I am developing racing game.
To add what other guys have said. It’s complex, but here is start solution. First you need to choose relative target point and rotation of camera. For example: you want camera to be 10m behind car, 3m above ground (or car to be more precise) and to point toward car and road ahead (that’s camera rotation). As car moves, target point moves. Camera itself has max acceleration and max speed, when trying to reach target. So camera is chasing target point, and since it has max acceleration, which acts as inertia, you get smoothing effect, no shaking.
Edit: typo
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