Create local coordinate system and update throughout flight

Question

hologramkazaam 2021-8-30

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1443544-create-local-coordinate-system-and-update-throughout-flight

回答： darova 2021-9-5

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;