SyMBA (Duncan, Levison, & Lee 1998)
- We need to do close encounter for planet formation simulations.
- Close encounters are very fast, thus we need a small timestep to resolve them.
- But, we cannot change the timestep in the symplectic integrator.
- Can fake the math out (Skeel & Biesiadecki 1994) by writing the Hamiltonian as
where
- Construct an integrator
with 
- If no encounter (
) then 
,
so large timesteps.
- If
then 
,
so small timesteps.
- So, in a practical sense we have a variable timestep integrator.
- Chambers (1999) used similar techniques to create Mercury.
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