坐标变换

概述

地球参考系之间的坐标变换是轨道计算的基础。从惯性系（J2000/ICRF）到地固系（ECF）的变换链路由四个环节组成：

J2000 → MOD       岁差 (precession)
MOD   → TOD       章动 (nutation)
TOD   → GTOD      地球自转 (Earth rotation, GAST)
GTOD  → ECF       极移 (polar motion)

本例演示完整的变换链路、快捷函数、矩阵获取以及往返精度。

使用示例

#include "ast/FrameTransform.hpp"
#include "ast/TimePoint.hpp"
#include "ast/Vector.hpp"
#include "ast/Matrix.hpp"

#include <iostream>
#include <iomanip>
#include <clocale>

AST_USING_NAMESPACE

int main()
{
    setlocale(LC_ALL, ".UTF-8");

    // ============================================================
    // 选定时刻和 J2000 坐标
    //   2024-01-01 00:00:00 UTC, 一颗 LEO 卫星
    // ============================================================
    TimePoint tp = TimePoint::FromUTC(2024, 1, 1, 0, 0, 0.0);

    Vector3d rJ2000{-4.463444e6,  4.463444e6,  3.644387e6};  // 位置 (m)
    Vector3d vJ2000{-5.668038e3, -5.233606e3,  1.773562e2};  // 速度 (m/s)

    std::cout << "===== J2000 坐标 (2024-01-01 00:00:00 UTC) =====" << std::endl;
    std::cout << "  r_J2000 = " << rJ2000.x() << "  " << rJ2000.y() << "  " << rJ2000.z() << std::endl;
    std::cout << "  v_J2000 = " << vJ2000.x() << "  " << vJ2000.y() << "  " << vJ2000.z() << std::endl;

    // ============================================================
    // 快捷转换: J2000 → ECF (位置+速度)
    // ============================================================
    Vector3d rECF, vECF;
    aJ2000ToECF(tp, rJ2000, vJ2000, rECF, vECF);

    std::cout << "\n===== J2000 → ECF (快捷, 含速度) =====" << std::endl;
    std::cout << "  r_ECF = " << rECF.x() << "  " << rECF.y() << "  " << rECF.z() << std::endl;
    std::cout << "  v_ECF = " << vECF.x() << "  " << vECF.y() << "  " << vECF.z() << std::endl;

    // ============================================================
    // 逐步转换: J2000 → MOD → TOD → GTOD → ECF
    // ============================================================
    Vector3d rMOD, rTOD, rGTOD, rECF2;
    aJ2000ToMOD(tp, rJ2000, rMOD);
    aMODToTOD(tp, rMOD, rTOD);
    aTODToGTOD(tp, rTOD, rGTOD);
    aGTODToECF(tp, rGTOD, rECF2);

    std::cout << "\n===== J2000 → MOD → TOD → GTOD → ECF (逐步) =====" << std::endl;
    std::cout << "  r_MOD  = " << rMOD.x()  << "  " << rMOD.y()  << "  " << rMOD.z()  << std::endl;
    std::cout << "  r_TOD  = " << rTOD.x()  << "  " << rTOD.y()  << "  " << rTOD.z()  << std::endl;
    std::cout << "  r_GTOD = " << rGTOD.x() << "  " << rGTOD.y() << "  " << rGTOD.z() << std::endl;
    std::cout << "  r_ECF  = " << rECF2.x() << "  " << rECF2.y() << "  " << rECF2.z() << std::endl;

    // ============================================================
    // 对比: 快捷 vs 逐步
    // ============================================================
    double diff = (rECF2 - rECF).norm();

    std::cout << "\n===== 快捷 vs 逐步 =====" << std::endl;
    std::cout << "  位置差 = " << std::scientific << diff << " m" << std::endl;

    // ============================================================
    // 获取各步的转换矩阵
    // ============================================================
    Matrix3d matJ2000ToMOD, matMODToTOD, matTODToGTOD, matGTODToECF;
    aJ2000ToMODMatrix(tp, matJ2000ToMOD);
    aMODToTODMatrix(tp, matMODToTOD);
    aTODToGTODMatrix(tp, matTODToGTOD);
    aGTODToECFMatrix(tp, matGTODToECF);

    std::cout << "\n===== 各步转换矩阵 =====" << std::endl;
    std::cout << "  M(J2000→MOD):" << std::endl;
    std::cout << "    [" << matJ2000ToMOD(0,0) << "  " << matJ2000ToMOD(0,1) << "  " << matJ2000ToMOD(0,2) << "]" << std::endl;
    std::cout << "    [" << matJ2000ToMOD(1,0) << "  " << matJ2000ToMOD(1,1) << "  " << matJ2000ToMOD(1,2) << "]" << std::endl;
    std::cout << "    [" << matJ2000ToMOD(2,0) << "  " << matJ2000ToMOD(2,1) << "  " << matJ2000ToMOD(2,2) << "]" << std::endl;

    std::cout << "  M(MOD→TOD):" << std::endl;
    std::cout << "    [" << matMODToTOD(0,0) << "  " << matMODToTOD(0,1) << "  " << matMODToTOD(0,2) << "]" << std::endl;
    std::cout << "    [" << matMODToTOD(1,0) << "  " << matMODToTOD(1,1) << "  " << matMODToTOD(1,2) << "]" << std::endl;
    std::cout << "    [" << matMODToTOD(2,0) << "  " << matMODToTOD(2,1) << "  " << matMODToTOD(2,2) << "]" << std::endl;

    // ============================================================
    // J2000 → ICRF 
    // ============================================================
    Vector3d rICRF;
    aJ2000ToICRF(tp, rJ2000, rICRF);

    double icrfJ2000Diff = (rICRF - rJ2000).norm();
    std::cout << "\n===== ICRF ↔ J2000 =====" << std::endl;
    std::cout << "  r_ICRF = " << rICRF.x() << "  " << rICRF.y() << "  " << rICRF.z() << std::endl;
    std::cout << "  |r_ICRF - r_J2000| = " << std::scientific << icrfJ2000Diff << " m" << std::endl;

    // ============================================================
    // ECF → J2000 (反向转换)
    // ============================================================
    Vector3d rJ2000_back;
    aECFToJ2000(tp, rECF, rJ2000_back);

    double roundTrip = (rJ2000_back - rJ2000).norm();
    std::cout << "\n===== ECF → J2000 (反向) =====" << std::endl;
    std::cout << "  r_J2000_back = " << rJ2000_back.x() << "  " << rJ2000_back.y() << "  " << rJ2000_back.z() << std::endl;
    std::cout << "  |r_back - r_orig| = " << std::scientific << roundTrip << " m" << std::endl;

    // ============================================================
    // 总结
    // ============================================================
    std::cout << "\n===== 坐标转换链路总结 =====" << std::endl;
    std::cout << "  ICRF ←→ J2000  (参考系偏差, |r_ICRF - r_J2000| = " << icrfJ2000Diff << " m)" << std::endl;
    std::cout << "  J2000 → MOD    (岁差)" << std::endl;
    std::cout << "  MOD   → TOD    (章动)" << std::endl;
    std::cout << "  TOD   → GTOD   (地球自转)" << std::endl;
    std::cout << "  GTOD  → ECF    (极移)" << std::endl;
    std::cout << "  快捷 J2000 → ECF 与逐步转换一致, 位置差 = " << diff << " m" << std::endl;
    std::cout << "  往返 J2000 → ECF → J2000 精度 = " << roundTrip << " m" << std::endl;

    std::cout << "\nexample completed." << std::endl;
    return 0;
}

注意事项

• ECI 为地球惯性系的统称，根据配置可能指 J2000 或 ICRF
• 带速度的转换会考虑旋转坐标系的牵连速度
• 极移校正需要 EOP 数据支持
• 可通过 aNutationMethodSet 在 IAU1980 和 JPL DE 章动模型之间切换