0
BRIEF NOTES

A New Lagrangian and a New Lagrange Equation of Motion for Fractionally Damped Systems

[+] Author and Article Information
O. P. Agrawal

Mechanical Engineering and Energy Processes, Southern Illinois University, Carbondale, IL 62901

J. Appl. Mech 68(2), 339-341 (Apr 24, 2000) (3 pages) doi:10.1115/1.1352017 History: Received June 07, 1999; Revised April 24, 2000

First Page Preview

View Large
First page PDF preview
Copyright © 2001 by ASME
Your Session has timed out. Please sign back in to continue.

References

Rossikhin,  Y. A., and Shitikova,  M. V., 1997, “Applications of Fractional Calculus to Dynamic Problems of Linear and Nonlinear Hereditary Mechanics of Solids,” Appl. Mech. Rev., 50, No. 1, pp. 15–67.
Riewe,  F., 1996, “Nonconservative Lagrangian and Hamiltonian Mechanics,” Phys. Rev. E, 53, No. 2, pp. 1890–1899.
Riewe,  F., 1997, “Mechanics With Fractional Derivative,” Phys. Rev. E, 55, No. 3, pp. 3581–3592.
Oldham, K. B., and Spanier, J., 1974, The Fractional Calculus, Academic Press, New York.
Suarez,  L. E., and Shokooh,  A., 1997, “An Eigenvector Expansion Method for the Solution of Motion Containing Fractional Derivatives,” ASME J. Appl. Mech., 64, pp. 629–635.
Miller, K. S., and Ross, B., 1993, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, New York.
Mainardi, F., 1997, “Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics,” Fractals and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F. Mainardi, eds., Springer-Verlag, New York, pp. 291–348.
Podlubny, I., 1999, Fractional Differential Equations, Academic Press, New York.
Yuan, L., and Agrawal, O. P., 1998, “A Numerical Scheme for Dynamical Systems Containing Fractional Derivatives, Proceedings of the DETC98, ASME Design Engineering Technical Conferences, Paper No. DETC98/MECH 5857, Sept. 13–16, Atlanta, GA.

Figures

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In