Constrained n-Body Problems
作者： Wojciech Szumiński , Maria Przybylska
DOI: 10.1007/978-3-319-08266-0_22
关键词: Mathematical analysis 、 Mathematics 、 Integrable system 、 Poincaré conjecture 、 Differential (mathematics) 、 Motion (geometry) 、 Holonomic constraints 、 Galois group 、 Variational equation
摘要: We consider a problem of mass points interacting gravitationally whose motion is subjected to certain holonomic constraints. The restricted curves or surfaces. illustrate the complicated behaviour trajectories these systems using Poincare cross sections. For some models we prove non-integrability analysing properties differential Galois group variational equations along particular solutions considered systems. Also integrable cases are identified.
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