I have object A, I can get any information I want from object A (global position, velocity, etc)

I have object B, which is positioned and oriented in a certain way relative to object B. There is no parent/child relation between the 2 objects. I can't change the global position of object B, nor can I simply translate or rotate it. The only thing I can do is set the angular and linear velocities.

Is there a way for me to keep the relative position and orientation of object B when object A moves, while using only velocity? I've tried using what I could find online (including ChatGPT), but nothing seems to work. (i'm in 3D)

(Edit: after a comment, here is an example to clarify: object A can be a human character and object B his a Backpack. When the character moves, you want the backpack to remain on his back. Normally this is easily done with matrix transforms but in this case, we need to move the backpack only by controlling its angular and linear velocities)