movement - Moving a ship forward from rotation

I am making a simple space simulator, where the player can control a ship using 2 controls, one for pitch and one for bank. The ship is properly rotated but I cannot figure out how to make the ship move forward based on that angle. Here's what the code looks like right now:

func renderer(renderer: SCNSceneRenderer, updateAtTime time: NSTimeInterval) {

    let t=CGFloat(time - lastTime)


    ship!.transform = CATransform3DRotate(CATransform3DRotate(CATransform3DRotate(ship!.transform, ud*t, -1, 0, 0), 0.00, 0, 1, 0), lr*t, 0, 0, 1);

    ship!.position = ?

}

I tried every combination of vector, euler angles, matrices, quaternions that I could think of/read about with no success. I am probably missing something stupid but cannot find what it is.

The code is in Swift using Scenekit, but language doesn't matter that much to me and I can translate any algorithm. It's also worth noting it does not work like Unity and Quarternions/Vectors don't have properties like .forward() etc.

Thank you for your help!