MATLAB Answers

Create local coordinate system and update throughout flight

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hologramkazaam
hologramkazaam on 30 Aug 2021
Answered: darova on 5 Sep 2021
I am trying to monitor the position of a rocket throughout its trajectory by creating a local coordinate system. I would like it to update throughout the flight. My vector calculus is a bit rusty, so I'm having trouble getting the right angles to get the new axes. Right now, I'm trying to plot the new axes in a crude way, but I would appreciate any help in figuring this out or advice for a better way to do this.
close;
clear;
clc;
t = 0:pi/16:pi;
x = sin(t);
y = cos(t);
z = t;
[m,n] = size(t);
radius = zeros(1,n);
theta = zeros(1,n); % angle from +z axis to vector (zenith)
phi = zeros(1,n); % angle from +x axis to vector projection on xy-plane (azimuth)
rocket_angle = zeros(1,n);
lsm = 0.25; % line size modifier
for i=1:length(x)
plot3(x(i),y(i),z(i),'*r');
%plot3(x(i),y(i),0,'*b'); % vector projection
hold on;
pause(0.01);
radius(i) = sqrt(x(i)^2 + y(i)^2 + z(i)^2);
theta(i) = acosd(z(i)/radius(i)); % global coordinate system
phi(i) = atand(y(i)/x(i)); % global coordinate system
if i > 1
rocket_angle(i) = atand((y(i)-y(i-1))/(x(i)-x(i-1)));
% show rocket x-axis
line([x(i)-lsm*sind(rocket_angle(i)) x(i)+lsm*sind(rocket_angle(i))], [y(i)+lsm*sind(rocket_angle(i)) y(i)-lsm*sind(rocket_angle(i))], [z(i)-lsm*sind(rocket_angle(i)) z(i)+lsm*sind(rocket_angle(i))]);
% show rocket y-axis
% show rocket z-axis (cross product of x and y)
end
end
xlabel('X');
ylabel('Y');
zlabel('Z');
grid on;

Answers (1)

darova
darova on 5 Sep 2021
Just find tangent of a trajectory
x = 0:.1:pi;
y = sin(x);
u0 = diff(x); % component of a tangent
v0 = diff(y); % component of a tangent
u1 = u0./hypot(u0,v0); % normalization
v1 = v0./hypot(u0,v0);
line(x,y)
h = line(0,0,'color', 'r');
axis equal
for i = 1:length(x)-1
set(h,'xdata',x(i)+[u1(i) 0 -v1(i)]/2); % tangent and normal
set(h,'ydata',y(i)+[v1(i) 0 u1(i)]/2); % tangent and normal
pause(0.5)
end

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