## Time reversibility is important because it guarantees conservation of energy, angular momentum, etc. (in many cases).

- Suppose the integrator makes an error after one orbital period. Now reverse. Is the error -? No! The time-reversed orbit is a solution of the original ODE (with
*v*replaced with -*v*), so the energy error is still +. But we've returned to our starting point, so we know the final energy error is zero. Hence = 0!

- Suppose the integrator makes an error after one orbital period. Now reverse. Is the error -? No! The time-reversed orbit is a solution of the original ODE (with
## Leapfrog is only second order, but

__very__stable.