Open Access

Noether’s theorems of variable mass systems on time scales

 and    | Oct 03, 2018

Cite

B.Aulbach and S. Hilger, A unified approach to continuous and discrete dynamics, Collo. Math. Sci. 1990, 53, 37.AulbachB.HilgerS.A unified approach to continuous and discrete dynamicsCollo. Math. Sci.19905337Search in Google Scholar

S. Hilger, Differential and difference calculus — Unified! Non. Anal. Theo. Meth. Appl, 1997, 30(5):2683-2694. 10.1016/S0362-546X(96)00204-010.1016/S0362-546X(96)00204-0HilgerS.Differential and difference calculus — Unified! NonAnal. Theo. Meth. Appl19973052683269410.1016/S0362-546X(96)00204-0Open DOISearch in Google Scholar

M. Bohner, Calculus of variations on time scales. Dyn. Syst. Appl, 2004, 13:339-349.BohnerM.Calculus of variations on time scalesDyn. Syst. Appl200413339349Search in Google Scholar

P. P. Cai, J. L. Fu, Lie symmetries and conserved quantities of the constraint mechanical systems on time scales. Reports Math. Phy, 2017, 79(3): 279-298. 10.1016/S0034-4877(17)30045-910.1016/S0034-4877(17)30045-9CaiP. P.FuJ. L.Lie symmetries and conserved quantities of the constraint mechanical systems on time scalesReports Math. Phy201779327929810.1016/S0034-4877(17)30045-9Open DOISearch in Google Scholar

P. P. Cai, J. L. Fu, Y. X. Guo, Noether symmetries of the nonconservative and nonholonomic systems on time scales. Science China, 2013, 56(5): 1017-1028.CaiP. P.FuJ. L.GuoY. X.Noether symmetries of the nonconservative and nonholonomic systems on time scalesScience China20135651017102810.1007/s11433-013-5065-xSearch in Google Scholar

C. J. Song, Y. Zhang, Noether theorem for Birkhoffian systems, J. Math. Phys, 2015, 56(10): 1-26. 10.1063/1.4932607SongC. J.ZhangY.Noether theorem for Birkhoffian systemsJ. Math. Phys2015561012610.1063/1.493260710.1155/2015/790139Search in Google Scholar

X. H. Zhai, Y. Zhang, Noether theorem for non-conservative systems with time delay on time scales, Commun. Non-linear. Sci. Numer. Simulat, 2017, 52: 32-43. 10.1016/j.cnsns.2017.04.01210.1016/j.cnsns.2017.04.012ZhaiX. H.ZhangY.Noether theorem for non-conservative systems with time delay on time scalesCommun. Nonlinear. Sci. Numer. Simulat201752324310.1016/j.cnsns.2017.04.012Open DOISearch in Google Scholar

M. Bohner, A. Peterson, Dynamic Equations on Time Scales-An Introduction with Applications. Boston: Birjhauser Boston Inc, 2001: 68-102. 10.1007/978-1-4612-0201-1BohnerM.PetersonA.Dynamic Equations on Time Scales-An Introduction with ApplicationsBoston: Birjhauser Boston Inc20016810210.1007/978-1-4612-0201-110.1007/978-1-4612-0201-1Search in Google Scholar

F. M. Atici, D. C. Biles, A. Lebedinsky, An application of time scales to economics. Math Comput Model, 2006, 43: 718–726. 10.1016/j.mcm.2005.08.01410.1016/j.mcm.2005.08.014AticiF. M.BilesD. C.LebedinskyA.An application of time scales to economicsMath Comput Model20064371872610.1016/j.mcm.2005.08.014Open DOISearch in Google Scholar

M. Dryl, D. F. M. Torres, A General Delta-Nabla Calculus of Variations on Time Scales with Application to Economics. Int. J. Dyn. Syst. Diff. Equ, 2014, 5(1):42-71.DrylM.TorresD. F. M.A General Delta-Nabla Calculus of Variations on Time Scales with Application to EconomicsInt. J. Dyn. Syst. Diff. Equ201451427110.1504/IJDSDE.2014.067108Search in Google Scholar

Z. Bartosiewicz, Dynamic feed equivalence of nonlinear systems on time scales. IFAC. Proc. Volu, 2005, 38(1):435-440. 10.3182/20050703-6-CZ-1902.0072710.3182/20050703-6-CZ-1902.00727BartosiewiczZ.Dynamic feed equivalence of nonlinear systems on time scalesIFAC. Proc. Volu200538143544010.3182/20050703-6-CZ-1902.00727Open DOISearch in Google Scholar

M. Bohner, G. S.Guseinov, Double integral calculus of variations on time scales. Comput. Math. Appl, 2007, 54(1):45-57. 10.1016/j.camwa.2006.10.03210.1016/j.camwa.2006.10.032BohnerM.GuseinovG. S.Double integral calculus of variations on time scalesComput. Math. Appl2007541455710.1016/j.camwa.2006.10.032Open DOISearch in Google Scholar

R. A. C. Ferreira, D. F. M. Torres, Remarks on the calculus of variations on time scales. Math, 2007, 9:65-73.FerreiraR. A. C.TorresD. F. M.Remarks on the calculus of variations on time scaleMath200796573Search in Google Scholar

S. P. S. Santos, N. Martins and D. F. M. Torres, Variational problems of Herglotz type with time delay: DuBois-Reymond condition and Noether’s first theorem. Discrete Contin. Dyn. Syst. 2015, 35(9): 4593-4610. 10.3934/dcds.2015.35.459310.3934/dcds.2015.35.4593SantosS. P. S.MartinsN.TorresD. F. M.Variational problems of Herglotz type with time delay: DuBois-Reymond condition and Noether’s first theoremDiscrete Contin. Dyn. Syst.20153594593461010.3934/dcds.2015.35.4593Open DOISearch in Google Scholar

E. Noether, Invariante variations problems. Nachr. Akad. Wiss. Gott. Math. Phys, 1918, 2: 235–237.NoetherE.Invariante variations problemsNachr. Akad. Wiss. Gott. Math. Phys19182235237Search in Google Scholar

B. Vujanovis, A study of conservation law of dynamical system by means of differential variational principle of Jourdain and Gauss. Acta. Mech, 1987, 65(1-4): 63-80. 10.1007/BF01176873VujanovisB.A study of conservation law of dynamical system by means of differential variational principle of Jourdain and GaussActa. Mech19876514638010.1007/BF0117687310.1007/BF01176873Search in Google Scholar

N. Martins, D. F. M. Torres, Noether’s symmetry theorem for nabla problems of the calculus of variations. Appl. Math. Lett. 2010, 23(12): 1432-1438. 10.1016/j.aml.2010.07.01310.1016/j.aml.2010.07.013MartinsN.TorresD. F. M.Noether’s symmetry theorem for nabla problems of the calculus of variationsAppl. Math. Lett.201023121432143810.1016/j.aml.2010.07.013Open DOISearch in Google Scholar

Z. Bartosiewicz, D. F. M. Torres, Noether’s theorem on time scales. Math. Anal. Appl. 2008, 342(2):1220-1226. 10.1016/j.jmaa.2008.01.01810.1016/j.jmaa.2008.01.018BartosiewiczZ.TorresD. F. M.Noether’s theorem on time scalesMath. Anal. Appl.200834221220122610.1016/j.jmaa.2008.01.018Open DOISearch in Google Scholar

F. X. Mei, Applications of Lie groups and Lie algebras to constrained mechanical systems (in Chinese). Beijing: Science Press, 1999.MeiF. X.Applications of Lie groups and Lie algebras to constrained mechanical systems (in Chinese)BeijingScience Press1999Search in Google Scholar

F. X. Mei, Foundations of Mechanics of Nonholonomic Systems. Beijing: Beijing Institute of Technology Press, 1985.MeiF. X.Foundations of Mechanics of Nonholonomic SystemsBeijingBeijing Institute of Technology Press1985Search in Google Scholar

F. Y. Li, X. Su, B. W. Long, et al. Noether’s theorem of a rotational relativistic variable mass system. Chin. Phys, 2002, 11(5):445-449. 10.1088/1009-1963/11/5/30710.1088/1009-1963/11/5/307LiF. Y.SuX.LongB. W.Noether’s theorem of a rotational relativistic variable mass systemChin. Phys200211544544910.1088/1009-1963/11/5/307Open DOISearch in Google Scholar

J. H. Fang, Mei Symmetry and Noether Symmetry of the Relativistic Variable Mass System. Theo. Phys, 2004, 41(3):269-272.FangJ. H.Mei Symmetry and Noether Symmetry of the Relativistic Variable Mass SystemTheo. Phys2004413269272Search in Google Scholar

R. L. Xu, J. H. Fang, B. Zhang, The Noether conserved quantity of Lie symmetry for discrete difference sequence Hamilton system with variable mass. Acta. Phy. Sin, 2013, 62(15): 154501-2230.XuR. L.FangJ. H.ZhangB.The Noether conserved quantity of Lie symmetry for discrete difference sequence Hamilton system with variable massActa. Phy. Sin20136215154501223010.7498/aps.62.154501Search in Google Scholar

J. H. Fang, S. Q. Zhao. Lie symmetries and conserved quantities of a relativistic rotational variable mass system. Acta. Phy. Sin, 2001, 50(3):392-393.FangJ. H.ZhaoS. Q.Lie symmetries and conserved quantities of a relativistic rotational variable mass systemActa. Phy. Sin2001503392393Search in Google Scholar

W.T. Thomaon, Equations of motion for the variable mass system, Aiaa. J, 2015, 4(2):91-94.ThomaonW.T.Equations of motion for the variable mass systemAiaa. J2015429194Search in Google Scholar

M. Bohner, A. Peterson, Dynamic Equations on Time Scales—An Introduction with Applications. Birkhäuser Boston, Inc., Boston, MA, 2001. 10.1007/978-1-4612-0201-1BohnerM.PetersonA.Dynamic Equations on Time Scales—An Introduction with ApplicationsBirkhäuser Boston, Inc.Boston, MA200110.1007/978-1-4612-0201-110.1007/978-1-4612-0201-1Search in Google Scholar

R. Hilscher, V. Zeidan, Calculus of variations on time scales: Weak local piecewise solutions with variable endpoints. Math. Anal. Appl. 2004, 289, 143–166. 10.1016/j.jmaa.2003.09.03110.1016/j.jmaa.2003.09.031HilscherR.ZeidanV.Calculus of variations on time scales: Weak local piecewise solutions with variable endpointsMath. Anal. Appl.200428914316610.1016/j.jmaa.2003.09.031Open DOISearch in Google Scholar

eISSN:
2444-8656
Language:
English
Publication timeframe:
2 times per year
Journal Subjects:
Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics