Numerical long-term integration of geodesic equations of motion

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OutlineProblem and motivationNumerical properties of the equationsStructure preserving integrator for Geodesic equationsNumerical experimentsSummary2/26 | Jonathan Seyrich (Numerical long-term integration) Tübingen | January 21, 2013
Problem and motivationGeodesic equations of motion◮ Comparably light particle m 0 in gravitational field of heavy central body◮ Described by Lagrangian L = 1 2 m 0g µν ẋ µ ẋ ν◮ Hamiltonian system with H = 12m 0g µν p µ p ν , p µ = ∂L∂ẋ µ◮ Equations of motion in short form y := (p, x):(dy dp) ( )dτ = −∇x H(p, x)dτ dx == f (y) (1)∇ p H(p, x)dτ3/26 | Jonathan Seyrich (Numerical long-term integration) Tübingen | January 21, 2013
Page 1: Numerical long-term integration of
Page 5 and 6: Numerical properties of the equatio
Page 11 and 12: Structure preserving integrator for
Page 13 and 14: Numerical experimentsTestcase: Mank
Page 15 and 16: Numerical experiments◮ We choose:
Page 17 and 18: Numerical experimentsρ(0) = 30.7:
Page 19 and 20: Numerical experimentsρ(0) = 1.7:st
Page 21 and 22: Numerical experimentsρ(0) = 0.7: c
Page 23 and 24: Numerical experiments◮ IGEM calcu
Page 25 and 26: Summary◮ Energy conservation impo
Page 27: SummaryReferences II26/26 | Jonatha

Numerical long-term integration of geodesic equations of motion

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