{"id":"W2318779023","doi":"10.1115/detc2003/vib-48592","title":"Computation of Normal Forms for High Dimensional Nonlinear Systems and Application to Nonplanar Motions of a Cantilever Beam","year":2003,"lang":"en","type":"article","venue":"","topic":"Dynamics and Control of Mechanical Systems","field":"Engineering","cited_by":17,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"National Natural Science Foundation of China","keywords":"Cantilever; Nonlinear system; Computation; Maple; Symbolic computation; Beam (structure); Equations of motion; Polynomial; Differential equation; Operator (biology); Canonical form; Computer science; Partial differential equation; Mathematical analysis; Mathematics; Applied mathematics; Algorithm; Physics; Structural engineering; Classical mechanics; Engineering; Pure mathematics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001112704,0.00005939678,0.0001550933,0.00004048024,0.00001747771,0.000005294553,0.0000286746,0.0000398184,0.000001663827],"category_scores_gemma":[0.00000734661,0.0000509849,0.00002395375,0.0000565633,0.000005145307,0.00002912004,0.000004922042,0.00001955558,0.000001301079],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001492003,"about_ca_system_score_gemma":0.000007758926,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000130721,"about_ca_topic_score_gemma":0.00005207449,"domain_scores_codex":[0.9995103,0.000004468625,0.0002396016,0.0000746626,0.00008840614,0.00008254428],"domain_scores_gemma":[0.9997525,0.00002651364,0.00003792257,0.00006222805,0.00007652328,0.00004433338],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00001477913,0.00005310655,0.0001409193,0.000332155,0.00006692599,1.150697e-7,0.00002892656,0.8850426,0.03449659,0.07823107,0.0001454933,0.001447336],"study_design_scores_gemma":[0.000424629,0.00007641242,0.0005059676,0.00002706928,0.00001418434,0.000002345788,0.00001973583,0.9971263,0.001264858,0.000234359,0.0002377415,0.00006642079],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.315214,0.0000314664,0.6839475,0.00001196436,0.00009277913,0.0004012757,0.00005727024,0.0000186398,0.0002250604],"genre_scores_gemma":[0.9959038,0.000001238411,0.003954451,0.000008079301,0.00001521451,0.00004338983,0.00002323183,0.000009220314,0.00004130423],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6806898,"threshold_uncertainty_score":0.2079104,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.004189423689262312,"score_gpt":0.1953988550119984,"score_spread":0.1912094313227361,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}