**Modeling the Dynamics of Two-Dimensional Flight**

In this project, we will investigate the dynamics of flight in two dimensions (involving changes in altitude but not direction). For steady-state flight, where there is no change in speed or altitude, the aircraft is subject to the forces of thrust (T) and drag (D) in the horizontal direction, and lift (L) and weight (W) in the vertical direction. These forces must balance so that T = D and L = W. For a jet airplane, thrust is primarily a function of altitude, and so it will be considered to be constant for a given altitude below 36,000 feet. It can be found that for a specific altitude, there are two speeds at which T and D are equal; they can be seen as equilibria. We want to find whether these speeds generate stable equilibria or not. For one of the speeds, termed V1, an increase in speed also results in an increase in drag, so the aircraft slows down. If the speed decreases, the drag decreases, so the aircraft speeds up. A displacement from equilibrium, so this speed is statistically stable. For the other speed, termed V2, the opposite is true. Increased speed results in decreased drag, so the aircraft continues to speed up, but decreased speed results in increased drag, slowing the aircraft down even further. This speed is statistically unstable. My project involves confirming the stability and instability of the speeds of 950 ft/sec and 170 ft/sec at an altitude of 20,000 ft. I will also find the lift coefficient for a specific initial altitude and speed. Flight in two dimensions at a certain starting speed (dx/dt) and starting altitude (y) will be modeled using the dimensions specified in the introduction, and the computer will follow the subsequent flight history.