Generalized mechanics with fractional derivatives applied to a system of anisotropic harmonic oscillators with anisotropic linear friction

Authors

Emmanuel T. Rodulfo ⋅ PH Physics Department, De La Salle University
Eduardo G. Lim ⋅ PH Physics Department, De La Salle University

Abstract

Generalized mechanics that supports interactions describable by generalized potentials that may depend on fractional derivatives of the generalized coordinates is discussed and applied to a system of anisotropic oscillators with anisotropic linear friction. We show that in this generalized version of Lagrangian mechanics a system of anisotropic oscillators subject to anisotropic linear frictional forces may be described by a generalized potential that is bilinear in the semi-derivatives of the coordinates. The Rayleigh dissipative force, which is traditionally derived from a dissipative function quadratic in the generalized velocities, comes as the isotropic special case and is seen to be derivable from a generalized potential that is quadratic in the semi-derivative of the coordinates. The appropriate definition of the Jacobi function is also proposed.

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Issue

2003: Proceedings of the 21st Samahang Pisika ng Pilipinas Physics Congress

Article ID

SPP-2003-PS-01

Section

Plenary Sessions

Published

2003-10-22

How to Cite

[1]

ET Rodulfo and EG Lim, Generalized mechanics with fractional derivatives applied to a system of anisotropic harmonic oscillators with anisotropic linear friction, Proceedings of the Samahang Pisika ng Pilipinas 21, SPP-2003-PS-01 (2003). URL: https://proceedings.spp-online.org/article/view/SPP-2003-PS-01.