Question

MATLAB

ICA 1: a) Using plot3, plot x, y and z given by the follow equations, for the range oft of 0.1, with R-10, r = 1.8, d :0.8, and a = 0.5: 0 to 200 in steps x(t) = (R-r) * cos (t) + d * cos R -r 佇r.r) . y(t) = |(R _ r) * sin(t) + d * sin (__ * t)|*cos (a * t) 2(t) = [A-r) * sin(t) + d * sin (--* t)| * sin (a * t) Your figure should look something like this 10 0 -5 -10 10 10 0 -5 -5 -10 -10

Answer 1

Note: Question consists of two subparts. Solved both the subparts Code 1(a): Givern Declare and initialize R R Val-10; Declare and initialize r r Val-1.8; Declare and initialize d d Val 0.8 Declare and initialize a a Val-0.5; %Declare and initialize steps steps = 0.1; Declare and initialize t t_Val-0: steps: 200; %Compute x r_Val) ./r_Val) . *t_Val))) %Compute y yval (((R Val-rVal ).*sin (tval) ) + (dVal.* sin ( ( (RVal- = ----- %Compute z %Plot 3D graph plot3 (x_Val, y_Val, z_Val)

Sample Output: -10 10 -5 -5 10 10 Code 1(b): &Given Declare and initialize R R Val-10; Declare and initialize r r Val-1.8; Declare and initialize d d Val-0.8 Declare and initialize a a Val-0.5; Declare and initialize steps steps 0.1; Declare and initialize t tVal = 0: steps: 40; - %Compute x x_Val -(((R_Val-r_Val) . *cos (t_Val)) r_Val) ./r_Val) . *t_Val))) (d Val.* Cos (( (R_Val-

%Compute y %Compute z Plot 3D graph with yellow color plot3 (x_Val, y_Val, z_Val, 'y') Hold hold on; Declare and initialize t t_Val -40: steps 80: %Compute x %Compute y %Compute z 8Plot 3D graph with red color plot3 (x_Val, y_Val, z_Val, 'r') Hold hold on; Declare and initialize t tval = 80: steps: 120; - %Compute x x_Val -(((R_Val-r_Val) . *cos (t_Val)) r_Val) ./r_Val) . *t_Val))) (d Val.* Cos (( (R_Val- %Compute y

%Compute z %Plot 3D graph with green color plot 3 (xval, yval, zVal, 'g') - - - Hold hold on; Declare and initialize t t Val -120: steps: 160; %Compute x r_Val) ./r_Val) . *t_Val))) %Compute y cos (a Val.*t Va %Compute z Plot 3D graph with magenta color plot 3 (xval, yval, zVal, 'm') - - - Hold hold on; Declare and initialize t t Val -160: steps: 200; %Compute x r_Val) ./r_Val) . *t_Val))) %Compute y %Compute z 8Plot 3D graph with blue color

plot3 (x_Val, y_Val, z_Val, 'b') %Hold hold on; Sample Output: 10 -5 -10 10 10 -5 -5 10 -10

Code to copy

%Code 1.a
%Given
%Declare and initialize R
R_Val=10;

%Declare and initialize r
r_Val=1.8;

%Declare and initialize d
d_Val=0.8;

%Declare and initialize a
a_Val=0.5;

%Declare and initialize steps
steps = 0.1;

%Declare and initialize t
t_Val=0: steps: 200;

%Compute x
x_Val = (((R_Val-r_Val).*cos(t_Val)) + (d_Val.* cos(((R_Val-r_Val)./r_Val).*t_Val)));

%Compute y
y_Val = (((R_Val-r_Val).*sin(t_Val)) + (d_Val.* sin(((R_Val-r_Val)./r_Val).*t_Val))) .* cos(a_Val.*t_Val);

%Compute z
z_Val = (((R_Val-r_Val).*sin(t_Val)) + (d_Val.* sin(((R_Val-r_Val)./r_Val).*t_Val))) .* sin(a_Val.*t_Val);

%Plot 3D graph
plot3(x_Val, y_Val, z_Val)

%Code 1.b
%Given
%Declare and initialize R
R_Val=10;

%Declare and initialize r
r_Val=1.8;

%Declare and initialize d
d_Val=0.8;

%Declare and initialize a
a_Val=0.5;

%Declare and initialize steps
steps = 0.1;

%Declare and initialize t
t_Val = 0: steps: 40;

%Compute x
x_Val = (((R_Val-r_Val).*cos(t_Val)) + (d_Val.* cos(((R_Val-r_Val)./r_Val).*t_Val)));

%Compute y
y_Val = (((R_Val-r_Val).*sin(t_Val)) + (d_Val.* sin(((R_Val-r_Val)./r_Val).*t_Val))) .* cos(a_Val.*t_Val);

%Compute z
z_Val = (((R_Val-r_Val).*sin(t_Val)) + (d_Val.* sin(((R_Val-r_Val)./r_Val).*t_Val))) .* sin(a_Val.*t_Val);

%Plot 3D graph with yellow color
plot3(x_Val, y_Val, z_Val, 'y')

%Hold
hold on;

%Declare and initialize t
t_Val = 40: steps: 80;

%Compute x
x_Val = (((R_Val-r_Val).*cos(t_Val)) + (d_Val.* cos(((R_Val-r_Val)./r_Val).*t_Val)));

%Compute y
y_Val = (((R_Val-r_Val).*sin(t_Val)) + (d_Val.* sin(((R_Val-r_Val)./r_Val).*t_Val))) .* cos(a_Val.*t_Val);

%Compute z
z_Val = (((R_Val-r_Val).*sin(t_Val)) + (d_Val.* sin(((R_Val-r_Val)./r_Val).*t_Val))) .* sin(a_Val.*t_Val);

%Plot 3D graph with red color
plot3(x_Val, y_Val, z_Val, 'r')

%Hold
hold on;

%Declare and initialize t
t_Val = 80: steps: 120;

%Compute x
x_Val = (((R_Val-r_Val).*cos(t_Val)) + (d_Val.* cos(((R_Val-r_Val)./r_Val).*t_Val)));

%Compute y
y_Val = (((R_Val-r_Val).*sin(t_Val)) + (d_Val.* sin(((R_Val-r_Val)./r_Val).*t_Val))) .* cos(a_Val.*t_Val);

%Compute z
z_Val = (((R_Val-r_Val).*sin(t_Val)) + (d_Val.* sin(((R_Val-r_Val)./r_Val).*t_Val))) .* sin(a_Val.*t_Val);

%Plot 3D graph with green color
plot3(x_Val, y_Val, z_Val, 'g')

%Hold
hold on;

%Declare and initialize t
t_Val = 120: steps: 160;

%Compute x
x_Val = (((R_Val-r_Val).*cos(t_Val)) + (d_Val.* cos(((R_Val-r_Val)./r_Val).*t_Val)));

%Compute y
y_Val = (((R_Val-r_Val).*sin(t_Val)) + (d_Val.* sin(((R_Val-r_Val)./r_Val).*t_Val))) .* cos(a_Val.*t_Val);

%Compute z
z_Val = (((R_Val-r_Val).*sin(t_Val)) + (d_Val.* sin(((R_Val-r_Val)./r_Val).*t_Val))) .* sin(a_Val.*t_Val);

%Plot 3D graph with magenta color
plot3(x_Val, y_Val, z_Val, 'm')

%Hold
hold on;

%Declare and initialize t
t_Val = 160: steps: 200;

%Compute x
x_Val = (((R_Val-r_Val).*cos(t_Val)) + (d_Val.* cos(((R_Val-r_Val)./r_Val).*t_Val)));

%Compute y
y_Val = (((R_Val-r_Val).*sin(t_Val)) + (d_Val.* sin(((R_Val-r_Val)./r_Val).*t_Val))) .* cos(a_Val.*t_Val);

%Compute z
z_Val = (((R_Val-r_Val).*sin(t_Val)) + (d_Val.* sin(((R_Val-r_Val)./r_Val).*t_Val))) .* sin(a_Val.*t_Val);

%Plot 3D graph with blue color
plot3(x_Val, y_Val, z_Val, 'b')

%Hold
hold on;