The　numerical　manifold　method　(NMM)　surmounting　the　mesh　dependence　has　successfully　solved　very　complicated　problems　involving　small　deformation　and　large　movement,　but　had　few　applications　to　large　deformation　and　large　rotation　problems　because　the　false　volume　expansion　and　other　issues　exist.　In　this　study　it　is　shown　that　the　false　volume　expansion　in　NMM　can　be　excellently　resolved　by　using　the　S-R　(strain-rotation)　decomposition　theorem　which　can　precisely　reflect　complex　physical　behaviors　occurring　in　the　process　of　large　rotation　and　large　deformation.　The　numerical　methods　based　on　the　S-R　decomposition　theorem　have　been　limited　to　the　static　analysis　of　large　deformations.　To　remove　this　limitation,　a　new　formulation　taking　into　account　dynamical　features　is　proposed　based　on　the　weak　form　of　momentum　conservation　law.　Under　the　framework　of　NMM,　the　generalized-a　method　is　employed　to　discretize　the　temporal　variables.　The　updates　of　variables　are　described　using　the　updated　co-moving　coordinate　system.　Thus,　a　new　method　named　S-R-D-based　NMM　is　established.　The　new　formulation　can　be　implemented　in　any　other　partition　of　unity　based　methods　as　well,　so　as　to　improve　the　performances　of　such　methods　in　the　analysis　of　dynamic　large　deformations.　(C)　2016　Elsevier　B.V.　All　rights　reserved.