One Dimensional Relativistic Free Particle in a Quadratic Dissipative Medium
ABSTRACT
The deduction of a constant of motion, a Lagrangian, and a Hamiltonian for relativistic particle moving in a dissipative medium characterized by a force which depends on the square of the velocity of the particle is done. It is shown that while the trajectories in the space (x,v), defined by the constant of motion, look as one might expected, the trajectories in the space (x,p), defined by the Hamiltonian, have an odd behavior.<
The deduction of a constant of motion, a Lagrangian, and a Hamiltonian for relativistic particle moving in a dissipative medium characterized by a force which depends on the square of the velocity of the particle is done. It is shown that while the trajectories in the space (x,v), defined by the constant of motion, look as one might expected, the trajectories in the space (x,p), defined by the Hamiltonian, have an odd behavior.<
Cite this paper
López, G. , Montes, G. and Zanudo, J. (2015) One Dimensional Relativistic Free Particle in a Quadratic Dissipative Medium. Journal of Modern Physics, 6, 121-125. doi: 10.4236/jmp.2015.62016.
López, G. , Montes, G. and Zanudo, J. (2015) One Dimensional Relativistic Free Particle in a Quadratic Dissipative Medium. Journal of Modern Physics, 6, 121-125. doi: 10.4236/jmp.2015.62016.
References
[1] Dodonov, V.P., Man’ko, V.I. and Skarzhinsky, V.D. (1981) Hadronic Journal, 4, 1734. [2] Havas, P. (1973) Act. Phys. Austr., 38, 145. [3] Okubo, S. (1980) Physical Review D, 22, 919.
http://dx.doi.org/10.1103/PhysRevD.22.919 [4] Glauber, R. and Man’ko, V.I. (1984) Soviet Physics—JETP, 60, 450. [5] Lopez, G. (1996) Annals of Physics, 251, 372-383.
http://dx.doi.org/10.1006/aphy.1996.0118 [6] Lopez, G. (1998) International Journal of Theoretical Physics, 37, 1617-1623.
http://dx.doi.org/10.1023/A:1026628221912 [7] Lopez, G., Lopez, X.E. and Gonzalez, G. (2007) International Journal of Theoretical Physics, 46, 149-156.
http://dx.doi.org/10.1007/s10773-006-9224-y [8] Lopez, G.V. (2009) arXiv:0901.4792 [9] Musielak, Z.E. (2008) Journal of Physics A: Mathematical and Theoretical, 41, Article ID: 055205.
http://dx.doi.org/10.1088/1751-8113/41/5/055205 [10] Carinena, J.F. and Ranada, M.F. (2005) Journal of Mathematical Physics, 46, Article ID: 062703.
http://dx.doi.org/10.1063/1.1920287 [11] Lopez, G. (2012) Partial Differential Equations of First Order and Their Applications to Physic, 2nd Edition, World Scientific, Singapore. [12] John, F. (1974) Partial Differential Equations. Springer-Verlag, Berlin. [13] Kobussen, J.A. (1979) Act. Phys. Austr., 51 193. [14] Leubner, C. (1987) Physical Review A, 86, 9. [15] Yan C.C. (1981) American Journal of Physics, 49, 296.
http://dx.doi.org/10.1119/1.12632 [16] See Reference 5.
[1] Dodonov, V.P., Man’ko, V.I. and Skarzhinsky, V.D. (1981) Hadronic Journal, 4, 1734. [2] Havas, P. (1973) Act. Phys. Austr., 38, 145. [3] Okubo, S. (1980) Physical Review D, 22, 919.
http://dx.doi.org/10.1103/PhysRevD.22.919 [4] Glauber, R. and Man’ko, V.I. (1984) Soviet Physics—JETP, 60, 450. [5] Lopez, G. (1996) Annals of Physics, 251, 372-383.
http://dx.doi.org/10.1006/aphy.1996.0118 [6] Lopez, G. (1998) International Journal of Theoretical Physics, 37, 1617-1623.
http://dx.doi.org/10.1023/A:1026628221912 [7] Lopez, G., Lopez, X.E. and Gonzalez, G. (2007) International Journal of Theoretical Physics, 46, 149-156.
http://dx.doi.org/10.1007/s10773-006-9224-y [8] Lopez, G.V. (2009) arXiv:0901.4792 [9] Musielak, Z.E. (2008) Journal of Physics A: Mathematical and Theoretical, 41, Article ID: 055205.
http://dx.doi.org/10.1088/1751-8113/41/5/055205 [10] Carinena, J.F. and Ranada, M.F. (2005) Journal of Mathematical Physics, 46, Article ID: 062703.
http://dx.doi.org/10.1063/1.1920287 [11] Lopez, G. (2012) Partial Differential Equations of First Order and Their Applications to Physic, 2nd Edition, World Scientific, Singapore. [12] John, F. (1974) Partial Differential Equations. Springer-Verlag, Berlin. [13] Kobussen, J.A. (1979) Act. Phys. Austr., 51 193. [14] Leubner, C. (1987) Physical Review A, 86, 9. [15] Yan C.C. (1981) American Journal of Physics, 49, 296.
http://dx.doi.org/10.1119/1.12632 [16] See Reference 5.