{ "classification": "reduced-manufacturing-tilt sensitivity case for passive axisymmetric-cylinder large-angle branch", "source_parameter_file": "/studies/passive-axisymmetric-cylinder/hamdi-reduced-tilt.parameters.json", "source_parameter_sha256": "4c7f083f6fb925238a44f34888c2d01ea32b60338f0b5a7801b0db9210a8dd1e", "scope": "three angular DOF; translational MBS dynamics omitted", "geometry": { "inertia_tensor_kg_m2": [ [ 1.0003294820575554e-07, 3.295950123334124e-11, 1.258241255645581e-09 ], [ 3.295950123334124e-11, 1.0003297079842296e-07, 1.2586725712997165e-09 ], [ 1.258241255645581e-09, 1.2586725712997165e-09, 1.4805029497597975e-07 ] ], "principal_moments_kg_m2": [ 9.999999999892008e-08, 9.99999999989201e-08, 1.4811621398231806e-07 ], "physical_symmetry_axis_in_magnetic_body_frame": [ 0.026167978121471928, 0.02617694830787311, 0.9993147673772869 ], "axisymmetry_relative_transverse_split": 1.323488980099137e-16, "axis_over_transverse_inertia": 1.4811621398391759, 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"rms_full_state_distance": 0.13534508957535124, "maximum_full_state_distance": 0.16092021123076006 }, { "lag_drive_cycles": 284, "lag_s": 4.733333333333333, "median_full_state_distance": 0.1474423994364086, "rms_full_state_distance": 0.14752410253760495, "maximum_full_state_distance": 0.17179965748849657 } ], "theta_spectrum_peaks_late_60_100_s": [ { "frequency_hz": 14.800000000034492, "amplitude_deg": 59.7795634673284, "relative_amplitude": 1.0 }, { "frequency_hz": 44.37500000010342, "amplitude_deg": 6.875583006219865, "relative_amplitude": 0.11501561081116976 }, { "frequency_hz": 29.575000000068925, "amplitude_deg": 3.9504243261891947, "relative_amplitude": 0.06608319126231556 }, { "frequency_hz": 88.75000000020684, "amplitude_deg": 1.137926185621339, "relative_amplitude": 0.019035371281077604 }, { "frequency_hz": 73.95000000017234, "amplitude_deg": 0.9255547957172573, "relative_amplitude": 0.015482796160314971 }, { "frequency_hz": 59.15000000013785, "amplitude_deg": 0.49417899394645753, "relative_amplitude": 0.008266687899394639 }, { "frequency_hz": 118.32500000027576, "amplitude_deg": 0.4608371628565599, "relative_amplitude": 0.007708941586842188 }, { "frequency_hz": 147.90000000034468, "amplitude_deg": 0.2838721849158179, "relative_amplitude": 0.0047486493452058055 }, { "frequency_hz": 177.47500000041362, "amplitude_deg": 0.20790991375374204, "relative_amplitude": 0.003477942990791025 }, { "frequency_hz": 103.52500000024126, "amplitude_deg": 0.2000599914732248, "relative_amplitude": 0.0033466285109720567 }, { "frequency_hz": 133.1000000003102, "amplitude_deg": 0.173258982315429, "relative_amplitude": 0.0028982978841945043 }, { "frequency_hz": 162.7000000003792, "amplitude_deg": 0.1499764659444376, "relative_amplitude": 0.0025088250439701675 } ], "interpretation": "A small stroboscopic distance would support a periodic orbit. The reported best residual and multiple spectral lines are used only to distinguish near-periodic from bounded quasiperiodic behavior; they are not a chaos proof." }, "comparison_to_original_5p476_deg_benchmark": { "original_benchmark_manufacturing_tilt_deg": 5.476228447888703, "reduced_case_manufacturing_tilt_deg": 2.1211991681897233, "tilt_ratio_reduced_over_original": 0.3873467274740022, "tilt_reduction_percent": 61.26532725259979, "original_tilt_azimuth_deg": 135.23482434892398, "reduced_case_tilt_azimuth_deg": 45.009818598520646, "wrapped_azimuth_change_deg": -90.22500575040334, "same_principal_moments_max_abs_difference_kg_m2": 6.2449886316487445e-18, "same_height_over_diameter_difference": 3.0984437238146256e-11, "important_nonisolated-variable_caveat": "The tilt azimuth and launch state also changed; this verifies persistence under the supplied modified parameter set, not a controlled one-parameter proof that tilt magnitude alone caused the difference.", "original_benchmark_late_160_200_s": { "range_s": [ 160.0, 200.0 ], "drive_cycles": 2400, "theta_mean_deg": 103.46905965668661, "theta_min_deg": 31.507608653447996, "theta_max_deg": 178.44916505844222, "theta_span_deg": 146.94155640499423, "theta_slope_deg_s": 0.001708857382917173, "cylinder_theta_mean_deg": 101.54481054498763, "symmetry_spin_mean_rad_s": -6.784346276738501, "symmetry_spin_abs_mean_rad_s": 6.784346276738501, "symmetry_spin_std_rad_s": 2.507203003890489, "symmetry_spin_slope_rad_s2": -4.443732875356196e-05, "body_speed_mean_rad_s": 104.02403089446989, "body_speed_slope_rad_s2": -0.0011739877795341742, "u_mean": 0.14803946598772638, "u_positive_fraction": 0.6715232847671523, "kinetic_mean_J": 0.000604953352411167, "potential_mean_J": 0.0003234308270184723, "total_mean_J": 0.0009283841794296393, "energy_change_rate_W": -3.130261477047978e-05, "field_power_mean_W": 8.757947944113056e-05, "damping_loss_mean_W": 0.00011892076525336958, "power_balance_W": -3.134128581223901e-05, "power_closure_error_W": 3.867104175922997e-08, "symmetry_torque_mean_Nm": -8.636759428765337e-08, "symmetry_spin_power_mean_W": 5.941463954221917e-07, "magnetic_body_omega3_mean_rad_s": -15.748726503299027, "magnetic_body_omega3_min_rad_s": -18.390467436061986, "magnetic_body_omega3_max_rad_s": -12.937514894011354, "ap_angular_error_mean_deg": 81.43254245533382, "ap_angular_error_median_deg": 80.22783486488464 }, "reduced_case_late_60_100_s": { "range_s": [ 60.0, 100.0 ], "drive_cycles": 2400, "theta_mean_deg": 102.76425042580067, "theta_min_deg": 29.859082734746274, "theta_max_deg": 179.8904567927216, "theta_span_deg": 150.03137405797534, "theta_slope_deg_s": -0.0012958984679569726, "cylinder_theta_mean_deg": 101.92737617652796, "symmetry_spin_mean_rad_s": -8.194704733618046, "symmetry_spin_abs_mean_rad_s": 8.194704733618046, "symmetry_spin_std_rad_s": 0.9749579608393216, "symmetry_spin_slope_rad_s2": -1.2289509278446519e-05, "body_speed_mean_rad_s": 103.95985174297122, "body_speed_slope_rad_s2": -0.0005347469206344024, "u_mean": 0.1475215417619229, "u_positive_fraction": 0.6758432415675844, "kinetic_mean_J": 0.0006054741898991704, "potential_mean_J": 0.0003222992864555091, "total_mean_J": 0.0009277734763546795, "energy_change_rate_W": -8.310385014328223e-06, "field_power_mean_W": 0.00011041843786176487, "damping_loss_mean_W": 0.00011872759510702909, "power_balance_W": -8.309157245264218e-06, "power_closure_error_W": -1.2277690640046933e-09, "symmetry_torque_mean_Nm": -7.945123643636501e-08, "symmetry_spin_power_mean_W": 6.6134405741769e-07, "magnetic_body_omega3_mean_rad_s": -11.669490010903152, "magnetic_body_omega3_min_rad_s": -12.668975433366375, "magnetic_body_omega3_max_rad_s": -10.59695731624315, "ap_angular_error_mean_deg": 81.46447002959422, "ap_angular_error_median_deg": 79.90574107581979 } }, "key_interpretation": { "sampled_theta_max_is_below_exact_180_deg": true, "closest_sampled_approach_to_180_deg": 0.08877887368538495, "near_south_pole_within_0p1_deg": true, "whole_run_theta_min_rad": 0.5208755765313077, "whole_run_theta_min_exceeds_0p75_rad": false, "amount_theta_min_is_below_0p75_rad": 0.22912442346869233, "passive_no_imposed_spin_acceleration": true, "sustains_large_angle": true, "negative_local_omega3_with_forward_body_x_lab_winding": true } }