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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.
Euler angles; Quaternions; The various Euler angles relating the three reference frames are important to flight dynamics. Many Euler angle conventions exist, but all of the rotation sequences presented below use the z-y'-x" convention. This convention corresponds to a type of Tait-Bryan angles, which are commonly referred to as Euler angles ...
The axes of the original frame are denoted as x, y, z and the axes of the rotated frame as X, Y, Z.The geometrical definition (sometimes referred to as static) begins by defining the line of nodes (N) as the intersection of the planes xy and XY (it can also be defined as the common perpendicular to the axes z and Z and then written as the vector product N = z × Z).
Member states are allowed to modify the low flying rule to suit their jurisdiction, for instance in the UK, the "500 ft Rule" allows pilots to fly below 500 ft as long as they are no closer than 500 ft to any person, vessel, vehicle, building or structure. The rules for flying near congested areas are the same in the UK as the rest of the EU [15]
Small circles are the spherical-geometry analog of circles in Euclidean space. Every circle in Euclidean 3-space is a great circle of exactly one sphere. The disk bounded by a great circle is called a great disk : it is the intersection of a ball and a plane passing through its center.
Such angles are called a linear pair of angles. [20] However, supplementary angles do not have to be on the same line and can be separated in space. For example, adjacent angles of a parallelogram are supplementary, and opposite angles of a cyclic quadrilateral (one whose vertices all fall on a single circle) are supplementary.
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The most external matrix rotates the other two, leaving the second rotation matrix over the line of nodes, and the third one in a frame comoving with the body. There are 3 × 3 × 3 = 27 possible combinations of three basic rotations but only 3 × 2 × 2 = 12 of them can be used for representing arbitrary 3D rotations as Euler angles. These 12 ...