Overview of the differential Galois integrability conditions for non-homogeneous potentials

• Autorzy: Andrzej J. Maciejewski , Maria Przybylska
• Języki publikacji: EN

Abstrakty

EN

We report our recent results concerning integrability of Hamiltonian systems governed by Hamilton's function of the form $H = 1/2 ∑_{i=1}^{n} p²_{i} + V(q)$, where the potential V is a finite sum of homogeneous components. In this paper we show how to find, in the differential Galois framework, computable necessary conditions for the integrability of such systems. Our main result concerns potentials of the form $V = V_k + V_K$, where $V_k$ and $V_K$ are homogeneous functions of integer degrees k and K > k, respectively. We present examples of integrable systems which were obtained by applying our main theorem.

Kategorie tematyczne

• 70Hxx: Hamiltonian and Lagrangian mechanics
• 37J30: Obstructions to integrability (nonintegrability criteria)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 94
• Numer: 1
• Strony: 221-232

Daty

wydano

2011

Twórcy

autor

Andrzej J. Maciejewski

• Institute of Astronomy, University of Zielona Góra, Licealna 9, 65-417, Zielona Góra, Poland

autor

Maria Przybylska

• Institute of Physics, University of Zielona Góra, Licealna 9, 65-417, Zielona Góra, Poland

Identyfikatory

DOI

10.4064/bc94-0-15