Application of Jacobi’s last multiplier for construction of Hamiltonians of certain biological systems

• Autorzy: A. Ghose Choudhury , Partha Guha
• Języki publikacji: EN

Abstrakty

EN

The relationship between Jacobi’s last multiplier and the Lagrangian of a second-order ordinary differential equation is quite well known. In this article we demonstrate the significance of the last multiplier in Hamiltonian theory by explicitly constructing the Hamiltonians of certain well known first-order systems of differential equations arising in biology.

Słowa kluczowe

EN

Jacobi’s last multiplier; time-dependent Hamiltonian system; singular Lagrangians; planar biological systems

• Czasopismo: Open Physics
• Rocznik: 2012
• Tom: 10
• Numer: 2
• Strony: 398-404

Daty

wydano

2012-04-01

online

2012-03-31

Twórcy

autor

A. Ghose Choudhury

• Department of Physics, Surendranath College, 24/2 Mahatma Gandhi Road, Calcutta, 700009, India,

autor

Partha Guha

• S.N. Bose National Centre for Basic Sciences JD Block, Sector III, Salt Lake, Kolkata, 700098, India,

Bibliografia

• [1] V.I. Arnold, Ordinary Differential Equations (Springer-Verlag, Berlin, 2006)
• [2] G. F. Torres del Castillo, J. Phys. A Math. Theor. 43, 265202 (2009) http://dx.doi.org/10.1088/1751-8113/42/26/265202[Crossref]
• [3] A. Ghose Choudhury, P. Guha, B. Khanra, J. Math. Anal. Appl. 360, 651 (2009) http://dx.doi.org/10.1016/j.jmaa.2009.06.052[Crossref]
• [4] A. Goriely, Integrability and nonintegrability of dynamical systems. Advanced Series in Nonlinear Dynamics, xviii+415 (World Scientific Publishing Co., Inc., River Edge, NJ, 2001) http://dx.doi.org/10.1142/9789812811943[Crossref]
• [5] P. Guha and A. Ghose Choudhury, Acta Appl. Math 116, 179 (2011) http://dx.doi.org/10.1007/s10440-011-9637-3[Crossref]
• [6] C. G. J. Jacobi, Giornale Arcadico di Scienze, Lettere ed Arti 99, 129 (1844)
• [7] C. G. J. Jacobi, J. Reine Angew. Math 27, 199 (1844) http://dx.doi.org/10.1515/crll.1844.27.199[Crossref]
• [8] C. G. J. Jacobi, J. Reine Angew. Math 29, 213 (1845) http://dx.doi.org/10.1515/crll.1845.29.213[Crossref]
• [9] C. G. J. Jacobi, Astrophys. J. 342, 635 (1989) http://dx.doi.org/10.1086/167623[Crossref]
• [10] C. A. Lucey, E. T. Newman, J. Math. Phys. 29, 2430 (1998) http://dx.doi.org/10.1063/1.528129[Crossref]
• [11] M. C. Nucci, P. G. L. Leach, arXiv:0709.3231v1 [WoS]
• [12] M. C. Nucci, J. Nonlinear Math. Phys. 12, 284 (2005) http://dx.doi.org/10.2991/jnmp.2005.12.2.9[Crossref]
• [13] M. C. Nucci, K. M. Tamizhmani, arXiv:1108.2301v1 [WoS]
• [14] G.H. Paine, Bull. Math. Biol. 44, 749 (1982) [PubMed]
• [15] G. Sardanashvily, J. Math. Phys. 39, 2714 (1998) http://dx.doi.org/10.1063/1.532416[Crossref]
• [16] A. Sarkar, J. K. Bhattacharjee, S. Chakraborty, D. B. Banerjee, Eur. Phys. J. D, DOI 10.1140/epjd/e2011-20060-1 [Crossref]
• [17] J. Struckmeier, J. Phys. A 38, 1257 (2005) http://dx.doi.org/10.1088/0305-4470/38/6/006[Crossref]
• [18] S. L. Trubatch, A. Franco, J. Theor. Biol. 48, 299 (1974) http://dx.doi.org/10.1016/S0022-5193(74)80003-2[Crossref]
• [19] B. S. Madhava Rao, Proceedings of the Benares Mathematical Society (New Series) 2, 53 (1940)
• [20] E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Cambridge University Press, Cambridge, 1988)

Identyfikatory

DOI

10.2478/s11534-012-0004-4