Generalized classical mechanics
TopQuark Inc. Toronto, ON M6P 2P2, Canada
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Received: 3 June 2013
Revised: 6 August 2013
Published online: 7 October 2013
Generalized classical mechanics has been introduced and developed as a classical counterpart of the fractional quantum mechanics. The Lagrangian of generalized classical mechanics has been introduced, and equation of motion has been obtained. Lagrange, Hamilton and Hamilton-Jacobi frameworks have been implemented. Oscillator model has been launched and solved in 1D case. A new equation for the period of oscillations of generalized classical oscillator has been found. The interplay between the energy dependency of the period of classical oscillations and the non-equidistant distribution of the energy levels for fractional quantum oscillator has been discussed. We discuss as well, the relationships between new equations of generalized classical mechanics and the well-known fundamental equations of classical mechanics.
© EDP Sciences, Springer-Verlag, 2013