar FS (01 Haziran 2020) Contact Hamiltonian Description of Systems with Exponentially Decreasing Force and Friction that is Quadratic in Velocity. Fundamental Journal of Mathematics and Applications 3 1 29–32.
IEEE F. S. Dündar, “Contact Hamiltonian Description of Systems with Exponentially Decreasing Force and Friction that is Quadratic in Velocity”, FUJMA, c. 3, sy. 1, ss. 29–32, 2020, doi: 10.33401/fujma.716406.
ISNAD Dündar, Furkan Semih. “Contact Hamiltonian Description of Systems With Exponentially Decreasing Force and Friction That Is Quadratic in Velocity”. Fundamental Journal of Mathematics and Applications 3/1 (Haziran 2020), 29-32. https://doi.org/10.33401/fujma.716406.
JAMA Dündar FS. Contact Hamiltonian Description of Systems with Exponentially Decreasing Force and Friction that is Quadratic in Velocity. FUJMA. 2020;3:29–32.
MLA Dündar, Furkan Semih. “Contact Hamiltonian Description of Systems With Exponentially Decreasing Force and Friction That Is Quadratic in Velocity”. Fundamental Journal of Mathematics and Applications, c. 3, sy. 1, 2020, ss. 29-32, doi:10.33401/fujma.716406.
Vancouver Dündar FS. Contact Hamiltonian Description of Systems with Exponentially Decreasing Force and Friction that is Quadratic in Velocity. FUJMA. 2020;3(1):29-32.

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