Non-Linear Forces and Irreversibility Problem in Classical Mechanics

ABSTRACT

Restrictions of classical mechanics which take place because of holonomic constraints hypothesis used for obtaining canonical Lagrange equation are analyzed. As it was shown that this hypothesis excludes non-linear terms in the expression for forces which are responsible for energy exchange between different degrees of freedom of a many-body system. An oscillator passing a potential barrier is considered as an example which demonstrated this fact. It was found that the oscillator can pass the barrier even if kinetic energy of its mass center is below the potential barrier’s height due to non-linear terms. This effect is lost because of holonomic constraints hypothesis. We also explained how one can derive a system’s motion equation without the use of holonomic constraints hypothesis. This equation can be used to describe non-linear irreversible processes within the frames of Newton’s laws.

Cite this paper

V. Somsikov and A. Mokhnatkin, "Non-Linear Forces and Irreversibility Problem in Classical Mechanics,"*Journal of Modern Physics*, Vol. 5 No. 1, 2014, pp. 17-22. doi: 10.4236/jmp.2014.51003.

V. Somsikov and A. Mokhnatkin, "Non-Linear Forces and Irreversibility Problem in Classical Mechanics,"

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[1] I. Prigogine, “From Being to Becoming,” Nauka, Moscow, 1980

[2] A. Poincare, “On Science,” Nauka, Moscow, 1983.

[3] V. M. Somsikov, New Advances in Physics, Vol. 2, 2008, pp. 125-140.

[4] V. M. Somsikov, Journal of material Sciences and Engineering A, Vol. 1, 2011, pp. 731-740.

[5] V. M. Somsikov, IJBC, 14, 2004, pp. 4027-4033.

[6] V. M. Somsikov, Journal of Physics: Conference Series, Vol. 23, 2005, pp. 7-16.

[7] C. Lanczos, “The Variational Principles of Mechanics,” Academic Press, Waltham, 1962.

[8] G. Goldstein, “Classical Mechanics,” Nauka, Moscow, 1975.

[9] V. M. Somsikov and M. I. Denisenya, Izvestiya VUZ, Fizika, Vol. 3, 2013, pp. 95-103.

[10] V. M. Somsikov, “Nonequilibrium Systems and Mechanics of the Structured Particles,” In: Chaos and Complex System, Elsever, Amsterdam, 2013, pp. 31-39.

[11] G. M. Zaslavsky, “Stochasticity of Dynamical Systems,” Nauka, Moscow, 1984.