How to rotate rigidbody's velocity with object's rotation

I have a character controller that climb walls like if it was ground, so the up vector (Y) won't always be the world up.

I also have a trigger that teleports the character to a certain place rotating it if needed (any direction). But only rotating it, the velocity won't go together, it keeps the momentum for the previous direction, world related.

How do I keep the momentum but to the correct relative direction? It needs to change the velocity direction according to the rotation, but I can't figure it out how.

Here's the transport code:

Code (CSharp):

1. public void ChangeTransform(Transform newTransform)
2. {
3.     transform.position = newTransform.position;
4.     transform.eulerAngles = newTransform.eulerAngles;
5.     transform.localScale = newTransform.localScale; // This is not needed right now
6. }

 

So basically you are in mario galaxy situation, I had something similar, I don't know if that helps:
https://gamedev.stackexchange.com/q...and-momentum-on-arbitrary-surface/53490#53490

 

Thanks. It seems similar to my problem, but I'm not entirely sure what to use from the code. It seems it is for a rotation over time according to inputs, and I don't see anything about rigidbody's velocity. I search for some way to rotate the velocity vector according to a instant rotation from the object. I think I should use

Quaternion target = Quaternion.LookRotation( relative_direction, MC.transform.up );

but I'm not sure how, as velocity is a Vector3