David W Dreisigmeyer and Peter M Young 2003 J. Phys. A: Math. Gen. 36 8297 doi:10.1088/0305-4470/36/30/307
David W Dreisigmeyer and Peter M Young
Show affiliationsWe reexamine the problem of having nonconservative equations of motion arise from the use of a variational principle. In particular, a formalism is developed that allows the inclusion of fractional derivatives. This is done within the Lagrangian framework by treating the action as a Volterra series. It is then possible to derive two equations of motion, one of these is an advanced equation and the other is retarded.
45D05 Volterra integral equations (See also 34A12)
70H08 Nearly integrable Hamiltonian systems, KAM theory
65K10 Optimization and variational techniques (See also 49Mxx, 93B40)
Issue 30 (1 August 2003)
Received 29 April 2003, in final form 17 June 2003
Published 16 July 2003
David W Dreisigmeyer and Peter M Young 2003 J. Phys. A: Math. Gen. 36 8297
Lior Shamir and Robert J. Nemiroff 2005 The Astronomical Journal 129 539
David Bowdley 2003 Phys. Educ. 38 406
A P Gibson et al 2005 Phys. Med. Biol. 50 R1
Alejandro Clocchiatti et al. 2006 ApJ 642 1
Fabien Silly et al 2004 New J. Phys. 6 16
Takaaki Kajita 2004 New J. Phys. 6 194
E Havard et al 2008 Semicond. Sci. Technol. 23 035001
N. Madhusudhan and Joshua N. Winn 2009 ApJ 693 784
M. E. C. Swanson et al. 2006 ApJ 652 206