The Distances in the Stable Systems Due to the Virial Theorem

Author(s)
Hasan Arslan

ABSTRACT

The virial theorem is written by using the canonical equations of motion in classical mechanics. A moving particle with an initial speed in an n-particle system is considered. The distance of the moving particle from the origin of the system to the final position is derived as a function of the kinetic energy of the particle. It is thought that the considered particle would not collide with other particles in the system. The relation between the final and initial distance of the particle from the origin of the system is given by a single equation.

Cite this paper

H. Arslan, "The Distances in the Stable Systems Due to the Virial Theorem,"*Applied Mathematics*, Vol. 4 No. 4, 2013, pp. 688-689. doi: 10.4236/am.2013.44094.

H. Arslan, "The Distances in the Stable Systems Due to the Virial Theorem,"

References

[1] G. W. Collins II, “The Virial Theorem in Stellar Astrophics,” 2003. http://ads.harvard.edu/books/1978vtsa.book/bookfnt.pdf

[2] S. L. Shapiro and S. A. Teukolsky, “Black Holes, White Dwarfs and Neutron Stars,” John Wiley, New York, 1983. doi:10.1002/9783527617661

[3] J. F. Ganghoffer, “On the Virial Theorem and Eshelby Stress,” International Journal of Solids and Structures, Vol. 47. No. 9, 2010, pp. 1209-1220. doi:10.1016/j.ijsolstr.2010.01.009

[4] R. Sunyk and P. Steinmann, “On Higher Gradients in Continuum-Atomistic Modeling,” International Journal of Solids and Structures, Vol. 40, No. 24, 2003, pp. 6877-6896. doi:10.1016/j.ijsolstr.2003.07.001

[5] H. Goldstein, “Classical Mechanics,” Addison-Wesley Publishing Company, Inc., Reading, 1959.

[6] S. T. Thornton and J. B. Marion, “Classical Dynamics of Particles and Systems,” Thomson Learning, Belmont, 2004.

[1] G. W. Collins II, “The Virial Theorem in Stellar Astrophics,” 2003. http://ads.harvard.edu/books/1978vtsa.book/bookfnt.pdf

[2] S. L. Shapiro and S. A. Teukolsky, “Black Holes, White Dwarfs and Neutron Stars,” John Wiley, New York, 1983. doi:10.1002/9783527617661

[3] J. F. Ganghoffer, “On the Virial Theorem and Eshelby Stress,” International Journal of Solids and Structures, Vol. 47. No. 9, 2010, pp. 1209-1220. doi:10.1016/j.ijsolstr.2010.01.009

[4] R. Sunyk and P. Steinmann, “On Higher Gradients in Continuum-Atomistic Modeling,” International Journal of Solids and Structures, Vol. 40, No. 24, 2003, pp. 6877-6896. doi:10.1016/j.ijsolstr.2003.07.001

[5] H. Goldstein, “Classical Mechanics,” Addison-Wesley Publishing Company, Inc., Reading, 1959.

[6] S. T. Thornton and J. B. Marion, “Classical Dynamics of Particles and Systems,” Thomson Learning, Belmont, 2004.