Aircraft principal axes
An aircraft in flight is free to rotate in three dimensions: pitch, nose up or down about an axis running from wing to wing, yaw, nose left or right about an axis running up and down; and roll, rotation about an axis running from nose to tail. The axes are alternatively designated as lateral, vertical, and longitudinal. These axes move with the vehicle, and rotate relative to the Earth along with the craft. These definitions were analogously applied to spacecraft when the first manned spacecraft were designed in the late 1950s.
These rotations are produced by torques (or moments) about the principal axes. On an aircraft, these are produced by means of moving control surfaces, which vary the distribution of the net aerodynamic force about the vehicle's center of gravity. Elevators (moving flaps on the horizontal tail) produce pitch, a rudder on the vertical tail produces yaw, and ailerons (moving flaps on the wings) produce roll. On a spacecraft, the moments are usually produced by a reaction control system consisting of small rocket thrusters used to apply asymmetrical thrust on the vehicle.
Principal axes 
- Vertical axis, or yaw axis — an axis drawn from top to bottom, and perpendicular to the other two axes. Parallel to the fuselage station.
- Lateral axis, transverse axis, or pitch axis — an axis running from the pilot's left to right in piloted aircraft, and parallel to the wings of a winged aircraft. Parallel to the buttock line.
- Longitudinal axis, or roll axis — an axis drawn through the body of the vehicle from tail to nose in the normal direction of flight, or the direction the pilot faces. Parallel to the waterline.
Normally these axes are represented by the letters X, Y and Z in order to compare them with some reference frame, usually named x, y, z. Normally this is made in such a way that the X is used for the longitudinal axis, but there are other possibilities to do it.
Vertical axis (yaw) 
The yaw axis is defined to be perpendicular to the body of the wings with its origin at the center of gravity and directed towards the bottom of the aircraft. A yaw motion is a movement of the nose of the aircraft from side to side. The pitch axis is perpendicular to the yaw axis and is parallel to the body of the wings with its origin at the center of gravity and directed towards the right wing tip. A pitch motion is an up or down movement of the nose of the aircraft. The roll axis is perpendicular to the other two axes with its origin at the center of gravity, and is directed towards the nose of the aircraft. A rolling motion is an up and down movement of the wing tips of the aircraft. The rudder is the primary control of yaw.
Lateral axis (pitch) 
The lateral axis (also called transverse axis) passes through the plane from wingtip to wingtips. Rotation about this axis is called pitch. Pitch changes the vertical direction the aircraft's nose is pointing. The elevators are the primary control of pitch.
Longitudinal axis (roll) 
The longitudinal axis passes through the plane from nose to tail. Rotation about this axis is called bank or roll. Bank changes the orientation of the aircraft's wings with respect to the downward force of gravity. The pilot changes bank angle by increasing the lift on one wing and decreasing it on the other. This differential lift causes bank rotation around the longitudinal axis. The ailerons are the primary control of bank. The rudder also has a secondary effect on bank.
Relationship with other systems of axes 
In aeronautical and aerospace engineering intrinsic rotations around these axes are often called Euler angles, but this conflicts with existing usage elsewhere. The calculus behind them is similar to the Frenet-Serret formulas. Performing a rotation in an intrinsic reference frame is equivalent to right-multiply its characteristic matrix (the matrix that has the vector of the reference frame as columns) by the matrix of the rotation.
See also 
- Aircraft flight control system
- Euler angles
- Fixed-wing aircraft
- Flight control surfaces
- Flight dynamics
- Moving frame
- Panning (camera)
- Screw theory
- Triad Method