Numerical integration of dynamical systems with Lie series. Relativistic acceleration and non-gravitational forces

Details Numerical integration of dynamical systems with Lie series. Relativistic acceleration and non-gravitational forces Numerical integration of dynamical systems with Lie series. Relativistic acceleration and non-gravitational forces

Feb 2012

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012cemda.112..221b&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 112, Issue 2, pp.221-234

Astronomy and Astrophysics

Astronomy

Numerical Integration, Lie Series, General Relativity, Yarkovsky Effect

Scientific paper

The integration of the equations of motion in gravitational dynamical systems—either in our Solar System or for extra-solar planetary systems—being non integrable in the global case, is usually performed by means of numerical integration. Among the different numerical techniques available for solving ordinary differential equations, the numerical integration using Lie series has shown some advantages. In its original form (Hanslmeier and Dvorak, Astron Astrophys 132, 203, 1984), it was limited to the N-body problem where only gravitational interactions are taken into account. We present in this paper a generalisation of the method by deriving an expression of the Lie terms when other major forces are considered. As a matter of fact, previous studies have been done but only for objects moving under gravitational attraction. If other perturbations are added, the Lie integrator has to be re-built. In the present work we consider two cases involving position and position-velocity dependent perturbations: relativistic acceleration in the framework of General Relativity and a simplified force for the Yarkovsky effect. A general iteration procedure is applied to derive the Lie series to any order and precision. We then give an application to the integration of the equation of motions for typical Near-Earth objects and planet Mercury.

Affiliated with

Also associated with

No associations

Rating

Numerical integration of dynamical systems with Lie series. Relativistic acceleration and non-gravitational forces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Numerical integration of dynamical systems with Lie series. Relativistic acceleration and non-gravitational forces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Numerical integration of dynamical systems with Lie series. Relativistic acceleration and non-gravitational forces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1837940