The discovery of planets in binaries is one the most interesting outcomes of planetary research .
With the growing number of discoveries has also grown the interest on describing their formation , long-term evolution and potential habitability .
In this work we revisit the dynamics of planets in S-type binary systems .
For that purpose we develop explicit formulas for the secularized octupolar Hamiltonian , coupled with general relativistic corrections and non-conservative interactions .
We implemented those formulas in an open-source package SecDev3B , that can be used to reproduce our results or test improved versions of the models .
In order to test it , we study the long-term dynamical evolution of S-type binary planets during the pre-main-sequence phase of stellar evolution .
During that phase , stellar radius significantly changes in timescales similar to secular timescales .
We hypothesize that when close-encounters between the planet and its host star happens ( e.g .
via Lidov-Kozai effect ) , particularities in the secular formalism plus changes in stellar radius may alter significantly the dynamical evolution .
We study the well-known binary planet HD 80606b and found that an octupolar expansion of the conservative Hamiltonian is required to properly predict its dynamical evolution .
We also apply the dynamical model , enriched with results coming from stellar evolutionary models , to demonstrate that in S-type systems around low-mass stars , with relative high inclinations ( i _ { \mathrm { tot } } \geq 60 ^ { \circ } ) , moderate eccentricities ( 0.2 \leq e \leq 0.4 ) and planets located around 1 AU , the evolution of stellar radius during the first few hundreds of Myr , alters significantly the timescales of dynamical evolution .