EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Chapter 9, Problem 16P
Develop, debug, and test a program in either a high-level language or macro language of your choice to multiply two matrices-that is,
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Fix my MATLAB code.
% Define unknown quantities in x-y system
% abc = Acceleration of B wrt C on beam CD in i direction
% vbc = Velocity of B wrt C on beam CD in i direction
% xacd = Angular acceleration of beam CD in k direction
% xvcd = Angular velocity of beam CD in k direction
syms abc vbc xacd xvcd;
% Create Unit Vectors in x-y coordinates
i = [1,0,0];
j = [0,1,0];
k = [0,0,1];
% Create Unit Vectors in X-Y coordinates (R is rotation Matrix)
Theta = 150; % Angle from X-axis to x-axis
R = [[cosd(Theta),-sind(Theta), 0]; ...
[sind(Theta), cosd(Theta), 0]; [0, 0, 1]];
XYZ = R*[i;j;k];
I = XYZ(1,:);
J = XYZ(2,:);
K = XYZ(3,:);
% Set known quantities for Beam AB (no slider connection).
xVab = -2.5*K; % Angular Velocity of Beam AB
xAab = -3*K; % Angular Acceleration of Beam AB
Rba = 0.2*(cosd(135)*I + sind(135)*J ); % Vector from A to B in X-Y
% Calculate velocity and acceleration of point B
% due to rotation of Beam AB (no slider connection).
Vb1 = cross(xVab,Rba);
Ab1 =…
I am trying to find a Direction Cosine Matrix (DCM) for the Euler angle body 1-2-3 sequence. I tried making my own function and using the MATLAB function, but the result is matrices that are not equal to each other. But, if I were to use the 'ZYX' sequence, I would get a matrix that is equal to the transpose of the matrix produced by my function.I mean that transpose(EA123toDCM) = E123toDCM if I changed the sequence to 'ZYX'. I never got two equal matrices. Can you fix my code so I would get two equal DCM matrices for the body 1-2-3 sequence?
Also, for the E123toDCM line, I am using the sequence 'XYZ'. Is that correct or should it be 'ZYX'? I know that that for a DCM of sequence 1-2-3 = R3(theta1)*R2(theta2)*R1(theta3). Is ZYX sequence the same as a 1-2-3 sequence?
EA = [pi/3; -pi/4; -pi/6];EA123toDCM = EA123DCM(EA)
E123toDCM = angle2dcm(EA(1,1), EA(2,1), EA(3,1), 'XYZ')
function [R] = EA123DCM(EA)
theta1 = EA(1,1); theta2 = EA(2,1); theta3 = EA(3,1); R1 =…
What is the return type of angles function in MATLAB ?
Chapter 9 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 9 - (a) Write the following set of equations in matrix...Ch. 9 - A number of matrices are defined as...Ch. 9 - Three matrices are defined as...Ch. 9 - Use the graphical method to solve...Ch. 9 - 9.5 Given the system of equations
(a) Solve...Ch. 9 - 9.6 For the set of equations
(a) Compute the...Ch. 9 - Given the equations 0.5x1x2=9.51.02x12x2=18.8 (a)...Ch. 9 - Given the equations...Ch. 9 - Use Gauss elimination to solve:...Ch. 9 - Given the system of equations...
Ch. 9 - 9.11 Given the equations
(a) Solve by Gauss...Ch. 9 - Use Gauss-Jordan elimination to solve:...Ch. 9 - 9.13 Solve:
with (a) naive Gauss elimination,...Ch. 9 - 9.14 Perform the same computation as in Example...Ch. 9 - 9.15 Solve
Ch. 9 - 9.16 Develop, debug, and test a program in either...Ch. 9 - Develop, debug, and test a program in either a...Ch. 9 - Develop, debug, and test a program in either a...Ch. 9 - 9.19 Three masses are suspended vertically by a...Ch. 9 - 9.20 Develop, debug, and test a program in either...Ch. 9 - 9.21 Recall from Sec. 8.2 that determining the...
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