Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

Characterization of partial Hamiltonian operators and related first integrals
Pages: 723 - 734, Issue 4, August 2018

doi:10.3934/dcdss.2018045      Abstract        References        Full text (349.5K)           Related Articles

Rehana Naz - Department of Mathematics and Statistical Sciences, Lahore School of Economics, Lahore, 53200, Pakistan (email)
Fazal M. Mahomed - DST-NRF Centre of Excellence in Mathematical and Statistical Sciences, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Wits 2050, South Africa (email)

1 A. C. Chiang, Elements of Dynamic Optimization, McGraw Hill, New York, 1992.
2 V. Dorodnitsyn and R. Kozlov, Invariance and first integrals of continuous and discrete Hamitonian equations, J. Eng. Math., 66 (2010), 253-270.       
3 A. H. Kara, F. M. Mahomed, I. Naeem and C. Wafo Soh, Partial Noether operators and first integrals via partial Lagrangians, Math. Methods in the Applied Sciences, 30 (2007), 2079-2089.       
4 V. V. Kozlov, Integrability and nonintegrability in Hamiltonian mechanics, Russ. Math. Surveys, 38 (1983), 1-76.       
5 P. G. L. Leach, First integrals for the modified Emden equation $\ddot q+\a(t)\dot q+q^n=0$, J. Math. Phys. 26 (1985), 2510-2514.       
6 T. Levi-Civita, Interpretazione gruppale degli integrali di un sistema canonico, Rend. Acc. Lincei, ser. III, 8 (1899), 235-238.
7 F. M. Mahomed and J. A. G. Roberts, Characterization of Hamiltonian symmetries and their first integrals, International Journal of Non-Linear Mechanics, 74 (2015), 84-91.
8 K. S. Mahomed and R. J. Moitsheki, First integrals of generalized Ermakov systems via the Hamiltonian formulation, International Journal of Modern Physics B, 30 (2016), 1640019, 12 pp.       
9 J. E. Marsden and A. Weinstein, Reduction of symplectic manifolds with symmetry, Rep. Math. Phys., 5 (1974), 121-130.       
10 R. Naz, F. M. Mahomed and A. Chaudhry, A partial Hamiltonian approach for current value Hamiltonian systems, Commu. Nonlinear. Sci. Numer. Simulat., 19 (2014), 3600-3610.       
11 R. Naz, A. Chaudhry and F. M. Mahomed, Closed-form solutions for the Lucas-Uzawa model of economic growth via the partial Hamiltonian approach, Commu. Nonlinear. Sci. Numer. Simulat, 30 (2016), 299-306.       
12 R. Naz, The applications of the partial Hamiltonian approach to mechanics and other areas, International Journal of Non-Linear Mechanics, 86 (2016), 1-6.
13 R. Naz, F. M. Mahomed and A. Chaudhry, A partial Lagrangian method for dynamical systems, Nonlinear Dynamics, 84 (2016), 1783-1794.       
14 P. J. Olver, Applications of Lie Groups to Differential Equations, Springer-Verlag, New York, 1993.       
15 G. Saccomandi and R. Vitolo, A Translation of the T. Levi-Civita paper: Interpretazione Gruppale degli Integrali di un Sistema Canonico, Regul. Chaotic Dyn., 17 (2012), 105-112, arXiv:1201.2388v1.       

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