Numerical long-term integration of geodesic equations of motion
Numerical long-term integration of geodesic equations of motion
Numerical long-term integration of geodesic equations of motion
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<strong>Numerical</strong> properties <strong>of</strong> the <strong>equations</strong>Flow Φ h ,y n+1 = Φ h (y n )<strong>of</strong> Gauss collocation schemes preserves (cf. [Hairer et al., 2006]):◮ Symmetry:◮ Symplecticity:( ) T ( )∂Φh (y) ∂Φh (y)J= J, J =∂y∂y◮ Reversibility:Φ −h = Φ −1h(2)( ) 0 Id. (3)−Id 0Φ −1h◦ ζ = ζ ◦ Φ h , ζ(p, x) = (−p, x). (4)7/26 | Jonathan Seyrich (<strong>Numerical</strong> <strong>long</strong>-<strong>term</strong> <strong>integration</strong>) Tübingen | January 21, 2013
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