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The interesting complexity originates from the interplay between the internal structure and external tidal forcing. Recent and upcoming observing missions of exoplanets and stars in the galaxy help to provide constraints on the physics of tidal dissipation. It is timely to develop new N-body codes, which allow for experimentation with various tidal models and numerical implementations. We present the open-source N-body code TIDYMESS, which stands for \u2018TIdal DYnamics of Multibody ExtraSolar Systems\u2019. This code implements a Creep deformation law for the bodies, parametrized by their fluid Love numbers and fluid relaxation times. Due to tidal and centrifugal deformations, we approximate the general shape of a body to be an ellipsoid. We calculate the associated gravitational field to quadruple order, from which we derive the gravitational accelerations and torques. The equations\u00a0of motion for the orbits, spins and deformations are integrated directly using a fourth-order integration method based on a symplectic composition. We implement a novel integration method for the deformations, which allows for a time-step solely dependent on the orbits, and not on the spin periods or fluid relaxation times. This feature greatly speeds up the calculations, while also improving the consistency when comparing different tidal regimes. We demonstrate the capabilities and performance of TIDYMESS, particularly in the niche regime of parameter space where orbits are chaotic and tides become non-linear.<\/jats:p>","DOI":"10.1093\/mnras\/stad1133","type":"journal-article","created":{"date-parts":[[2023,4,19]],"date-time":"2023-04-19T06:07:50Z","timestamp":1681884470000},"page":"2885-2900","source":"Crossref","is-referenced-by-count":7,"title":["A direct <i>N<\/i>-body integrator for modelling the chaotic, tidal dynamics of multibody extrasolar systems: <tt>TIDYMESS<\/tt>"],"prefix":"10.1093","volume":"522","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6911-6584","authenticated-orcid":false,"given":"Tjarda C N","family":"Boekholt","sequence":"first","affiliation":[{"name":"Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, University of Oxford , Parks Road, Oxford, OX1 3PU , UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8946-8579","authenticated-orcid":false,"given":"Alexandre C M","family":"Correia","sequence":"additional","affiliation":[{"name":"CFisUC, Departamento de F\u00edsica, Universidade de Coimbra , 3004-516 Coimbra , Portugal"},{"name":"IMCCE, UMR8028 CNRS, Observatoire de Paris, PSL Universit\u00e9 , 77 Avenue Denfert-Rochereau, 75014 Paris , France"}]}],"member":"286","published-online":{"date-parts":[[2023,4,18]]},"reference":[{"key":"2024013011121988500_bib1","doi-asserted-by":"publisher","first-page":"2268","DOI":"10.1111\/j.1365-2966.2009.14694.x","volume":"395","author":"Barker","year":"2009","journal-title":"MNRAS"},{"key":"2024013011121988500_bib2","doi-asserted-by":"publisher","first-page":"4749","DOI":"10.1093\/mnras\/sty1758","volume":"479","author":"Bataille","year":"2018","journal-title":"MNRAS"},{"key":"2024013011121988500_bib3","doi-asserted-by":"publisher","first-page":"1069","DOI":"10.1046\/j.1365-8711.2002.05736.x","volume":"336","author":"Baumgardt","year":"2002","journal-title":"MNRAS"},{"key":"2024013011121988500_bib4","doi-asserted-by":"publisher","first-page":"L119","DOI":"10.1088\/0004-637X\/751\/2\/119","volume":"751","author":"Beaug\u00e9","year":"2012","journal-title":"ApJ"},{"key":"2024013011121988500_bib5","doi-asserted-by":"publisher","first-page":"L175","DOI":"10.1086\/171983","volume":"400","author":"Bildsten","year":"1992","journal-title":"ApJ"},{"key":"2024013011121988500_bib6","doi-asserted-by":"publisher","first-page":"3576","DOI":"10.1093\/mnras\/stw1504","volume":"461","author":"Boekholt","year":"2016","journal-title":"MNRAS"},{"key":"2024013011121988500_bib7","doi-asserted-by":"publisher","first-page":"3932","DOI":"10.1093\/mnras\/staa452","volume":"493","author":"Boekholt","year":"2020","journal-title":"MNRAS"},{"key":"2024013011121988500_bib8","doi-asserted-by":"publisher","first-page":"3281","DOI":"10.1093\/mnras\/stac3777","volume":"519","author":"Boekholt","year":"2023","journal-title":"MNRAS"},{"key":"2024013011121988500_bib9","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1051\/0004-6361\/201525909","volume":"583","author":"Bolmont","year":"2015","journal-title":"A&A"},{"key":"2024013011121988500_bib10","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/s10569-016-9708-x","volume":"126","author":"Bou\u00e9","year":"2016","journal-title":"Cel. 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