Adding a centripetal force to stop spaceship slipping at corners

I'm trying to make an arcade-y space sim type game. There are 6 degrees of freedom (throttle, strafe, elevation, pitch, roll, yaw) and I currently have the drag of the rigidbody set so that when decelerating in any direction the ship slows down in a nice gradual way. However I would like the ship to 'stick' to the corners while turning instead of slipping sideways.

One way of solving this (which I have tried) is to set the drag value very high but this means the ship slows down very quickly. I tried to solve this by making the actual throttle value slow down slower than the input throttle value but this quickly got complicated when dealing with the 3 directions of linear movement.

Now I would like to try and keep the ship traveling forwards by adding a centripetal force pointing inwards that will always counteract the side-slipping. I know realistic space sims like Elite Dangerous implement this system.

However, I'm not sure of an elegant way to apply such a force. What I'm trying to do right now is something like: void FixedUpdate () { // add forces from input script rb.AddRelativeForce (appliedLinearForce * forceMultiplier, ForceMode.Force); rb.AddRelativeTorque (appliedAngularForce * forceMultiplier, ForceMode.Force); // ADD CENTRIPETAL FORCE // find delta rotation and combine with forward velocity to find centrifugal Vector3 angleDifference = -rb.transform.InverseTransformDirection (lastDirection); float centripetalMagnitude = lastSpeed * Mathf.Sin ( angleDifference.z* (Mathf.PI/180)); Vector3 centripetalDirection = new Vector3(angleDifference.x,angleDifference.y,0); centripetalDirection.Normalize (); Vector3 centripetalForce = centripetalDirection * centripetalMagnitude * SOME_VALUE; rb.AddRelativeForce (centripetalForce, ForceMode.Force); lastDirection = transform.forward; lastSpeed = transform.InverseTransformDirection(rb.velocity).z; } I think this is sort of doing what I want but I am SURE this is not the best way of doing it, and also the centripetal force must be multiplied by some value (probably dependent on the mass) so it exactly cancels out the centrifugal force.

Any help would be greatly appreciated!