Building on the results of a previous paper, we compute for the first time a full first-order perturbative solution for the angular coordinates in the restricted post-Newtonian two-body problem with spin. The analytical integration of the angular coordinates, based on the theory of the Weierstrassian functions, allows us to investigate thoroughly the spin-orbit and spin-spin interactions, and to derive several new results. The application of our solution to a selection of idealized physical systems of interest reveals a rich variety of dynamical behaviours driven by purely relativistic effects. In particular, we highlight a new relativistic nutational motion resulting from the combined spin-orbit and spin-spin interactions.
A first-order secular theory for the post-newtonian two-body problem with spin - II. A complete solution for the angular coordinates in the restricted case
Carloni S.
2014-01-01
Abstract
Building on the results of a previous paper, we compute for the first time a full first-order perturbative solution for the angular coordinates in the restricted post-Newtonian two-body problem with spin. The analytical integration of the angular coordinates, based on the theory of the Weierstrassian functions, allows us to investigate thoroughly the spin-orbit and spin-spin interactions, and to derive several new results. The application of our solution to a selection of idealized physical systems of interest reveals a rich variety of dynamical behaviours driven by purely relativistic effects. In particular, we highlight a new relativistic nutational motion resulting from the combined spin-orbit and spin-spin interactions.
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