although no output filtering was done when the numerical integrations were in process， we applied a low-pass filter to the raw orbital data after we had completed all the calculations. see section 4.1 for more detail.
2.4 error estimation
2.4.1 relative errors in total energy and angular momentum
according to one of the basic properties of symplectic integrators， which conserve the physically conservative quantities well (total orbital energy and angular momentum)， our long-