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The yaw plane translational equation, as in the pitch plane, equates the centripetal acceleration to the side force. = where (beta) is the sideslip angle, Y the side force and r the yaw rate. The moment equations are a bit trickier.
A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. In classical mechanics , a trajectory is defined by Hamiltonian mechanics via canonical coordinates ; hence, a complete trajectory is defined by position and momentum , simultaneously.
Flight dynamics is the science of air-vehicle orientation and control in three dimensions. The critical flight dynamics parameters are the angles of rotation with respect to the three aircraft's principal axes about its center of gravity, known as roll, pitch and yaw.
The position of all three axes, with the right-hand rule for describing the angle of its rotations. An aircraft in flight is free to rotate in three dimensions: yaw, nose left or right about an axis running up and down; pitch, nose up or down about an axis running from wing to wing; and roll, rotation about an axis running from nose to tail.
The most general maneuver described by the steady flight equations above is a steady climbing or descending coordinated turn. The trajectory the aircraft flies during this maneuver is a helix with z E as its axis and a circular projection on the x E-y E plane. [6] Other steady flight maneuvers are special cases of this helical trajectory.
This ballistic trajectory is referred to as the bullet path. If the projectile is spin stabilized, aerodynamic forces will also predictably arc the trajectory slightly to the right, if the rifling employs "right-hand twist." Some barrels are cut with left-hand twist, and the bullet will arc to the left, as a result.
A loop is when the pilot pulls the plane up into the vertical, continues around until they are heading back in the same direction, like making a 360 degree turn, except it is in the vertical plane instead of the horizontal. The pilot will be inverted (upside down) at the top of the loop.
However, it is likely that this term, describing a lateral asymmetric motion of an airplane, was borrowed from a reference to similar-appearing motion in ice skating. In 1916, aeronautical engineer Jerome C. Hunsaker published: "Dutch roll – the third element in the [lateral] motion [of an airplane] is a yawing to the right and left, combined ...