摘要: Fractional dynamics of relativistic particle is discussed. Derivatives fractional orders with respect to proper time describe long-term memory effects that correspond intrinsic dissipative processes. Relativistic subjected a non-potential four-force considered as nonholonomic system. The constraint in four-dimensional space-time represents the invariance by equation for four-velocity u_{\mu} u^{\mu}+c^2=0, where c speed light vacuum. In general case, described non-Hamiltonian and dissipative. Conditions be Hamiltonian system are considered.
arxiv.org
128.84.21.199
springer.com参考文章(42)
J. D. E. Stokes, S. V. Vladimirov, A. A. Samarian, Reformulation of Hamiltonian dynamics for dust particle interactions in complex plasma ,(2007)
ECG Sudarshan, None, Higher Spin Fields and Non-Holonomic Constraints Foundations of Physics. ,vol. 33, pp. 707- 717 ,(2003) , 10.1023/A:1025640705548
Vasily E. Tarasov, Quantum Mechanics of Non-Hamiltonian and Dissipative Systems ,(2008)
G. M. Zaslavskiĭ, Hamiltonian Chaos and Fractional Dynamics ,(2005)
Alberto Carpinteri, Francesco Mainardi, Fractals and fractional calculus in continuum mechanics Springer-Verlag. ,(1997) , 10.1007/978-3-7091-2664-6
Oleg Igorevich Marichev, Stefan G Samko, Anatoly A Kilbas, Fractional Integrals and Derivatives: Theory and Applications ,(1993)
V.V. Rumiantsev, On Hamilton's principle for nonholonomic systems: PMM vol. 42, n≗ 3, 1978, pp. 387–399 Journal of Applied Mathematics and Mechanics. ,vol. 42, pp. 407- 419 ,(1978) , 10.1016/0021-8928(78)90108-9
Hari M Srivastava, Anatoly A Kilbas, Juan J Trujillo, Theory and Applications of Fractional Differential Equations ,(2006)
Małgorzata Klimek, Lagrangean and Hamiltonian fractional sequential mechanics Czechoslovak Journal of Physics. ,vol. 52, pp. 1247- 1253 ,(2002) , 10.1023/A:1021389004982
R. Kompaneets, S. V. Vladimirov, A. V. Ivlev, V. Tsytovich, G. Morfill, Dust clusters with non-Hamiltonian particle dynamics Physics of Plasmas. ,vol. 13, pp. 072104- ,(2006) , 10.1063/1.2212396