2015MNRAS.449.1691B

A system of equations is derived for the secular motion of a hierarchic triple stellar system. Mean anomalies of the inner binary system and of the outer star orbit are eliminated up to order 9 in the ratio of their Delaunay momenta. Thanks to the use of vectorial elements (angular momenta and Laplace vectors) the equations are non-singular, compact, and independent on the choice of the reference frame axes directions. In the limit of circular outer orbit, the secular Hamiltonian agrees with the forgotten solution by Brown. Being more complete, yet simpler, the present model differs from that of Krymolowski & Mazeh, except for the circular outer orbit limit. A simple extension of the secular equations of motion describing tidal friction is also provided.