Question

Write a computer program that takes as input an angle β and the components of a position vector in frame A (i.e. r). The transformation from frame A to frame B is a rotation about the 1-axis. Your code should calculate the DCM CAB, and the components of the vector in frame B (i.e.rB. Your code should output all of the following, including a label and units (if applicable) for each: CAB 4.8 Run your program using these input values: β-o3 rad and rA- 1-6.3 | (km). 2.7

Please use matlab to code this program.

Answer 1

Given that

for the problem to get the rotated matrix you should multiply the position in A coordinate system with the rotation matrix cos()-sin(0) 0 M |sin(0) cos(0) 0 0 Where for rotation in the z axis. for the Matlab code to take the input, write "ra- input(give the initial position in the form [x y z: similarly for angle beta "b-input(enter the angle you want to rotate by: then from beta find the transformation matrix defined as " Mt0s(b)-sin(b) O:sin(b) cos(b) 0; 0 0 1]; " the spaces enter the elements in a fixed row in different columns while semi-colon takes the elements to a new row so to get the translated position use the code "rb;N-(ra):" where ra: denotes ra transpose to write the output to a file you can generally use xlswrite command for this you need to create an excel file before hand in the same folder as the matlab code, assume that the name of the folder is 'answer' then write the code as "xlswrite(answer, rb, 'A1); where A1 represents the starting point in the excel where the answer is written. (the excel file should not be open when the matlab code is running)

so the complete code is closely of the form, ra- inputgive the initial position in the form [x y z]): b-input'enter the angle you want to rotate by M-[cos(b) -sin(b) O;sin(b) cos(b) 0; 0 0 1]; rb-M (ra:) xlswrite('answer'the roteted matrix is:, 'A1); xlswrite('answer, rb, 'A4): xlswrite(answer, rotation matrix is: , 'E1): xlswrite('answer. M. 'E1');

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