Cross product magnitude computation

조회 수: 5(최근 30일)
Hugo Hernández Hernández
Hugo Hernández Hernández 2021년 1월 22일
댓글: Hugo Hernández Hernández 2021년 5월 15일
Hi,
Trying to get the elements for a RSW reference frame (orbital mechanics concept), I have problems regarding to the magnitude of one cross product between 2 vectors, the results are very innacurate and after searching on internet I got the conclusion that the problem is on the way that I'm trying to compute the cross product magnitude. My code section is as follows:
Please, could you help me to have a better idea of this cross product magnitude?
SZp = [SZ1; SZ2; SZ3]; % Position difference % 3x262 double
SZv = [SZ4; SZ5; SZ6]; % Velocity difference % 3x262 double
% Axes of the RSW system
er = R_p./sqrt((Sen1).^2 + (Sen2).^2 + (Sen3).^2); % | eR = r/|r| % Sen1,2,3 1x262 double, | | eR, eW, eS 3x262 double
rxv = cross(R_p,V_vel); % r x v % 3x262 double
mrxv = sqrt((rxv(1,:)).^2 + (rxv(2,:)).^2 + (rxv(3,:)).^2); % |r x v| !!! TRYING TO COMPUTE CROSS PRODUCT MAGNITUDE
ew = rxv./mrxv; % r x v / |r x v| ALSO THE PROBLEM COULD BE AT THIS STEP, eW is getting strange results despite eR and eS
es = cross(ew,er); % ew x er
% Projection of the difference on each vector, basis vector
R = dot(SZp,er);
S = dot(SZp,es);
W = dot(SZp,ew);

답변(1개)

Gaurav Garg
Gaurav Garg 2021년 1월 27일
Hi Hugo,
The cross-product between two 3xm matrices (C = cross(A,B)) is calculated as follows -
1.) For the third row of resultant matrix C, element-wise product of second row of A and first row of B is subtracted from element-wise product of first row of A and second row of B
2.) For the first row of resultant matrix C, element-wise product of third row of A and second row of B is subtracted from element-wise product of second row of A and third row of B
3.) For the second row of resultant matrix C, element-wise product of first row of A and third row of B is subtracted from element-wise product of third row of A and first row of B
  댓글 수: 1
Hugo Hernández Hernández
Hugo Hernández Hernández 2021년 5월 15일
Thanks @Gaurav Garg, that time my problem was oriented to other structure, the problem was in the using of norm, unfortunately I did not get that exercise in the correct way and was because for the calculation of the magnitude norm is not always the best option, even the way I did it was not correct, eventually I realized some months after my question that the best way was:
eztmv = zeros(size(tan'));
eytmv = zeros(size(tan'));
extmv = zeros(size(tan'));
eytmv = cross(tan',vtan',2)./sqrt(sum(cross(tan',vtan',2).^2,2));
eztmv = tan'./sqrt(sum(tan'.^2,2));
extmv = cross(ey,ez,2);
Rtmv = zeros(2,1);
Wtmv = zeros(2,1);
Stmv = zeros(2,1);
Rtmv = sum(vtan'.*ez,2);
Wtmv = sum(vtan'.*ey,2);
Stmv = sum(vtan'.*ex,2);
With the use of sum and zeros matrices that time could have worked correctly. Anyway thanks for your support.
Hugo

댓글을 달려면 로그인하십시오.

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by