The following code is used to plot a circular path:
% Head velocity
v = 1.5;
% Angular velocity
w = 1;
% Radius
R = v/w;
% Time
dt = 0.1;
t = 0:dt:(2*pi*R/v);
% Initial mobile robot position vector
x0 = 0; y0 = 0; th0 = 0;
P = [];
P(:,1) = [x0 y0 th0];
% Loop for all time steps
for k = 1 : length(t)
P(:,k+1) = P(:,k) + dt*[v*cos(P(3,k));v*sin(P(3,k));w];
plot(P(1,1:k+1),P(2,1:k+1))
pause(0.01)
axis square
axis([-2 2 -0.5 3.5])
end
, how can I manipulate the position vector to plot a right triangle path.
Thanks in advance.
Related
I am attempting to plot an elliptical orbit based on a 2-D position array, beginning at p= [5 0]. The plot charts positions from a timeframe t, here between 0 and 100. The calculation uses the formula F = -(p/||p||)(m*M/(p^2) to approximate acceleration and velocity. The result should look like the following:
This is my current code. It plots a completely different shape. Is the problem in my way of interpreting the force equation?
Any other help and comments are much appreciated.
t = 0; p = [50 0]; v = [0 8]; %Initial conditions
dt = 0.05;
M = 10000; m= 1;
tmax = 100;
figure, hold on
d = 0.001
clf;
while t < tmax
F = -(p./norm(p)).*(m*M./(p*p'));
a = F./m - d*v;
v = v + a*dt;
p = p + v*dt;
t = t + dt;
plot(p(1),t,'o','MarkerSize',0.5);
hold on;
plot(p(2),t,'o','MarkerSize',0.5);
end
You want p(1) in the x axis and p(2) in the y axis, with t as a parameter. So you need to replace the two plot lines by plot(p(1),p(2),'o','MarkerSize',0.5); (keeping hold on):
t = 0; p = [50 0]; v = [0 8]; %Initial conditions
dt = 0.05;
M = 10000; m= 1;
tmax = 100;
figure, hold on
d = 0.001
clf;
while t < tmax
F = -(p./norm(p)).*(m*M./(p*p'));
a = F./m - d*v;
v = v + a*dt;
p = p + v*dt;
t = t + dt;
hold on
plot(p(1),p(2),'o','MarkerSize',0.5); %%% modified line
end
What my plot looks like
What the plot should look like
The code is working like it should but im trying to get the labels to show up on each line from (1-8). Just like the picture above.
I have read a bunch of posts and tried to search Matlab but i havent been able to figure it out.
clc;clear;close all;
V_inf = 20; % freestream velocity
R = 1; % cylinder radius
n = 8; % number of panels
d_theta = 2*pi/n; % resolution of angles
alpha = 0; % angle of attack
theta = pi+pi/n:-d_theta:-pi+pi/n; % angles of boundary points of panels
X = R*cos(theta); % X coordinates of boundary points of panels
Y = R*sin(theta); % Y coordinates of boundary points of panels
Phi = zeros(n,1); % angle from Vinf to bottom of panel
beta = zeros(n,1); % angle from Vinf to outward normal of panel
conX = zeros(n,1); % X coordinates of control points
conY = zeros(n,1); % Y coordinates of control points
S = zeros(n,1); % panel length
for i = 1:n
Phi(i) = -alpha + atan2((Y(i+1)-Y(i)),(X(i+1)-X(i)));
beta(i) = Phi(i)+pi/2;
if beta(i)>2*pi, beta(i)=beta(i)-2*pi;
elseif beta(i)<0, beta(i)=beta(i)+2*pi; end
conX(i) = (X(i+1)+X(i))/2;
conY(i) = (Y(i+1)+Y(i))/2;
S(i) = sqrt((X(i+1)-X(i))^2 + (Y(i+1)-Y(i))^2);
end
close all
plot(R*cos(0:0.01:2*pi),R*sin(0:0.01:2*pi),'b', X,Y,'r',conX,conY,'g^');
axis equal; legend('Exact shape','Panel approximation','Control points')
xlabel('x, m'); ylabel('y, m'); title('Fig. 1 Panel layout (n = 8, R = 1m)');
Possibly plotting the labels along the points of a circle using the text() function may suffice. There's some shifting of points and flipping that needs to be done to get the order you wish but otherwise it's just 8 points taken along a circle that is smaller in diameter in comparison to the octagon. An alternative would be using the green triangles as reference instead but that involves more math. As long as your octagon is expected to be symmetrical vertically and horizontally this should work alright.
clc;clear;close all;
V_inf = 20; % freestream velocity
R = 1; % cylinder radius
n = 8; % number of panels
d_theta = 2*pi/n; % resolution of angles
alpha = 0; % angle of attack
theta = pi+pi/n:-d_theta:-pi+pi/n; % angles of boundary points of panels
X = R*cos(theta); % X coordinates of boundary points of panels
Y = R*sin(theta); % Y coordinates of boundary points of panels
Phi = zeros(n,1); % angle from Vinf to bottom of panel
beta = zeros(n,1); % angle from Vinf to outward normal of panel
conX = zeros(n,1); % X coordinates of control points
conY = zeros(n,1); % Y coordinates of control points
S = zeros(n,1); % panel length
for i = 1:n
Phi(i) = -alpha + atan2((Y(i+1)-Y(i)),(X(i+1)-X(i)));
beta(i) = Phi(i)+pi/2;
if beta(i)>2*pi, beta(i)=beta(i)-2*pi;
elseif beta(i)<0, beta(i)=beta(i)+2*pi; end
conX(i) = (X(i+1)+X(i))/2;
conY(i) = (Y(i+1)+Y(i))/2;
S(i) = sqrt((X(i+1)-X(i))^2 + (Y(i+1)-Y(i))^2);
end
close all
plot(R*cos(0:0.01:2*pi),R*sin(0:0.01:2*pi),'b', X,Y,'r',conX,conY,'g^');
axis equal; legend('Exact shape','Panel approximation','Control points')
xlabel('x, m'); ylabel('y, m'); title('Fig. 1 Panel layout (n = 8, R = 1m)');
%*************************************************************************%
%ADDING LABELS BY PLOTTING LABELS ALONG CIRCLE%
%*************************************************************************%
Radius = 0.8;
Number_Of_Data_Points = 9;
theta = linspace(0,2*pi,Number_Of_Data_Points);
X_Circle = Radius*cos(theta);
X_Circle = X_Circle(1:end-1);
Y_Circle = Radius*sin(theta);
Y_Circle = Y_Circle(1:end-1);
X_Circle = flip(circshift(X_Circle,3));
Y_Circle = flip(circshift(Y_Circle,3));
for Point_Index = 1: numel(conX)
X_Displacement = X_Circle(Point_Index);
Y_Displacement = Y_Circle(Point_Index);
text(X_Displacement,Y_Displacement,num2str(Point_Index),'HorizontalAlignment','center','fontsize',20);
end
To Plot on Control Points:
%*************************************************************************%
%ADDING LABELS BY PLOTTING LABELS ALONG CONTROL POINTS%
%*************************************************************************%
for Point_Index = 1: numel(conX)
text(conX(Point_Index),conY(Point_Index),num2str(Point_Index),'HorizontalAlignment','center','fontsize',20);
end
With the following code I am generating a V plane with 2 different slopes, 10° and 20° respectively.
% /*
% Assumptions
% */
% resolution [m]
res = 1;
% inclination [deg]
i1 = 10; i2 = 20;
% /*
% DEM -> V shape
% */
% pre-allocate output
testDEM = zeros(513);
% required elevation step [m]
hstep = res*tan(i1*(pi/180));
% elevation start right [m]
k = 513*(2/3)*tan(i1*(pi/180));
% coordinates
q = length(1:513*(2/3));
% initialize
nStep = 0;
for jj = 1:q
testDEM(:,jj) = k-nStep;
nStep = nStep + hstep;
end
% change elevation step
step = res*tan(i2*(pi/180));
% update nStep
nStep = step;
% elevation start left [m]
start = testDEM(end,q);
for jj = q+1:513
testDEM(:,jj) = start + nStep;
nStep = nStep + step;
end
testDEM = testDEM(1:507,1:507);
%//Plot test DEM
f_tSlope = figure();
set(gca,'PlotBoxAspectRatio',[1 1 1]);
surf(testDEM, 'EdgeColor', 'none')
colormap jet;
hb = colorbar('location','eastoutside');
hb.Label.String = '[m]';
hb.Label.Rotation = 0;
hb.Label.HorizontalAlignment = 'Left';
With the following I'm adding noise in every location
sigma = 1;
testDEM = testDEM + sigma*randn(size(testDEM));
But what I'd like instead is to add random noise in random location, not everywhere. How can I do it?
Thanks in advance
How about this:
N_locations = 100; % no. of locations to add random noise
% randomize 'N_locations' linear indecies in 'testDEM':
noise_location = randi(numel(testDEM),N_locations,1);
% add the noise:
testDEM(noise_location) = testDEM(noise_location)+sigma*randn(N_locations,1);
This will randomize N_locations random locations on the map, and apply different random noise to each of them.
If you prefer to add the same noise to all random locations, just write sigma*randn, without the parenthesis after it.
For small N_locations this should suffice. However, if you want to make sure you don't pick the same location twice, or N_locations is large, you can set noise_location like this:
noise_location = randperm(numel(testDEM),N_locations);
so you'll have only non-repeating values of indices in testDEM.
This code adds noise with 0.5 probability
testDEM = testDEM + sigma*randn(size(testDEM)) .* (rand(size(testDEM)) > 0.5);
I want to use streamline to show a vector field. The vector field is singular in a point. I want to remove regions near the singularity (fo example regions which their distance to singularity is less than 1). I wrote below code but it doesn't show anything. Could anyone help me?
clear all;
close all;
r1 = 1; r2 = 5; % Radii of your circles
x_0 = 0; y_0 = 0; % Centre of circles
[x,y] = meshgrid(x_0-r2:0.2:x_0+r2,y_0-r2:0.2:y_0+r2); % meshgrid of points
idx = ((x-x_0).^2 + (y-y_0).^2 > r1^2 & (x-x_0).^2 + (y-y_0).^2 < r2^2);
x = sort(x(idx));
[x, index] = unique(x);
y = sort(y(idx));
[y, index] = unique(y);
U=cos(x)/sqrt(x.^2+y.^2);
V=sin(x)/sqrt(x.^2+y.^2);
streamslice(x,y,U,V);
The problem with your code is that U and V are all zeros, so you get white space. The reason for that is that you don't use elementwise division with ./. So as a first step you should write:
U = cos(x)./sqrt(x.^2+y.^2);
V = sin(x)./sqrt(x.^2+y.^2);
Now U and V are not zeros but are also not matrices anymore, so they are not a valid input for streamslice. The reason for that is that x and y are converted to vectors when calling:
x = sort(x(idx));
y = sort(y(idx));
My guess is that you can remove all this indexing, and simply write:
r1 = 1; r2 = 5; % Radii of your circles
x_0 = 0; y_0 = 0; % Centre of circles
[x,y] = meshgrid(x_0-r2:0.2:x_0+r2,y_0-r2:0.2:y_0+r2); % meshgrid of points
U = cos(x)./sqrt(x.^2+y.^2);
V = sin(x)./sqrt(x.^2+y.^2);
streamslice(x,y,U,V);
so you get:
I think you misunderstood the concept of streamslice. Is this you expecting?
close all;
r1 = 1; r2 = 5; % Radii of your circles
x_0 = 0; y_0 = 0; % Centre of circles
[xx,yy] = meshgrid(x_0-r2:0.2:x_0+r2,y_0-r2:0.2:y_0+r2); % meshgrid of points
% idx = ((xx-x_0).^2 + (yy-y_0).^2 > r1^2 & (xx-x_0).^2 + (yy-y_0).^2 < r2^2);
% x = sort(xx(idx));
% [x, index] = unique(x);
% y = sort(yy(idx));
% [y, index] = unique(y);
U=cos(xx)./sqrt(xx.^2+yy.^2);
V=sin(xx)./sqrt(xx.^2+yy.^2);
streamslice(xx,yy,U,V);
I'm trying to model projectile motion with air resistance.
This is my code:
function [ time , x , y ] = shellflightsimulator(m,D,Ve,Cd,ElAng)
% input parameters are:
% m mass of shell, kg
% D caliber (diameter)
% Ve escape velocity (initial velocity of trajectory)
% Cd drag coefficient
% ElAng angle in RADIANS
A = pi.*(D./2).^2; % m^2, shells cross-sectional area (area of circle)
rho = 1.2 ; % kg/m^3, density of air at ground level
h0 = 6800; % meters, height at which density drops by factor of 2
g = 9.8; % m/s^2, gravity
dt = .1; % time step
% define initial conditions
x0 = 0; % m
y0 = 0; % m
vx0 = Ve.*cos(ElAng); % m/s
vy0 = Ve.*sin(ElAng); % m/s
N = 100; % iterations
% define data array
x = zeros(1,N + 1); % x-position,
x(1) = x0;
y = zeros(1,N + 1); % y-position,
y(1) = y0;
vx = zeros(1,N + 1); % x-velocity,
vx(1) = vx0;
vy = zeros(1,N + 1); % y-velocity,
vy(1) = vy0;
i = 1;
j = 1;
while i < N
ax = -Cd*.5*rho*A*(vx(i)^2 + vy(i)^2)/m*cos(ElAng); % acceleration in x
vx(i+1) = vx(i) + ax*dt; % Find new x velocity
x(i+1) = x(i) + vx(i)*dt + .5*ax*dt^2; % Find new x position
ay = -g - Cd*.5*rho*A*(vx(i)^2 + vy(i)^2)/m*sin(ElAng); % acceleration in y
vy(i+1) = vy(i) + ay*dt; % Find new y velocity
y(i+1) = y(i) + vy(i)*dt + .5*ay*dt^2; % Find new y position
if y(i+1) < 0 % stops when projectile reaches the ground
i = N;
j = j+1;
else
i = i+1;
j = j+1;
end
end
plot(x,y,'r-')
end
This is what I am putting into Matlab:
shellflightsimulator(94,.238,1600,.8,10*pi/180)
This yields a strange plot, rather than a parabola. Also it appears the positions are negative values. NOTE: ElAng is in radians!
What am I doing wrong? Thanks!
You have your vx and vy incorrect... vx= ve*sin(angle in radians) and opposite for vy. U also u do not need a dot in between ur initial velocity and the *... That is only used for element by element multiplication and initial velocity is a constant variable. However the dot multiplier will not change the answer, it just isn't necessary..