The　vibrations　of　gyroscopic　continua　may　induce　complex　mode　functions.　The　continuous　model　governed　by　partial　differential　equations　(PDEs)　as　well　as　the　discretized　model　governed　by　ordinary　differential　equations　(ODEs)　are　used　in　the　dynamical　study　of　the　gyroscopic　continua.　The　invariant　manifold　method　is　employed　to　derive　the　complex　mode　functions　of　the　discretized　models,　which　are　compared　to　the　mode　functions　derived　from　the　continuous　model.　It　is　found　that　the　complex　mode　functions　constituted　by　trial　functions　of　the　discretized　system　yield　good　agreement　with　that　derived　by　the　continuous　system.　On　the　other　hand,　the　modal　analysis　of　discretized　system　demonstrates　the　phase　difference　among　the　general　coordinates　presented　by　trial　functions,　which　reveals　the　physical　explanation　of　the　complex　modes.