The Journal of Geometric Mechanics (JGM)

A unifying mechanical equation with applications to non-holonomic constraints and dissipative phenomena
Pages: 473 - 482, Issue 4, December 2015

doi:10.3934/jgm.2015.7.473      Abstract        References        Full text (307.9K)           Related Articles

E. Minguzzi - Dipartimento di Matematica e Informatica "U. Dini", Università degli Studi di Firenze, Via S. Marta 3, I-50139 Firenze, Italy (email)

1 H. Bateman, On dissipative systems and related variational principles, Physical Review, 38 (1931), 815-819.
2 P. Bauer, Dissipative dynamical systems I, Proc. Natl. Acad. Sci. USA, 17 (1931), 311-314.
3 A. M. Bloch, J. Baillieul, P. Crouch and J. Marsden, Nonholonomic Mechanics and Control, Springer, New York, 2003.       
4 A. M. Bloch and A. G. Rojo, Quantization of a nonholonomic system, Phys. Rev. Lett., 101 (2008), 030402, 4pp.       
5 I. Bucataru and R. Miron, The geometry of systems of third order differential equations induced by second order regular Lagrangians, Mediterr. J. Math., 6 (2009), 483-500.       
6 A. Carati, A Lagrangian Formulation for the Abraham-Lorentz-Dirac Equation, vol. Quaderno del GFNM n. 54, 1998.
7 H. V. Craig, On a generalized tangent vector, Amer. J. Math., 57 (1935), 457-462.       
8 H. Dekker, Classical and quantum mechanics of the damped harmonic oscillator, Phys. Rep., 80 (1981), 1-112.       
9 H. H. Denman, On linear friction in Lagrange's equation, Am. J. Phys., 34 (1966), 1147-1149.
10 C. R. Galley, Classical mechanics of nonconservative systems, Phys. Rev. Lett., 110 (2013), 174301.
11 J. D. Jackson, Classical Electrodynamics, John Wiley & Sons, New York, 1975.       
12 Y. Kuwahara, Y. Nakamura and Y. Yamanaka, From classical mechanics with doubled degrees of freedom to quantum field theory for nonconservative systems, Phys. Lett. A, 377 (2013), 3102-3105.       
13 T. Levi-Civita, Sul moto di un sistema di punti materiali soggetti a resistenze proporzionali alle rispettive velocità, Atti Ist. Ven., 54 (1895/96), 1004-1008, Serie 7.
14 A. Lurie, Analytical Mechanics, Springer, Berlin, 2002.       
15 C.-M. Marle, Various approaches to conservative and nonconservative nonholonomic systems, Rep. Math. Phys., 42 (1998), 211-229.       
16 R. Y. Matsyuk, Higher order variational origin of the Dixon's system and its relation to the quasi-classical 'zitterbewegung' in general relativity, Diff. Geom. Appl., 29 (2011), S149-S155.       
17 E. Minguzzi, Rayleigh's dissipation function at work, Eur. J. Phys., 36 (2015), 035014, arXiv:1409.4041.
18 J. I. Neimark and N. A. Fufaev, Dynamics of Nonholonomic Systems, vol. 33 of Translations of Mathematical Monographs, American Mathematical Society, 2004.
19 F. Riewe, Nonconservative Lagrangian and Hamiltonian mechanics, Phys. Rev. E, 53 (1996), 1890-1899.       
20 P. Riewe, Relativistic classical spinning-particle mechanics, Nuovo Cimento B, 8 (1972), 271-277.
21 H. Rund, The Hamilton-Jacobi Theory in the Calculus of Variations, Van Nostrand, New York, 1966.       
22 J. L. Synge, Some intrinsic and derived vectors in a Kawaguchi space, Amer. J. Math., 57 (1935), 679-691.       
23 C. Yuce, A. Kilic and A. Coruh, Inverted oscillator, Phys. Scr., 74 (2006), 114-116.       

Go to top