Aircraft flight mechanics are relevant to gliders, helicopters and aeroplanes.
An Aeroplane (Airplane in US usage), is defined as: a power-driven heavier than air aircraft, deriving its lift chiefly from aerodynamic reactions on surface which remain fixed under given conditions of flight. (ICAO Document 9110)
In straight and level flight, lift is approximately equal to weight. In addition, if the aircraft is not accelerating, thrust is approximately equal to drag.
In straight, climbing flight, thrust exceeds drag, and lift is less than weight. At first, this seems incorrect because if an aircraft is climbing it seems lift must exceed weight. When an aircraft is climbing at constant speed it is its thrust that enables it to climb and gain extra potential energy. Lift acts perpendicular to the velocity vector so lift is unable to alter the aircraft's potential energy or kinetic energy. This can be seen by considering an aerobatic aircraft in straight vertical flight - one that is climbing straight upwards (or descending straight downwards.) Vertical flight requires no lift! When flying straight upwards the aircraft can reach zero airspeed before falling earthwards - the wing is generating no lift and so does not stall.
In straight, descending flight thrust is less than drag, and lift is less than weight. In turning flight, lift exceeds weight and produces a load factor greater than one, determined by the aircraft's angle of bank.
It should be realized that using yaw alone is not a very efficient way of executing a level turn in an aircraft and will result in some sideslip. A precise combination of bank and lift must be generated to cause the required centripetal forces without producing a sideslip.
Pitch is controlled by the rear part of the tailplane's horizontal stabilizer being hinged to create an elevator. By moving the elevator control backwards the pilot moves the elevator up (a position of negative camber) and the downwards force on the horizontal tail is increased. The angle of attack on the wings increased so the nose is pitched up and lift is generally increased. In micro-lights and hang gliders the pitch action is reversed - the pitch control system is much simpler so when the pilot moves the elevator control backwards it produces a nose-down pitch and the angle of attack on the wing is reduced.
The system of a fixed tail surface and moveable elevators is standard in subsonic aircraft. Craft capable of supersonic flight often have a stabilator, an all-moving tail surface. Pitch is changed in this case by moving the entire horizontal surface of the tail. This seemingly simple innovation was one of the key technologies that made supersonic flight possible. In early attempts, as pilots exceeded the critical Mach number, a strange phenomenon made their control surfaces useless, and their aircraft uncontrollable. It was determined that as an aircraft approaches the speed of sound, the air approaching the aircraft is compressed and shock waves begin to form at all the leading edges and around the hinge lines of the elevator. These shock waves caused movements of the elevator to cause no pressure change on the stabilizer upstream of the elevator. The problem was solved by changing the stabilizer and hinged elevator to an all-moving stabilizer - the entire horizontal surface of the tail became a one-piece control surface. Also, in supersonic flight the change in camber has less effect on lift and a stabilator produces less drag.
Aircraft that need control at extreme angles of attack are sometimes fitted with a canard configuration, in which pitching movement is created using a forward foreplane (roughly level with the cockpit). Such a system produces an immediate increase in lift and therefore a better response to pitch controls. This system is common in delta-wing aircraft (deltaplane), which use a stabilator-type canard foreplane. A disadvantage to a canard configuration compared to an aft tail is that the wing cannot use as much extension of flaps to increase wing lift at slow speeds due to stall performance. A combination tri-surface aircraft uses both a canard and an aft tail (in addition to the main wing) to achieve advantages of both configurations.
A further design of tailplane is the V-tail, so named because that instead of the standard inverted T or T-tail, there are two vertical fins angled away from each other in a V (if they're arranged like a V, at least one of them isn't vertical). To produce yaw like a rudder, the two trailing edge control surfaces move in the same direction. To produce pitch like an elevator, the surfaces move in opposite directions.
Roll is controlled by movable sections on the trailing edge of the wings called ailerons. The ailerons move differentially - one goes up as the other goes down. The difference in camber of the wing cause a difference in lift and thus a rolling movement. As well as ailerons, there are sometimes also spoilers - small hinged plates on the upper surface of the wing, originally used to produce drag to slow the aircraft down and to reduce lift when descending. On modern aircraft, which have the benefit of automation, they can be used in combination with the ailerons to provide roll control.
The earliest powered aircraft built by the Wright brothers did not have ailerons. The whole wing was warped using wires. Wing warping is efficient since there is no discontinuity in the wing geometry. But as speeds increased unintentional warping became a problem and so ailerons were developed.
The actual linkages within the aircraft are discussed in aircraft flight control systems.