objects moving on 3D terrain

I wanna have a vehicle moving in a 3D scene in which the terrain is not just a plane. Thus I need to transform the object to “stick” to the terrain correctly. Of course I also need to know when the terrain height is chanaged and requires me to transform my object so it moves on the changing terrain. Is there a name for this programming problem? Where do I find material on that?
I’d be most grateful for answers.

I don’t know the name of the problem, but you can first make the “up” vector of your model being the same as the normal of the polygon of the terrain the vehicle is touching.