06faa3c1-215c-4a42-b074-1abd705fb51120220309013841565naun:naunmdt@crossref.orgMDT DepositInternational Journal of Mathematics and Computers in Simulation1998-015910.46300/9102http://www.naun.org/cms.action?id=2826110202211020221610.46300/9102.2022.16https://npublications.com/journals/mcs/2022.phpMaxim V.ShamolinInstitute of Mechanics, Lomonosov Moscow State University, Moscow, 119192, Russian FederationStudy of the dynamics of a multidimensional solid depends on the force-field structure. As reference results, we consider the equations of motion of low-dimensional solids in the field of a medium-drag force. Then it becomes possible to generalize the dynamic part of equations to the case of the motion of a solid, which is multidimensional in a similarly constructed force field, and to obtain the full list of transcendental first integrals. The obtained results are of importance in the sense that there is a nonconservative moment in the system, whereas it is the potential force field that was used previously.38202238202242588https://npublications.com/journals/mcs/2022/a162002-008(2022).pdf10.46300/9102.2022.16.8https://npublications.com/journals/mcs/2022/a162002-008(2022).pdfM. V. Shamolin, Methods of analysis of dynamical systems with various disssipation in rigid body dynamics, Moscow, Russian Federation: Ekzamen, 2007. M. V. Shamolin, Some questions of the qualitative theory of ordinary differential equations and dynamics of a rigid body interacting with a medium, Journal of Mathematical Sciences, Vol. 110, No. 2, 2002, p. 2526–2555. M. V. Shamolin, Foundations of differential and topological diagnostics, Journal of Mathematical Sciences, Vol. 114, No. 1, 2003, p. 976–1024. M. V. Shamolin, New integrable cases and families of portraits in the plane and spatial dynamics of a rigid body interacting with a medium, Journal of Mathematical Sciences, Vol. 114, No. 1, 2003, p. 919–975. 10.1023/b:joth.0000029572.16802.e6M. V. Shamolin, Classes of variable dissipation systems with nonzero mean in the dynamics of a rigid body, Journal of Mathematical Sciences, Vol. 122, No. 1, 2004, p. 2841–2915. M. V. Shamolin, Structural stable vector fields in rigid body dynamics, Proc. of 8th Conf. on Dynamical Systems (Theory and Applications) (DSTA 2005), Lodz, Poland, Dec. 12–15, 2005; Tech. Univ. Lodz, 2005, Vol. 1, p. 429–436. 10.1002/pamm.201010024M. V. Shamolin, The cases of integrability in terms of transcendental functions in dynamics of a rigid body interacting with a medium, Proc. of 9th Conf. on Dynamical Systems (Theory and Applications) (DSTA 2007), Lodz, Poland, Dec. 17–20, 2007; Tech. Univ. Lodz, 2007, Vol. 1, p. 415–422. 10.1002/pamm.200810137M. V. Shamolin, Methods of analysis of dynamic systems with various dissipation in dynamics of a rigid body, ENOC-2008, CD-Proc., June 30–July 4, 2008, Saint Petersburg, Russia, 6 p. 10.1002/pamm.200810137M. V. Shamolin, Some methods of analysis of the dynami systems with various dissipation in dynamics of a rigid body, PAMM (Proc. Appl. Math. Mech.), 8, 10137–10138 (2008) / DOI 10.1002/pamm.200810137. 10.1007/s10958-009-9657-yM. V. Shamolin, Dynamical systems with variable dissipation: methods and applications, Proc. of 10th Conf. on Dynamical Systems (Theory and Applications) (DSTA 2009), Lodz, Poland, Dec. 7–10, 2009; Tech. Univ. Lodz, 2009, p. 91–104. 10.1002/pamm.200910044M. V. Shamolin, New cases of integrability in dynamics of a rigid body with the cone form of its shape interacting with a medium, PAMM (Proc. Appl. Math. Mech.), 9, 139–140 (2009) / DOI 10.1002/pamm. 200910044. 10.1002/pamm.200910044M. V. Shamolin, The various cases of complete integrability in dynamics of a rigid body interacting with a medium, Multibody Dynamics, ECCOMAS Thematic Conf. Warsaw, Poland, 29 June–2 July 2009, CD-Proc.; Polish Acad. Sci., Warsaw, 2009, 20 p. M. V. Shamolin, Dynamical systems with various dissipation: background, methods, applications // CD-Proc. of XXXVIII Summer SchoolConf. ”Advances Problems in Mechanics” (APM 2010), July 1–5, 2010, St. Petersburg (Repino), Russia; St. Petersburg, IPME, 2010, p. 612–621. 10.1002/pamm.201010024M. V. Shamolin, Integrability and nonintegrability in terms of transcendental functions in dynamics of a rigid body, PAMM (Proc. Appl. Math. Mech.), 10, 63–64 (2010) / DOI 10.1002/pamm.201010024. 10.1002/pamm.201210013M. V. Shamolin, Cases of complete integrability in transcendental functions in dynamics and certain invariant indices, CD-Proc. 5th Int. Sci. Conf. on Physics and Control PHYSCON 2011, Leon, Spain, September 5–8, 2011. Leon, Spain, 5 p. M. V. Shamolin, Variety of the cases of integrability in dynamics of a 2D-, 3D-, and 4D-rigid body interacting with a medium, Proc. of 11th Conf. on Dynamical Systems (Theory and Applications) (DSTA 2011), Lodz, Poland, Dec. 5–8, 2011; Tech. Univ. Lodz, 2011, p. 11–24. M. V. Shamolin, Cases of integrability in dynamics of a rigid body interacting with a resistant medium, CD-proc., 23th International Congress of Theoretitical and Applied Mechanics, August 19–24, 2012, Beijing, China; Beijing, China Science Literature Publishing House, 2012, 2 p. 10.17925/eor.2012.06.05.283M. V. Shamolin, Variety of the cases of integrability in dynamics of a 2D-, and 3D-rigid body interacting with a medium, 8th ESMC 2012, CD-Materials (Graz, Austria, July 9–13, 2012), Graz, Graz, Austria, 2012, 2 p.