Numerical integration in celestial mechanics: a case for contact geometry
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Several dynamical systems of interest in celestial mechanics can be written in the form q̈ + ∂ V(q,t)/∂ q+f(t)q̇=0 . i=1,...,n . For instance, the modified Kepler problem, the spin--orbit model and the Lane--Emden equation all belong to this class. In this work we start an investigation of these models from the point of view of contact geometry. In particular we focus on the (contact) Hamiltonisation of these models and on the construction of the corresponding geometric integrators.
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