Fractional Euler Lagrange Equations for Irregular Lagrangian with Holonomic Constraints
, PP. 1690-1696 10.4236/jmp.2018.98105
Keywords: Fractional Derivatives, Euler-Lagrange Equations, Irregular Lagrangian, Holonomic Constraints
In this paper the fractional Euler Lagrange equations for irregular Lagrangian with holonomic constraints have been presented. The equations of motion are obtained using fractional Euler Lagrange equations in a similar manner to the usual mechanics. The results of fractional calculus reduce to those obtained from classical calculus (the standard Euler Lagrange equations) when
and γ →0 are equal unity only. Two problems are considered to demonstrate the application of the formalism. α, β
[ 1] Atam, A.P. (1990) Introduction to Classical Mechanics. Allyn and Bacon, Needham Heights.
[ 2] Goldstein, H. (1980) Classical Mechanics. 2nd Edition, Addison-Wesley, Reading.
[ 3] Rabei, E.M. (1999) Turkish Journal of Physics, 23, 1083. http://adsabs.harvard.edu/abs/2000NCimB.115.1159R
[ 4] Serhan, M., Abusini, M. and Rabei, E.M. (2009) Journal of Theoretical Physics, 48, 2731. https://doi.org/10.1007/s10773-009-0063-5
[ 5] Miller, K.S. and Ross, B. (1993) An Introduction to the Fractional Integrals and Derivatives-Theory and Applications. John Willey and Sons, New York.
[ 6] Samko, S.G., Kilbas, A.A. and Marichev, O.I. (1993) Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach Science Publishers, Amsterdam.
[ 7] Gorenflo, R. and Mainardi, F. (1997) Fractional Calculus: Integral and Differential Equations of Fractional Orders, Fractals and Fractional Calculus in Continuums Mechanics. Springer Verlag, Wien and New York.
[ 8] Riewe, F. (1996) Physical Review E, 53, 1890. https://doi.org/10.1103/PhysRevE.53.1890
[ 9] Riewe, F. (1997) Physical Review E, 55, 3581. https://doi.org/10.1103/PhysRevE.55.3581
[ 10] Tarawneh, K.M., Rabei, E.M. and Ghassib, H.B. (2010) Journal of Dynamics Systems and Theories, 8, 59-70. https://doi.org/10.1080/1726037X.2010.10698578
[ 11] Hilfer, R. (2000) Applications of Fractional Calculus in Physics. World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong. https://doi.org/10.1142/3779
[ 12] Malkawi, E., Rousan, A., Rabei, E. and Widyan, H. (2002) Fractional Calculus and Applied Analysis, 5, 155.
[ 13] Agrawal, O.P. (1999) An Analytical Scheme for Stochastic Dynamics Systems Containing Fractional Derivatives. ASME Design Engineering Technical Conferences, (7), 243-250.
[ 14] Hasan, E.H. (2016) Applied Physics Research, 8, 60. https://doi.org/10.5539/apr.v8n3p60
[ 15] Jarab’ah, O. (2016) Science International Lahore, 28, 3365. http://www.sci-int.com/Search?catid=71
[ 16] Agrawal, O.P. (2001) Journal of Applied Mechanics, 68, 339. https://doi.org/10.1115/1.1352017
[ 17] Agrawal, O.P. (2002) Journal of Mathematical Analysis and Applications, 272, 368. https://doi.org/10.1016/S0022-247X(02)00180-4
[ 18] Igor, M., Sokolove, J.K. and Blumen, A. (2002) Physics Today, American Institute of Physics S-0031-9228-0211-030-1.
[ 19] Jarab’ah, O., Nawafleh, K. and Ghassib, H.B. (2013) European Scientific Journal, 9, 70. http://www.eujournal.org/index.php/esj/article/download/1946/1888
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