How to Rotate a 3D Force Vector to Align with Another?

[IMK]

Hello
How do I manipulate (rotate) one 3D force vector so they are relative (in the same plane) as another 3D force vector please.

First I have is a static reference vector SF that is the accelerometer stationary at some orientation. Next I rotate the accelerometer around one or more axis and take another set of stationary measurements that are the SI vector.

What I want to do is to apply some function (rotation?) to the SI vector that will produce a new vector N that it is in alignment and proportional with the SF vector.

Thus:
N = SF ? SI
N = SF
Where SF is a static vector, SI is the current vector, N is a new vector

As you will see below I have included some sample accelerometer x,y,z axis data for SF and SI vector where
___________
/x*x+y*y+z*z = Eg

I have tried a very simple 2D axis subtraction method with only the Y and Z axis and this works well, but I have no idea how to do it for 3D can someone help please.

NB The accelerometer axis output value is the sine of the force on the axis.


Many thanks in advance

IMK

SF= Xg = 0.020615 Yg = -0.014522 Zg = 0.999183 Eg=0.999502
SI= Xg = 0.001649 Yg = -0.660823 Zg = 0.748382 Eg=0.998384

 

[LightHero]

The solution to your problem can be found using a combination of matrix rotation and vector normalization. First, you'll need to calculate the three Euler angles (yaw, pitch, and roll) that describe the angle between the SF vector and the SI vector. You can do this by using a 3x3 rotation matrix, as described here: https://en.wikipedia.org/wiki/Rotation_matrix#In_three_dimensions.Once you have the Euler angles, you can use them to rotate the SI vector so that it is aligned with the SF vector. To do this, you'll need to construct a 4x4 rotation matrix using the three Euler angles. You can then apply this rotation matrix to the SI vector to produce a new vector N that is aligned with the SF vector. Finally, you'll need to normalize N so that it has the same magnitude as SF.

 

[charng]

Hello,

Thank you for your question. I understand your desire to manipulate and rotate 3D force vectors in order to align them with a static reference vector. This type of manipulation is commonly used in various fields such as physics, engineering, and computer graphics.

To rotate a 3D force vector, you need to use a transformation matrix. This matrix is a mathematical tool that allows you to rotate, scale, and translate objects in 3D space. In order to align your SI vector with the SF vector, you will need to use a rotation matrix that will rotate the SI vector around one or more axes. The rotation matrix will depend on the desired angle and axis of rotation.

There are various methods for calculating rotation matrices, but one commonly used method is the Euler angles method. This method involves breaking down the rotation into three separate rotations around each axis. Once you have calculated the rotation matrix, you can apply it to your SI vector to obtain the new vector N that is aligned with the SF vector.

I understand that you have already tried a 2D axis subtraction method, which worked for the Y and Z axes. However, in order to rotate in 3D, you will need to use a more complex approach such as the one mentioned above.

I hope this helps. If you need further assistance, I recommend consulting with a mathematics or physics expert who has experience with 3D vector rotations. Good luck with your research!