Presentation
Phase portraits of separable Hamiltonian systems
Author/s | Guillamon Grabolosa, Antoni
Pantazi, Chara |
Publication Date | 2007-09 |
Deposit Date | 2016-02-19 |
Published in |
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Abstract | We study some generalizations of potential Hamiltonian systems (H(x, y) = y
2 + F(x)) with one degree of freedom. In particular, we are interested in Hamiltonian systems with Hamiltonian functions of type H(x, y) = F(x) ... We study some generalizations of potential Hamiltonian systems (H(x, y) = y 2 + F(x)) with one degree of freedom. In particular, we are interested in Hamiltonian systems with Hamiltonian functions of type H(x, y) = F(x) + G(y) arising in applied mechanical problems. We present an algorithm to plot the phase portrait (include the behavior at infinity) of any Hamiltonian system of type H(x, y) = F(x) +G(y), where F and G are arbitrary polynomials. We are able to give the full description in the Poincaré disk according to the graphs of F and G, extending the well-known method for the “finite”phase portrait of potential systems. |
Project ID. | MTM2005-06098-C02-1
2005SGR-986 MTM2006-00478 |
Citation | Guillamon Grabolosa, A. y Pantazi, C. (2007). Phase portraits of separable Hamiltonian systems. |
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