I have decided that in order to improve my math skills and game programming skills I am going to work on a two-dimensional space simulator. The view of the player or camera will be from inside the cockpit of a spaceship. This presents quite a few challenges which I am looking to the gd.net community for help with. I'm not asking for any code or any specific answers, just suggestions on what subjects to research.
My first challenge is going to be related to perspective correction. Since I'm only working with two-dimensions I need to fake flight dynamics. If you imagine that you are sitting in a cockpit of a spaceship, when you move the flight stick to the right or left the ship would yaw in either direction. Simulating this in two dimensions is much more difficult than in three dimensions, as you have to apply some sort of perspective correction.
The same is true if you were to pitch the nose of the spacecraft up or down. Simply moving the camera along the x / y axes won't be enough. I need to correct the perspective of my camera so that it appears that the aircraft is actually yawing / pitching in the desired direction and not just panning upwards / to the side.
What is the basic mathematical formula for applying this kind of perspective correction? If a formula is too much to ask for, where can I read about examples of this being done / read about the basic concepts I need to understand to accomplish this?