Angle of Attack -(α)- the pitch[G] of an aircraft; low angles of attack will not typically create surplus lift, and high angles of attack can induce stalling.
Degrees of Freedom -- the number of directions an object can move in or axes the object can rotate about.
Elastic -- when one selects two arbitrary points on the aircraft, the distance between these two points changes over the course of motion. This is usually because the structure of the aircraft vibrates.
Flight Dynamics -- Flight Dynamics is a discipline that deals with the motion of rigid aircraft. Once we assume the aircraft is rigid[G], the aircraft can do only six motions; it can move in the x, y and z directions and it can rotate about the x, y and z axes. Hence, we say the aircraft has 6 degrees of freedom. The motion of rigid aircraft can be expressed by 6 second-order ordinary differential equations, or 12 first-order ordinary differential equations. By making further appropriate assumptions, the systems degrees of freedom can be reduced. For example, if we confine the motion of the aircraft to a vertical plane, then the degrees of freedom of the aircraft will be only 3.
Pitch -- The rotation about the lateral axis through an airframe that travels through the center of gravity (from left side to right side). When the pitch changes, the nose rises (+) and the tail drops or vice versa. Controlled by ailerons or flaps working in conjunction See Angle of Attack[G]
Rigid -- when one selects two arbitrary points on the aircraft, the distance between these two points remains the same over the course of motion. This is just an assumption to simplify things; in reality, the distance between any two points changes over the course of the motion because the structure of the aircraft vibrates.
Roll -- The rotation about the longitudinal axis through the center of gravity (from nose to tail). Rotation is also referred to as Banking. Rotating the craft to the right (right wingtip down) is considered positive. Banking is required to turn the aircraft. Controlled by ailerons in opposition to each other
Yaw -- The rotation about the vertical axis through the center of gravity (from top to bottom). Yaw is important to manipulate during turns to prevent a Slip; Helicopters utilize yaw in maneuvering. Guidance during taxi requires yaw. Positive to the right, controlled by the rudder.