{"id":"W2000777285","doi":"10.1109/tac.2012.2218671","title":"Geometric Criteria for the Quasi-Linearization of the Equations of Motion of Mechanical Systems","year":2012,"lang":"en","type":"article","venue":"IEEE Transactions on Automatic Control","topic":"Control and Stability of Dynamical Systems","field":"Engineering","cited_by":10,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Scalar curvature; Mathematical analysis; Tangent bundle; Riemannian manifold; Linearization; Constant curvature; Pointwise; Riemannian geometry; Manifold (fluid mechanics); Ricci curvature; Fundamental theorem of Riemannian geometry; Tangent space; Curvature; Nonlinear system; Geometry; Physics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009570791,0.0008187344,0.0003826443,0.001461981,0.0005640938,0.001395567,0.0007275587,0.0007588432,0.008078975],"category_scores_gemma":[0.002503506,0.000313684,0.0006160232,0.0002922197,0.002240753,0.001821536,0.002185631,0.001104753,0.001417078],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009217102,"about_ca_system_score_gemma":0.0006379064,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001292956,"about_ca_topic_score_gemma":0.0007949129,"domain_scores_codex":[0.9993067,0.0001890806,0.00004897552,0.0001131253,0.0002595177,0.00008261504],"domain_scores_gemma":[0.9985233,0.0003258438,0.0003850588,0.00009564526,0.0005183914,0.0001518229],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00002974339,0.00003923419,0.0007618482,0.0001065109,0.00002360655,0.0002493792,0.0004105221,0.03316631,0.008726445,0.9452947,0.001439643,0.009751941],"study_design_scores_gemma":[0.00005247464,0.0004553299,0.002486666,0.00004390889,0.00002592898,0.000407985,0.0003374816,0.3521667,0.005548811,0.6217592,0.01662983,0.00008581773],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1389447,0.0008245136,0.8219219,0.00159458,0.0001874527,0.0002990215,0.0003436082,0.0004799522,0.03540425],"genre_scores_gemma":[0.937799,0.0004927421,0.04830813,0.000328238,0.0002890707,0.0002696468,0.0004827575,0.000162573,0.01186782],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008078975,"threshold_uncertainty_score":0.02702683,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0182256129332916,"score_gpt":0.2407160607187116,"score_spread":0.22249044778542,"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."}}