first version for gauss-jordan matrix inversion
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/*
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* MathOperations.h
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*
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* Created on: 3 Mar 2022
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* Author: rooob
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*/
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#ifndef MATH_MATHOPERATIONS_H_
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#define MATH_MATHOPERATIONS_H_
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#include <math.h>
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#include <sys/time.h>
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#include <stdint.h>
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#include <string.h>
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#include <fsfw/src/fsfw/globalfunctions/constants.h>
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#include <fsfw/src/fsfw/globalfunctions/math/MatrixOperations.h>
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#include <math.h>
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#include <stdint.h>
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#include <string.h>
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#include <sys/time.h>
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#include <iostream>
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using namespace Math;
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template<typename T1, typename T2 = T1>
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template <typename T1, typename T2 = T1>
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class MathOperations {
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public:
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static void skewMatrix(const T1 vector[], T2 *result) {
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// Input Dimension [3], Output [3][3]
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result[0] = 0;
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result[1] = -vector[2];
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result[2] = vector[1];
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result[3] = vector[2];
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result[4] = 0;
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result[5] = -vector[0];
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result[6] = -vector[1];
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result[7] = vector[0];
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result[8] = 0;
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}
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static void vecTransposeVecMatrix(const T1 vector1[], const T1 transposeVector2[],
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T2 *result, uint8_t size = 3) {
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// Looks like MatrixOpertions::multiply is able to do the same thing
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for (uint8_t resultColumn = 0; resultColumn < size; resultColumn++) {
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for (uint8_t resultRow = 0; resultRow < size; resultRow++) {
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result[resultColumn + size * resultRow] = vector1[resultRow]
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* transposeVector2[resultColumn];
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public:
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static void skewMatrix(const T1 vector[], T2 *result) {
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// Input Dimension [3], Output [3][3]
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result[0] = 0;
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result[1] = -vector[2];
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result[2] = vector[1];
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result[3] = vector[2];
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result[4] = 0;
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result[5] = -vector[0];
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result[6] = -vector[1];
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result[7] = vector[0];
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result[8] = 0;
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}
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static void vecTransposeVecMatrix(const T1 vector1[], const T1 transposeVector2[], T2 *result,
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uint8_t size = 3) {
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// Looks like MatrixOpertions::multiply is able to do the same thing
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for (uint8_t resultColumn = 0; resultColumn < size; resultColumn++) {
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for (uint8_t resultRow = 0; resultRow < size; resultRow++) {
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result[resultColumn + size * resultRow] =
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vector1[resultRow] * transposeVector2[resultColumn];
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}
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}
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/*matrixSun[i][j] = sunEstB[i] * sunEstB[j];
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matrixMag[i][j] = magEstB[i] * magEstB[j];
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matrixSunMag[i][j] = sunEstB[i] * magEstB[j];
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matrixMagSun[i][j] = magEstB[i] * sunEstB[j];*/
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}
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}
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}
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/*matrixSun[i][j] = sunEstB[i] * sunEstB[j];
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matrixMag[i][j] = magEstB[i] * magEstB[j];
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matrixSunMag[i][j] = sunEstB[i] * magEstB[j];
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matrixMagSun[i][j] = magEstB[i] * sunEstB[j];*/
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}
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static void selectionSort(const T1 *matrix, T1 *result, uint8_t rowSize, uint8_t colSize) {
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int min_idx;
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T1 temp;
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memcpy(result, matrix, rowSize * colSize * sizeof(*result));
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// One by one move boundary of unsorted subarray
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for (int k = 0; k < rowSize; k++) {
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for (int i = 0; i < colSize - 1; i++) {
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// Find the minimum element in unsorted array
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min_idx = i;
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for (int j = i + 1; j < colSize; j++) {
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if (result[j + k * colSize] < result[min_idx + k * colSize]) {
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min_idx = j;
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}
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}
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// Swap the found minimum element with the first element
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temp = result[i + k * colSize];
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result[i + k * colSize] = result[min_idx + k * colSize];
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result[min_idx + k * colSize] = temp;
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}
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}
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}
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static void selectionSort(const T1 *matrix, T1 *result, uint8_t rowSize,
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uint8_t colSize) {
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int min_idx;
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T1 temp;
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memcpy(result, matrix, rowSize * colSize * sizeof(*result));
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// One by one move boundary of unsorted subarray
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for (int k = 0; k < rowSize; k++) {
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for (int i = 0; i < colSize - 1; i++) {
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// Find the minimum element in unsorted array
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min_idx = i;
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for (int j = i + 1; j < colSize; j++) {
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if (result[j + k * colSize]
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< result[min_idx + k * colSize]) {
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min_idx = j;
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}
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}
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// Swap the found minimum element with the first element
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temp = result[i + k * colSize];
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result[i + k * colSize] = result[min_idx + k * colSize];
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result[min_idx + k * colSize] = temp;
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}
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}
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}
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static void convertDateToJD2000(const T1 time, T2 julianDate) {
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// time = { Y, M, D, h, m,s}
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// time in sec and microsec -> The Epoch (unixtime)
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julianDate = 1721013.5 + 367 * time[0] - floor(7 / 4 * (time[0] + (time[1] + 9) / 12)) +
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floor(275 * time[1] / 9) + time[2] +
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(60 * time[3] + time[4] + (time(5) / 60)) / 1440;
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}
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static void convertDateToJD2000(const T1 time, T2 julianDate){
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static T1 convertUnixToJD2000(timeval time) {
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// time = {{s},{us}}
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T1 julianDate2000;
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julianDate2000 = (time.tv_sec / 86400.0) + 2440587.5 - 2451545;
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return julianDate2000;
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}
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// time = { Y, M, D, h, m,s}
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// time in sec and microsec -> The Epoch (unixtime)
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julianDate = 1721013.5 + 367*time[0]- floor(7/4*(time[0]+(time[1]+9)/12))
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+floor(275*time[1]/9)+time[2]+(60*time[3]+time[4]+(time(5)/60))/1440;
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}
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static void dcmFromQuat(const T1 vector[], T1 *outputDcm) {
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// convention q = [qx,qy,qz, qw]
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outputDcm[0] = pow(vector[0], 2) - pow(vector[1], 2) - pow(vector[2], 2) + pow(vector[3], 2);
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outputDcm[1] = 2 * (vector[0] * vector[1] + vector[2] * vector[3]);
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outputDcm[2] = 2 * (vector[0] * vector[2] - vector[1] * vector[3]);
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static T1 convertUnixToJD2000(timeval time){
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//time = {{s},{us}}
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T1 julianDate2000;
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julianDate2000 = (time.tv_sec/86400.0)+2440587.5-2451545;
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return julianDate2000;
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}
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outputDcm[3] = 2 * (vector[1] * vector[0] - vector[2] * vector[3]);
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outputDcm[4] = -pow(vector[0], 2) + pow(vector[1], 2) - pow(vector[2], 2) + pow(vector[3], 2);
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outputDcm[5] = 2 * (vector[1] * vector[2] + vector[0] * vector[3]);
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static void dcmFromQuat(const T1 vector[], T1 *outputDcm){
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// convention q = [qx,qy,qz, qw]
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outputDcm[0] = pow(vector[0],2) - pow(vector[1],2) - pow(vector[2],2) + pow(vector[3],2);
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outputDcm[1] = 2*(vector[0]*vector[1] + vector[2]*vector[3]);
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outputDcm[2] = 2*(vector[0]*vector[2] - vector[1]*vector[3]);
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outputDcm[6] = 2 * (vector[2] * vector[0] + vector[1] * vector[3]);
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outputDcm[7] = 2 * (vector[2] * vector[1] - vector[0] * vector[3]);
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outputDcm[8] = -pow(vector[0], 2) - pow(vector[1], 2) + pow(vector[2], 2) + pow(vector[3], 2);
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}
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outputDcm[3] = 2*(vector[1]*vector[0] - vector[2]*vector[3]);
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outputDcm[4] = -pow(vector[0],2) + pow(vector[1],2) - pow(vector[2],2) + pow(vector[3],2);
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outputDcm[5] = 2*(vector[1]*vector[2] + vector[0]*vector[3]);
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static void cartesianFromLatLongAlt(const T1 lat, const T1 longi, const T1 alt,
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T2 *cartesianOutput) {
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double radiusPolar = 6378137;
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double radiusEqua = 6356752.314;
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outputDcm[6] = 2*(vector[2]*vector[0] + vector[1]*vector[3]);
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outputDcm[7] = 2*(vector[2]*vector[1] - vector[0]*vector[3]);
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outputDcm[8] = -pow(vector[0],2) - pow(vector[1],2) + pow(vector[2],2) + pow(vector[3],2);
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double eccentricity = sqrt(1 - pow(radiusPolar, 2) / pow(radiusEqua, 2));
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double auxRadius = radiusEqua / sqrt(1 - pow(eccentricity, 2) * pow(sin(lat), 2));
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}
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cartesianOutput[0] = (auxRadius + alt) * cos(lat) * cos(longi);
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cartesianOutput[1] = (auxRadius + alt) * cos(lat) * sin(longi);
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cartesianOutput[2] = ((1 - pow(eccentricity, 2)) * auxRadius + alt) * sin(lat);
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}
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static void cartesianFromLatLongAlt(const T1 lat, const T1 longi, const T1 alt, T2 *cartesianOutput){
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/* @brief: dcmEJ() - calculates the transformation matrix between ECEF and ECI frame
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* @param: time Current time
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* outputDcmEJ Transformation matrix from ECI (J) to ECEF (E) [3][3]
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* @source: Fundamentals of Spacecraft Attitude Determination and Control, P.32ff
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* Landis Markley and John L. Crassidis*/
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static void dcmEJ(timeval time, T1 *outputDcmEJ) {
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double JD2000Floor = 0;
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double JD2000 = convertUnixToJD2000(time);
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// Getting Julian Century from Day start : JD (Y,M,D,0,0,0)
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JD2000Floor = floor(JD2000);
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if ((JD2000 - JD2000Floor) < 0.5) {
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JD2000Floor -= 0.5;
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} else {
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JD2000Floor += 0.5;
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}
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double radiusPolar = 6378137;
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double radiusEqua = 6356752.314;
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double JC2000 = JD2000Floor / 36525;
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double sec = (JD2000 - JD2000Floor) * 86400;
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double gmst = 0; // greenwich mean sidereal time
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gmst = 24110.54841 + 8640184.812866 * JC2000 + 0.093104 * pow(JC2000, 2) -
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0.0000062 * pow(JC2000, 3) + 1.002737909350795 * sec;
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double rest = gmst / 86400;
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double FloorRest = floor(rest);
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double secOfDay = rest - FloorRest;
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secOfDay *= 86400;
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gmst = secOfDay / 240 * PI / 180;
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double eccentricity = sqrt(1 - pow(radiusPolar,2) / pow(radiusEqua,2));
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double auxRadius = radiusEqua / sqrt(1 - pow(eccentricity,2) * pow(sin(lat),2));
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outputDcmEJ[0] = cos(gmst);
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outputDcmEJ[1] = sin(gmst);
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outputDcmEJ[2] = 0;
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outputDcmEJ[3] = -sin(gmst);
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outputDcmEJ[4] = cos(gmst);
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outputDcmEJ[5] = 0;
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outputDcmEJ[6] = 0;
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outputDcmEJ[7] = 0;
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outputDcmEJ[8] = 1;
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}
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cartesianOutput[0] = (auxRadius + alt) * cos(lat) * cos(longi);
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cartesianOutput[1] = (auxRadius + alt) * cos(lat) * sin(longi);
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cartesianOutput[2] = ((1 - pow(eccentricity,2)) * auxRadius + alt) * sin(lat);
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/* @brief: ecfToEciWithNutPre() - calculates the transformation matrix between ECEF and ECI frame
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* give also the back the derivative of this matrix
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* @param: unixTime Current time in Unix format
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* outputDcmEJ Transformation matrix from ECI (J) to ECEF (E) [3][3]
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* outputDotDcmEJ Derivative of transformation matrix [3][3]
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* @source: Entwicklung einer Simulationsumgebung und robuster Algorithmen für das Lage- und
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Orbitkontrollsystem der Kleinsatelliten Flying Laptop und PERSEUS, P.244ff
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* Oliver Zeile
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*
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https://eive-cloud.irs.uni-stuttgart.de/index.php/apps/files/?dir=/EIVE_Studenten/Marquardt_Robin&openfile=896110*/
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static void ecfToEciWithNutPre(timeval unixTime, T1 *outputDcmEJ, T1 *outputDotDcmEJ) {
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// TT = UTC/Unix + 32.184s (TAI Difference) + 27 (Leap Seconds in UTC since 1972) + 10
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//(initial Offset) International Atomic Time (TAI)
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}
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double JD2000UTC1 = convertUnixToJD2000(unixTime);
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/* @brief: dcmEJ() - calculates the transformation matrix between ECEF and ECI frame
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* @param: time Current time
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* outputDcmEJ Transformation matrix from ECI (J) to ECEF (E) [3][3]
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* @source: Fundamentals of Spacecraft Attitude Determination and Control, P.32ff
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* Landis Markley and John L. Crassidis*/
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static void dcmEJ(timeval time, T1 * outputDcmEJ){
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// Julian Date / century from TT
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timeval terestrialTime = unixTime;
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terestrialTime.tv_sec = unixTime.tv_sec + 32.184 + 37;
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double JD2000TT = convertUnixToJD2000(terestrialTime);
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double JC2000TT = JD2000TT / 36525;
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double JD2000Floor = 0;
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double JD2000 = convertUnixToJD2000(time);
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// Getting Julian Century from Day start : JD (Y,M,D,0,0,0)
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JD2000Floor = floor(JD2000);
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if ( ( JD2000 - JD2000Floor) < 0.5) {
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JD2000Floor -= 0.5;
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}
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else {
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JD2000Floor += 0.5;
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}
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//-------------------------------------------------------------------------------------
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// Calculation of Transformation from earth rotation Theta
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//-------------------------------------------------------------------------------------
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double theta[3][3] = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}};
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// Earth Rotation angle
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double era = 0;
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era = 2 * PI * (0.779057273264 + 1.00273781191135448 * JD2000UTC1);
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// Greenwich Mean Sidereal Time
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double gmst2000 = 0.014506 + 4612.15739966 * JC2000TT + 1.39667721 * pow(JC2000TT, 2) -
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0.00009344 * pow(JC2000TT, 3) + 0.00001882 * pow(JC2000TT, 4);
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double arcsecFactor = 1 * PI / (180 * 3600);
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gmst2000 *= arcsecFactor;
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gmst2000 += era;
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double JC2000 = JD2000Floor / 36525;
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double sec = (JD2000 - JD2000Floor) * 86400;
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double gmst = 0; //greenwich mean sidereal time
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gmst = 24110.54841 + 8640184.812866 * JC2000 + 0.093104 * pow(JC2000,2) -
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0.0000062 * pow(JC2000,3) + 1.002737909350795 * sec;
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double rest = gmst / 86400;
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double FloorRest = floor(rest);
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double secOfDay = rest-FloorRest;
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secOfDay *= 86400;
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gmst = secOfDay / 240 * PI / 180;
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theta[0][0] = cos(gmst2000);
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theta[0][1] = sin(gmst2000);
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theta[0][2] = 0;
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theta[1][0] = -sin(gmst2000);
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theta[1][1] = cos(gmst2000);
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theta[1][2] = 0;
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theta[2][0] = 0;
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theta[2][1] = 0;
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theta[2][2] = 1;
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outputDcmEJ[0] = cos(gmst);
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outputDcmEJ[1] = sin(gmst);
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outputDcmEJ[2] = 0;
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outputDcmEJ[3] = -sin(gmst);
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outputDcmEJ[4] = cos(gmst);
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outputDcmEJ[5] = 0;
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outputDcmEJ[6] = 0;
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outputDcmEJ[7] = 0;
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outputDcmEJ[8] = 1;
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//-------------------------------------------------------------------------------------
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// Calculation of Transformation from earth Precession P
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//-------------------------------------------------------------------------------------
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double precession[3][3] = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}};
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}
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double zeta = 2306.2181 * JC2000TT + 0.30188 * pow(JC2000TT, 2) + 0.017998 * pow(JC2000TT, 3);
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double theta2 = 2004.3109 * JC2000TT - 0.42665 * pow(JC2000TT, 2) - 0.041833 * pow(JC2000TT, 3);
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double ze = zeta + 0.79280 * pow(JC2000TT, 2) + 0.000205 * pow(JC2000TT, 3);
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/* @brief: ecfToEciWithNutPre() - calculates the transformation matrix between ECEF and ECI frame
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* give also the back the derivative of this matrix
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* @param: unixTime Current time in Unix format
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* outputDcmEJ Transformation matrix from ECI (J) to ECEF (E) [3][3]
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* outputDotDcmEJ Derivative of transformation matrix [3][3]
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* @source: Entwicklung einer Simulationsumgebung und robuster Algorithmen für das Lage- und
|
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Orbitkontrollsystem der Kleinsatelliten Flying Laptop und PERSEUS, P.244ff
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* Oliver Zeile
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* https://eive-cloud.irs.uni-stuttgart.de/index.php/apps/files/?dir=/EIVE_Studenten/Marquardt_Robin&openfile=896110*/
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static void ecfToEciWithNutPre(timeval unixTime, T1 * outputDcmEJ, T1 * outputDotDcmEJ ) {
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zeta *= arcsecFactor;
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theta2 *= arcsecFactor;
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ze *= arcsecFactor;
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// TT = UTC/Unix + 32.184s (TAI Difference) + 27 (Leap Seconds in UTC since 1972) + 10 (initial Offset)
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// International Atomic Time (TAI)
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precession[0][0] = -sin(ze) * sin(zeta) + cos(ze) * cos(theta2) * cos(zeta);
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precession[1][0] = cos(ze) * sin(zeta) + sin(ze) * cos(theta2) * cos(zeta);
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precession[2][0] = sin(theta2) * cos(zeta);
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precession[0][1] = -sin(ze) * cos(zeta) - cos(ze) * cos(theta2) * sin(zeta);
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precession[1][1] = cos(ze) * cos(zeta) - sin(ze) * cos(theta2) * sin(zeta);
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precession[2][1] = -sin(theta2) * sin(zeta);
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precession[0][2] = -cos(ze) * sin(theta2);
|
||||
precession[1][2] = -sin(ze) * sin(theta2);
|
||||
precession[2][2] = cos(theta2);
|
||||
|
||||
double JD2000UTC1 = convertUnixToJD2000(unixTime);
|
||||
//-------------------------------------------------------------------------------------
|
||||
// Calculation of Transformation from earth Nutation size
|
||||
//-------------------------------------------------------------------------------------
|
||||
double nutation[3][3] = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}};
|
||||
// lunar asc node
|
||||
double Om = 125 * 3600 + 2 * 60 + 40.28 - (1934 * 3600 + 8 * 60 + 10.539) * JC2000TT +
|
||||
7.455 * pow(JC2000TT, 2) + 0.008 * pow(JC2000TT, 3);
|
||||
Om *= arcsecFactor;
|
||||
// delta psi approx
|
||||
double dp = -17.2 * arcsecFactor * sin(Om);
|
||||
|
||||
// Julian Date / century from TT
|
||||
timeval terestrialTime = unixTime;
|
||||
terestrialTime.tv_sec = unixTime.tv_sec + 32.184 + 37;
|
||||
double JD2000TT = convertUnixToJD2000(terestrialTime);
|
||||
double JC2000TT = JD2000TT / 36525;
|
||||
// delta eps approx
|
||||
double de = 9.203 * arcsecFactor * cos(Om);
|
||||
|
||||
//-------------------------------------------------------------------------------------
|
||||
// Calculation of Transformation from earth rotation Theta
|
||||
//-------------------------------------------------------------------------------------
|
||||
double theta[3][3] = {{0,0,0},{0,0,0},{0,0,0}};
|
||||
// Earth Rotation angle
|
||||
double era = 0;
|
||||
era = 2* PI *(0.779057273264 + 1.00273781191135448 * JD2000UTC1);
|
||||
// Greenwich Mean Sidereal Time
|
||||
double gmst2000 = 0.014506 + 4612.15739966 * JC2000TT + 1.39667721 * pow(JC2000TT,2) -
|
||||
0.00009344 * pow(JC2000TT,3) + 0.00001882 * pow(JC2000TT,4);
|
||||
double arcsecFactor = 1 * PI / (180 * 3600);
|
||||
gmst2000 *= arcsecFactor;
|
||||
gmst2000 += era;
|
||||
// % true obliquity of the ecliptic eps p.71 (simplified)
|
||||
double e = 23.43929111 * PI / 180 - 46.8150 / 3600 * JC2000TT * PI / 180;
|
||||
;
|
||||
|
||||
theta[0][0] = cos(gmst2000);
|
||||
theta[0][1] = sin(gmst2000);
|
||||
theta[0][2] = 0;
|
||||
theta[1][0] = -sin(gmst2000);
|
||||
theta[1][1] = cos(gmst2000);
|
||||
theta[1][2] = 0;
|
||||
theta[2][0] = 0;
|
||||
theta[2][1] = 0;
|
||||
theta[2][2] = 1;
|
||||
nutation[0][0] = cos(dp);
|
||||
nutation[1][0] = cos(e + de) * sin(dp);
|
||||
nutation[2][0] = sin(e + de) * sin(dp);
|
||||
nutation[0][1] = -cos(e) * sin(dp);
|
||||
nutation[1][1] = cos(e) * cos(e + de) * cos(dp) + sin(e) * sin(e + de);
|
||||
nutation[2][1] = cos(e) * sin(e + de) * cos(dp) - sin(e) * cos(e + de);
|
||||
nutation[0][2] = -sin(e) * sin(dp);
|
||||
nutation[1][2] = sin(e) * cos(e + de) * cos(dp) - cos(e) * sin(e + de);
|
||||
nutation[2][2] = sin(e) * sin(e + de) * cos(dp) + cos(e) * cos(e + de);
|
||||
|
||||
//-------------------------------------------------------------------------------------
|
||||
// Calculation of Transformation from earth Precession P
|
||||
//-------------------------------------------------------------------------------------
|
||||
double precession[3][3] = {{0,0,0},{0,0,0},{0,0,0}};
|
||||
//-------------------------------------------------------------------------------------
|
||||
// Calculation of Derivative of rotation matrix from earth
|
||||
//-------------------------------------------------------------------------------------
|
||||
double thetaDot[3][3] = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}};
|
||||
double dotMatrix[3][3] = {{0, 1, 0}, {-1, 0, 0}, {0, 0, 0}};
|
||||
double omegaEarth = 0.000072921158553;
|
||||
MatrixOperations<double>::multiply(*dotMatrix, *theta, *thetaDot, 3, 3, 3);
|
||||
MatrixOperations<double>::multiplyScalar(*thetaDot, omegaEarth, *thetaDot, 3, 3);
|
||||
|
||||
double zeta = 2306.2181 * JC2000TT + 0.30188 * pow(JC2000TT,2) + 0.017998 * pow(JC2000TT,3);
|
||||
double theta2 = 2004.3109 * JC2000TT - 0.42665 * pow(JC2000TT,2) - 0.041833 * pow(JC2000TT,3);
|
||||
double ze = zeta + 0.79280 * pow(JC2000TT,2) + 0.000205 * pow(JC2000TT,3);
|
||||
//-------------------------------------------------------------------------------------
|
||||
// Calculation of transformation matrix and Derivative of transformation matrix
|
||||
//-------------------------------------------------------------------------------------
|
||||
double nutationPrecession[3][3] = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}};
|
||||
MatrixOperations<double>::multiply(*nutation, *precession, *nutationPrecession, 3, 3, 3);
|
||||
MatrixOperations<double>::multiply(*nutationPrecession, *theta, outputDcmEJ, 3, 3, 3);
|
||||
|
||||
zeta *= arcsecFactor;
|
||||
theta2 *= arcsecFactor;
|
||||
ze *= arcsecFactor;
|
||||
MatrixOperations<double>::multiply(*nutationPrecession, *thetaDot, outputDotDcmEJ, 3, 3, 3);
|
||||
}
|
||||
|
||||
precession[0][0]=-sin(ze)*sin(zeta)+cos(ze)*cos(theta2)*cos(zeta);
|
||||
precession[1][0]=cos(ze)*sin(zeta)+sin(ze)*cos(theta2)*cos(zeta);
|
||||
precession[2][0]=sin(theta2)*cos(zeta);
|
||||
precession[0][1]=-sin(ze)*cos(zeta)-cos(ze)*cos(theta2)*sin(zeta);
|
||||
precession[1][1]=cos(ze)*cos(zeta)-sin(ze)*cos(theta2)*sin(zeta);
|
||||
precession[2][1]=-sin(theta2)*sin(zeta);
|
||||
precession[0][2]=-cos(ze)*sin(theta2);
|
||||
precession[1][2]=-sin(ze)*sin(theta2);
|
||||
precession[2][2]=cos(theta2);
|
||||
static void inverseMatrixDimThree(const T1 *matrix, T1 *output) {
|
||||
int i, j;
|
||||
double determinant;
|
||||
double mat[3][3] = {{matrix[0], matrix[1], matrix[2]},
|
||||
{matrix[3], matrix[4], matrix[5]},
|
||||
{matrix[6], matrix[7], matrix[8]}};
|
||||
|
||||
//-------------------------------------------------------------------------------------
|
||||
// Calculation of Transformation from earth Nutation N
|
||||
//-------------------------------------------------------------------------------------
|
||||
double nutation[3][3] = {{0,0,0},{0,0,0},{0,0,0}};
|
||||
// lunar asc node
|
||||
double Om = 125 * 3600 + 2 * 60 + 40.28 - (1934 * 3600 + 8 * 60 + 10.539) * JC2000TT +
|
||||
7.455 * pow(JC2000TT,2) + 0.008 * pow(JC2000TT,3);
|
||||
Om *= arcsecFactor;
|
||||
// delta psi approx
|
||||
double dp = -17.2 * arcsecFactor *sin(Om);
|
||||
for (i = 0; i < 3; i++) {
|
||||
determinant = determinant + (mat[0][i] * (mat[1][(i + 1) % 3] * mat[2][(i + 2) % 3] -
|
||||
mat[1][(i + 2) % 3] * mat[2][(i + 1) % 3]));
|
||||
}
|
||||
// cout<<"\size\ndeterminant: "<<determinant;
|
||||
// cout<<"\size\nInverse of matrix is: \size";
|
||||
for (i = 0; i < 3; i++) {
|
||||
for (j = 0; j < 3; j++) {
|
||||
output[i * 3 + j] = ((mat[(j + 1) % 3][(i + 1) % 3] * mat[(j + 2) % 3][(i + 2) % 3]) -
|
||||
(mat[(j + 1) % 3][(i + 2) % 3] * mat[(j + 2) % 3][(i + 1) % 3])) /
|
||||
determinant;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// delta eps approx
|
||||
double de = 9.203 * arcsecFactor *cos(Om);
|
||||
|
||||
// % true obliquity of the ecliptic eps p.71 (simplified)
|
||||
double e = 23.43929111 * PI / 180 - 46.8150 / 3600 * JC2000TT * PI / 180;;
|
||||
|
||||
nutation[0][0]=cos(dp);
|
||||
nutation[1][0]=cos(e+de)*sin(dp);
|
||||
nutation[2][0]=sin(e+de)*sin(dp);
|
||||
nutation[0][1]=-cos(e)*sin(dp);
|
||||
nutation[1][1]=cos(e)*cos(e+de)*cos(dp)+sin(e)*sin(e+de);
|
||||
nutation[2][1]=cos(e)*sin(e+de)*cos(dp)-sin(e)*cos(e+de);
|
||||
nutation[0][2]=-sin(e)*sin(dp);
|
||||
nutation[1][2]=sin(e)*cos(e+de)*cos(dp)-cos(e)*sin(e+de);
|
||||
nutation[2][2]=sin(e)*sin(e+de)*cos(dp)+cos(e)*cos(e+de);
|
||||
|
||||
//-------------------------------------------------------------------------------------
|
||||
// Calculation of Derivative of rotation matrix from earth
|
||||
//-------------------------------------------------------------------------------------
|
||||
double thetaDot[3][3] = {{0,0,0},{0,0,0},{0,0,0}};
|
||||
double dotMatrix[3][3] = {{0,1,0},{-1,0,0},{0,0,0}};
|
||||
double omegaEarth = 0.000072921158553;
|
||||
MatrixOperations<double>::multiply(*dotMatrix, *theta, *thetaDot, 3, 3, 3);
|
||||
MatrixOperations<double>::multiplyScalar(*thetaDot, omegaEarth, *thetaDot, 3, 3);
|
||||
|
||||
//-------------------------------------------------------------------------------------
|
||||
// Calculation of transformation matrix and Derivative of transformation matrix
|
||||
//-------------------------------------------------------------------------------------
|
||||
double nutationPrecession[3][3] = {{0,0,0},{0,0,0},{0,0,0}};
|
||||
MatrixOperations<double>::multiply(*nutation, *precession, *nutationPrecession, 3, 3, 3);
|
||||
MatrixOperations<double>::multiply(*nutationPrecession, *theta, outputDcmEJ, 3, 3, 3);
|
||||
|
||||
MatrixOperations<double>::multiply(*nutationPrecession, *thetaDot, outputDotDcmEJ, 3, 3, 3);
|
||||
|
||||
}
|
||||
|
||||
static void inverseMatrixDimThree(const T1 *matrix, T1 * output){
|
||||
|
||||
int i,j;
|
||||
double determinant;
|
||||
double mat[3][3] = {{matrix[0], matrix[1], matrix[2]},{matrix[3], matrix[4], matrix[5]},
|
||||
{matrix[6], matrix[7], matrix[8]}};
|
||||
|
||||
for(i = 0; i < 3; i++) {
|
||||
determinant = determinant + (mat[0][i] * (mat[1][(i+1)%3] * mat[2][(i+2)%3] - mat[1][(i+2)%3] * mat[2][(i+1)%3]));
|
||||
}
|
||||
// cout<<"\n\ndeterminant: "<<determinant;
|
||||
// cout<<"\n\nInverse of matrix is: \n";
|
||||
for(i = 0; i < 3; i++){
|
||||
for(j = 0; j < 3; j++){
|
||||
output[i*3+j] = ((mat[(j+1)%3][(i+1)%3] * mat[(j+2)%3][(i+2)%3]) - (mat[(j+1)%3][(i+2)%3] * mat[(j+2)%3][(i+1)%3]))/ determinant;
|
||||
}
|
||||
}
|
||||
}
|
||||
static float matrixDeterminant(const T1 *inputMatrix, uint8_t size) {
|
||||
float det = 0;
|
||||
T1 matrix[size][size], submatrix[size][size];
|
||||
for (uint8_t row = 0; row < size; row++) {
|
||||
for (uint8_t col = 0; col < size; col++) {
|
||||
matrix[row][col] = inputMatrix[row * size + col];
|
||||
}
|
||||
}
|
||||
if (size == 2)
|
||||
return ((matrix[0][0] * matrix[1][1]) - (matrix[1][0] * matrix[0][1]));
|
||||
else {
|
||||
for (uint8_t x = 0; x < size; x++) {
|
||||
int subi = 0;
|
||||
for (uint8_t i = 1; i < size; i++) {
|
||||
int subj = 0;
|
||||
for (uint8_t j = 0; j < size; j++) {
|
||||
if (j == x) continue;
|
||||
submatrix[subi][subj] = matrix[i][j];
|
||||
subj++;
|
||||
}
|
||||
subi++;
|
||||
}
|
||||
det = det + (pow(-1, x) * matrix[0][x] *
|
||||
MathOperations<T1>::matrixDeterminant(*submatrix, size - 1));
|
||||
}
|
||||
}
|
||||
return det;
|
||||
}
|
||||
|
||||
static int inverseMatrix(const T1 *inputMatrix, T1 *inverse, uint8_t size) {
|
||||
if (MathOperations<T1>::matrixDeterminant(*inputMatrix, size) == 0) {
|
||||
return 0; // Matrix is singular and not invertible
|
||||
}
|
||||
T1 matrix[size][size], identity[size][size] = {0};
|
||||
// reformat array to matrix
|
||||
for (uint8_t row = 0; row < size; row++) {
|
||||
for (uint8_t col = 0; col < size; col++) {
|
||||
matrix[row][col] = inputMatrix[row * size + col];
|
||||
}
|
||||
}
|
||||
// init identity matrix
|
||||
for (uint8_t diag = 0; diag < size; diag++) {
|
||||
identity[diag][diag] = 1;
|
||||
}
|
||||
// gauss-jordan algo
|
||||
for (uint8_t row = 0; row < size; row++) {
|
||||
uint8_t rowIndex = row;
|
||||
// check if diag entry is 0
|
||||
// in case it is, find next row whose diag entry is not 0
|
||||
while (matrix[rowIndex][row] == 0) {
|
||||
if (rowIndex < size) {
|
||||
rowIndex++;
|
||||
} else {
|
||||
return 0; // Matrix is not invertible
|
||||
}
|
||||
}
|
||||
// swap rows if needed
|
||||
if (rowIndex != row) {
|
||||
for (uint8_t colIndex = 0; colIndex < size; colIndex++) {
|
||||
std::swap(matrix[row][colIndex], matrix[rowIndex][colIndex]);
|
||||
std::swap(identity[row][colIndex], identity[rowIndex][colIndex]);
|
||||
}
|
||||
}
|
||||
// normalize line
|
||||
for (uint8_t colIndex = row; colIndex < size; colIndex++) {
|
||||
matrix[row][colIndex] = matrix[row][colIndex] / matrix[row][row];
|
||||
identity[row][colIndex] = identity[row][colIndex] / matrix[row][row];
|
||||
}
|
||||
// make elements of the same col in following rows to 0
|
||||
for (uint8_t rowIndex = row + 1; rowIndex < size; rowIndex++) {
|
||||
for (uint8_t colIndex = row; colIndex < size; colIndex++) {
|
||||
matrix[rowIndex][colIndex] -= matrix[row][colIndex] * matrix[rowIndex][row];
|
||||
identity[rowIndex][colIndex] -= identity[row][colIndex] * matrix[rowIndex][row];
|
||||
}
|
||||
}
|
||||
}
|
||||
std::memcpy(inverse, identity, size * size * sizeof(T1));
|
||||
return 1; // successful inversion
|
||||
}
|
||||
};
|
||||
|
||||
#endif /* ACS_MATH_MATHOPERATIONS_H_ */
|
||||
|
||||
Loading…
Reference in New Issue
Block a user