Why does the rotate function let the body rotate around the wrong axis?

Hello everyone,

I have a problem regarding the rotate fuction.

I want to rotate the earth (sphere function) around it's z-axis in a heliocentric coordinate system (HCI).

The problem is: The rotation occurs around the x-axis or any other point in space, even though i specifically defined as followed.

origin: earth-center in HCI

direction: point in north pole direction in HCI

Edit: Maybe this picture helps -> I want the body to rotate around the Z_J2000 vector, expressed in HCI-coordinates (co-planar to the ecliptic plane).

Thanks in advance!

My code looks something like this:

[x,y,z]= sphere; %Defining the sphere

%Load Image file to project on sphere
image_file_earth = 'pic/earth_mercator.jpg';
cdata_ea = imread(image_file_earth);

%Plot earth
earth = surf(x*r_earth+x_coord_earth_HCI,...
             y*r_earth+y_coord_earth_HCI,...
             z*r_earth+z_coord_earth_HCI,'some settings');
%Some settings    
set(earth,'some settings');    

%Define axis of rotation
Q_GCI = [0 0 1] %z-axis in GCI

%Coordinate transformation from geocentric to heliocentric
eps = 23.439 %"obliquity of the ecliptic"

T_eps = [1 0 0;...
         0 cosd(eps) sind(eps);...
         0 -sind(eps) cosd(eps);]; 
%Transformation matrix for rotation around geocentric x-axis
          
Q_HCI = xyz_coord_earth_HCI'+T_eps*Q_GCI; 
%earth's position vector in heliocentric cs + rotated z-axis vector

rate = 10 %deg

%The rotation
rotate(earth,Q_HCI,rate,xyz_coord_earth_HCI);

[darova]

Why can't you just rotate data about X axis and the about Z?

[Felix Richter]

That is what i am trying to do. It just does not work.

And I am sure the coordinate transformation and therefore the rotation axis (Q_HCI) is right. The plot shows the axis is correctly defined.

But when i am trying to rotate the sphere-object about this axis, it rotates instead around the x-axis or any other point.

Now is my question: Am I using the rotate function wrong? I do understand the syntax as following:

rotate(object to rotate , one point in space (direction point) , angle of rotation , one point in space (origin point))

Am right about this?

[darova]

What about this?

[X,Y] = meshgrid(-1:1);
Z = X*0;
h = surf(X,Y,Z);
rotate(h, [0 0 1], 10, [0 0 0])
rotate(h, [1 0 0], 10, [0 0 0])

Answer 1

[David Goodmanson]

Hello Felix,

this shold be (assuming that the object's center is at (0,0,0) )

tilt = 23.4;
rotationangle = 30;  % for example
rotate(earth,[0 sind(tilt) cosd(tilt)],rotationangle)

You may have to change one or both of these angles to their negatives to get the right result.

[Felix Richter]

Hello David,

thanks for you answer!

Unfortunately the origin is not (0,0,0), but at a changing point in space (earth's center coasting through the solar system). The origin lies in the center of earth expressed in heliocentric coordinate system.

So:

axis_rot_geocentric = [0 0 1] -->

coordinate transformation -->

axis_rot_heliocentric = [0 0.3978 0.9175] + position_earth_in_heliocentric_cs

But:

The rotation just does not happen around this axis.