"""Bölüm 15: kutupsal ve rasyonel konik laboratuvarı. Uygulama, bir odağı merkez alan sentetik ideal bir eliptik yörünge geometrisidir. Dinamik, zaman yasası, kütleçekim parametresi, efemeris, bozucu etkiler, koordinat zamanı ve görev güvenliği modele dahil değildir. """ from __future__ import annotations import numpy as np from agbook import ( canonical_array_sha256, focus_directrix_residuals, polar_conic_algebraic_residuals, polar_conic_diagnostics, polar_conic_frame, polar_conic_points, rational_conic_points, rotation_matrix_2d, ) def main() -> None: length_unit = "km" focus_km = np.array([0.0, 0.0]) periapsis_direction_deg = 35.0 angle_rad = np.deg2rad(periapsis_direction_deg) axis_direction = np.array([np.cos(angle_rad), np.sin(angle_rad)]) eccentricity = 0.4 semilatus_rectum_km = 8400.0 frame = polar_conic_frame( focus_km, axis_direction, eccentricity, semilatus_rectum_km, ) semi_major_km = semilatus_rectum_km / (1.0 - eccentricity**2) semi_minor_km = semilatus_rectum_km / np.sqrt(1.0 - eccentricity**2) focal_distance_km = eccentricity * semi_major_km center_km = focus_km - focal_distance_km * frame.axis_direction second_focus_km = center_km - focal_distance_km * frame.axis_direction characteristic_angles_rad = np.deg2rad([0.0, 60.0, 90.0, 120.0, 180.0]) diagnosis = polar_conic_diagnostics( frame.focus, frame.axis_direction, frame.eccentricity, frame.semilatus_rectum, characteristic_angles_rad, ) periapsis_km = diagnosis.radii[0] apoapsis_km = diagnosis.radii[-1] comparison_angles_rad = np.deg2rad([-140.0, -90.0, -30.0, 0.0, 45.0, 110.0]) tangent_half_angles = np.tan(comparison_angles_rad / 2.0) polar_points_km = polar_conic_points( frame.focus, frame.axis_direction, frame.eccentricity, frame.semilatus_rectum, comparison_angles_rad, ) rational_points_km = rational_conic_points( frame.focus, frame.axis_direction, frame.eccentricity, frame.semilatus_rectum, tangent_half_angles, ) representation_gap_km = np.linalg.norm( polar_points_km - rational_points_km, axis=1, ) uniform_angles_rad = np.linspace(-np.pi, np.pi, 145) uniform_points_km = polar_conic_points( frame.focus, frame.axis_direction, frame.eccentricity, frame.semilatus_rectum, uniform_angles_rad, ) chord_lengths_km = np.linalg.norm(np.diff(uniform_points_km, axis=0), axis=1) chord_ratio = float(np.max(chord_lengths_km) / np.min(chord_lengths_km)) rotation = rotation_matrix_2d(np.deg2rad(23.0)) translation_km = np.array([1300.0, -700.0]) moved_focus_km = rotation @ frame.focus + translation_km moved_axis = rotation @ frame.axis_direction moved_points_km = polar_conic_points( moved_focus_km, moved_axis, frame.eccentricity, frame.semilatus_rectum, comparison_angles_rad, ) expected_moved_points_km = polar_points_km @ rotation.T + translation_km rigid_gap_km = np.linalg.norm(moved_points_km - expected_moved_points_km, axis=1) points_m = 1000.0 * polar_points_km residual_km = polar_conic_algebraic_residuals( polar_points_km, frame.focus, frame.axis_direction, frame.eccentricity, frame.semilatus_rectum, ) residual_m = polar_conic_algebraic_residuals( points_m, 1000.0 * frame.focus, frame.axis_direction, frame.eccentricity, 1000.0 * frame.semilatus_rectum, ) np.testing.assert_allclose(semi_major_km, 10000.0, atol=1e-12) np.testing.assert_allclose(periapsis_km, 6000.0, atol=1e-12) np.testing.assert_allclose(apoapsis_km, 14000.0, atol=3e-12) np.testing.assert_allclose(polar_points_km, rational_points_km, atol=4e-12) np.testing.assert_allclose(rigid_gap_km, 0.0, atol=4e-12) np.testing.assert_allclose(residual_m, residual_km, atol=3e-15) assert diagnosis.maximum_absolute_algebraic_residual < 2e-15 assert diagnosis.maximum_absolute_focus_directrix_residual < 4e-12 assert chord_ratio > 1.5 rational_algebraic = polar_conic_algebraic_residuals( rational_points_km, frame.focus, frame.axis_direction, frame.eccentricity, frame.semilatus_rectum, ) rational_geometric_km = focus_directrix_residuals( rational_points_km, frame.focus, frame.directrix, frame.eccentricity, ) signature_values = np.concatenate( [ focus_km, axis_direction, np.array([eccentricity, semilatus_rectum_km]), frame.directrix, np.array([semi_major_km, semi_minor_km, focal_distance_km]), center_km, second_focus_km, characteristic_angles_rad, diagnosis.radii, diagnosis.points.ravel(), comparison_angles_rad, tangent_half_angles, polar_points_km.ravel(), rational_points_km.ravel(), uniform_angles_rad, chord_lengths_km, rotation.ravel(), translation_km, moved_points_km.ravel(), residual_km, residual_m, ] ) print("uzunluk_birimi:", length_unit) print("model: sentetik_ideal_eliptik_yorunge_geometrisi") print("dinamik_ve_efemeris_modeli_mi: False") print("gercek_gorev_veya_guvenlik_hesabi_mi: False") print("odak_km:", frame.focus) print("periapsis_yonu_derece:", periapsis_direction_deg) print("dismerkezlik:", frame.eccentricity) print("yari_odak_kirisi_km:", frame.semilatus_rectum) print("yari_buyuk_eksen_km:", f"{semi_major_km:.6f}") print("yari_kucuk_eksen_km:", f"{semi_minor_km:.6f}") print("merkez_km:", center_km) print("ikinci_odak_km:", second_focus_km) print("periapsis_uzakligi_km:", f"{periapsis_km:.6f}") print("apoapsis_uzakligi_km:", f"{apoapsis_km:.6f}") print("ornek_acilar_derece:", np.rad2deg(characteristic_angles_rad)) print("ornek_yaricaplar_km:", diagnosis.radii) print( "en_buyuk_cebirsel_artik:", f"{max(diagnosis.maximum_absolute_algebraic_residual, np.max(np.abs(rational_algebraic))):.3e}", ) print( "en_buyuk_odak_dogrultman_artigi_km:", f"{max(diagnosis.maximum_absolute_focus_directrix_residual, np.max(np.abs(rational_geometric_km))):.3e}", ) print("en_buyuk_kutupsal_rasyonel_fark_km:", f"{np.max(representation_gap_km):.3e}") print("esit_aci_adimi_kiris_orani:", f"{chord_ratio:.6f}") print("rijit_hareket_kovaryant_mi:", bool(np.max(rigid_gap_km) < 4e-12)) print("ortak_olcekte_boyutsuz_artik_korundu_mu:", bool(np.allclose(residual_m, residual_km, atol=3e-15))) print("bilimsel_imza:", canonical_array_sha256(signature_values)) if __name__ == "__main__": main()