Chin. Phys. Lett.  2008, Vol. 25 Issue (5): 1720-1723    DOI:
Original Articles |
Hamiltonian Formulation of Singular Lagrangians on Time Scales
JARAD Fahd;BALEANU Dumitru;MARAABA Abdeljawad Thabet
Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Cankaya University-06530, Ankara, Turkey
Cite this article:   
JARAD Fahd, BALEANU Dumitru, MARAABA Abdeljawad Thabet 2008 Chin. Phys. Lett. 25 1720-1723
Download: PDF(156KB)  
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract The Hamiltonian formulation of Lagrangian on time scale isinvestigated and the equivalence of Hamilton and Euler--Lagrange equations is obtained. The role of Lagrange multipliers is discussed.
Keywords: 45.10.Db      45.20.Jj     
Received: 22 February 2008      Published: 29 April 2008
PACS:  45.10.Db (Variational and optimization methods)  
  45.20.Jj (Lagrangian and Hamiltonian mechanics)  
TRENDMD:   
URL:  
https://cpl.iphy.ac.cn/       OR      https://cpl.iphy.ac.cn/Y2008/V25/I5/01720
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
JARAD Fahd
BALEANU Dumitru
MARAABA Abdeljawad Thabet
[1] Hilger S 1990 Results Math. 18 18
[2] Hilger S 1997 Nonlin. Anal.: Theor. 30 2683
[3] Agarwal R, Bohner M, O'Regan D and PetersonA 2002 J. Comput. Appl. Math. 141 1
[4] Bohner M 2004 Dynam. Systems Appl. 13 339
[5] Bohner M and Peterson A 2001 Dynamic Equations onTime Scales (Boston: Birkh\v auser)
[6] Hilscher R and Zeidan V 2004 J. Math. Anal. Appl. 289 143
[7] Atici F M, Biles D C and Lebedinsky A 2006 Math.Comp. Model. 43 718
[8] Ahlbrandt C D, Bohner M and Ridenhour J 2000 J.Math. Anal. Appl. 250 561
[9] Dirac P A M 1950 Can. J. Math. 2 129 Dirac P A M 1964 Lectures on Quantum Mechanics (New York:Yeshiva University)
[10] Bergmann P G and Goldberg I 1955 Phys. Rev. 98 531
[11] Henneaux M and Teitelboim C 1992 Quantization ofGauge Systems (Princeton, NJ: Princeton University Press)
[12] Cari\~{nena J F, Fern\'{andez-N\'{u\~{nez J and Ra\~{nada F M 2003 J. Phys. A: Math. Gen. 36 3789
[13] Baleanu D and Avkar T 2003 Nuovo Cimento B 119 1 73
[14] Baleanu D and Guler Y 2000 Nuovo Cimento B 115 3 319
[15] Sugano R and Kimura T 1990 Phys. Rev. D 41 1247
[16] Ferreira R A C and Torres D F M arXiv:0706.3141v2
[math.OC]
Related articles from Frontiers Journals
[1] ZHENG Shi-Wang, WANG Jian-Bo, CHEN Xiang-Wei, XIE Jia-Fang. Mei Symmetry and New Conserved Quantities of Tzénoff Equations for the Variable Mass Higher-Order Nonholonomic System[J]. Chin. Phys. Lett., 2012, 29(2): 1720-1723
[2] XU Wei, YUAN Bo, AO Ping, ** . Construction of Lyapunov Function for Dissipative Gyroscopic System[J]. Chin. Phys. Lett., 2011, 28(5): 1720-1723
[3] XIA Li-Li . A Field Integration Method for a Nonholonomic Mechanical System of Non-Chetaev's Type[J]. Chin. Phys. Lett., 2011, 28(4): 1720-1723
[4] XIA Li-Li . Poisson Theory and Inverse Problem in a Controllable Mechanical System[J]. Chin. Phys. Lett., 2011, 28(12): 1720-1723
[5] HUANG Wei-Li, CAI Jian-Le** . Conformal Invariance of Higher-Order Lagrange Systems by Lie Point Transformation[J]. Chin. Phys. Lett., 2011, 28(11): 1720-1723
[6] ZHANG Yi** . The Method of Variation of Parameters for Solving a Dynamical System of Relative Motion[J]. Chin. Phys. Lett., 2011, 28(10): 1720-1723
[7] XIA Li-Li, CAI Jian-Le. Symmetry of Lagrangians of Nonholonomic Controllable Mechanical Systems[J]. Chin. Phys. Lett., 2010, 27(8): 1720-1723
[8] TIAN Jing, QIU Hai-Bo, CHEN Yong,. Nonlocal Measure Synchronization in Coupled Bosonic Josephson Junctions[J]. Chin. Phys. Lett., 2010, 27(7): 1720-1723
[9] ZHENG Shi-Wang, XIE Jia-Fang, WANG Jian-Bo, CHEN Xiang-Wei. Another Conserved Quantity by Mei Symmetry of Tzénoff Equation for Non-Holonomic Systems[J]. Chin. Phys. Lett., 2010, 27(3): 1720-1723
[10] XIE Yin-Li, JIA Li-Qun. Special Lie–Mei Symmetry and Conserved Quantities of Appell Equations Expressed by Appell Fun[J]. Chin. Phys. Lett., 2010, 27(12): 1720-1723
[11] XIE Guang-Xi, CUI Jin-Chao, ZHANG Yao-Yu, JIA Li-Qun. Structural Equation and Mei Conserved Quantity of Mei Symmetry for Appell Equations with Redundant Coordinates[J]. Chin. Phys. Lett., 2009, 26(7): 1720-1723
[12] PANG Ting, FANG Jian-Hui, ZHANG Ming-Jiang, LIN Peng, LU Kai. Perturbation to Mei Symmetry and Generalized Mei Adiabatic Invariants for Nonholonomic Systems in Terms of Quasi-Coordinates[J]. Chin. Phys. Lett., 2009, 26(7): 1720-1723
[13] XUE Yun, SHANG Hui-Lin. Jourdain Principle of a Super-Thin Elastic Rod Dynamics[J]. Chin. Phys. Lett., 2009, 26(7): 1720-1723
[14] WANG Peng, FANG Jian-Hui, WANG Xian-Ming. Discussion on Perturbation to Weak Noether Symmetry and Adiabatic Invariants for Lagrange Systems[J]. Chin. Phys. Lett., 2009, 26(3): 1720-1723
[15] JIA Li-Qun, CUI Jin-Chao, LUO Shao-Kai, YANG Xin-Fang. Special Lie Symmetry and Hojman Conserved Quantity of Appell Equations for a Holonomic System[J]. Chin. Phys. Lett., 2009, 26(3): 1720-1723
Viewed
Full text


Abstract