Phase fitted variational integrators using interpolation techniques on non regular grids
Abstract
The possibility of deriving a high order variational integrator that utilizes intermediate nodes within one time interval time to approximate the action integral is investigated. To this purpose, we consider time nodes chosen through linear or exponential expressions and through the roots of Chebyshev polynomial of the first kind in order to approximate the configurations and velocities at those nodes. Then, by defining the Lagrange function as a weighted sum over the discrete Lagrangians corresponding to the curve segments, we apply the phase fitted technique to obtain an exponentially fitted numerical scheme. The resulting integrators are tested for the numerical simulation of the planar two body problem with high eccentricity and of the threebody orbital motion within a solar system.
 Publication:

Numerical Analysis and Applied Mathematics ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics
 Pub Date:
 September 2012
 DOI:
 10.1063/1.4756679
 Bibcode:
 2012AIPC.1479.2402K
 Keywords:

 exponential distribution;
 integral equations;
 interpolation;
 polynomials;
 02.60.Ed;
 Interpolation;
 curve fitting