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  2. Rotation of axes in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotation_of_axes_in_two...

    In mathematics, a rotation of axes in two dimensions is a mapping from an xy - Cartesian coordinate system to an x′y′ -Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle . A point P has coordinates (x, y) with respect to the ...

  3. Rotations and reflections in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotations_and_reflections...

    A rotation in the plane can be formed by composing a pair of reflections. First reflect a point P to its image P′ on the other side of line L1. Then reflect P′ to its image P′′ on the other side of line L2. If lines L1 and L2 make an angle θ with one another, then points P and P′′ will make an angle 2θ around point O, the ...

  4. Euler angles - Wikipedia

    en.wikipedia.org/wiki/Euler_angles

    ] In four dimensions and above, the concept of "rotation about an axis" loses meaning and instead becomes "rotation in a plane." The number of Euler angles needed to represent the group SO( n ) is n ( n − 1)/2 , equal to the number of planes containing two distinct coordinate axes in n -dimensional Euclidean space.

  5. Aircraft principal axes - Wikipedia

    en.wikipedia.org/wiki/Aircraft_principal_axes

    Aircraft principal axes. 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 axes are alternatively designated as vertical, lateral (or transverse ...

  6. Axes conventions - Wikipedia

    en.wikipedia.org/wiki/Axes_conventions

    Axes named according to the air norm DIN 9300. In ballistics and flight dynamics, axes conventions are standardized ways of establishing the location and orientation of coordinate axes for use as a frame of reference. Mobile objects are normally tracked from an external frame considered fixed. Other frames can be defined on those mobile objects ...

  7. Flight dynamics - Wikipedia

    en.wikipedia.org/wiki/Flight_dynamics

    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. Aircraft engineers develop control systems for a vehicle's orientation ...

  8. Aircraft flight dynamics - Wikipedia

    en.wikipedia.org/wiki/Aircraft_flight_dynamics

    Aircraft flight dynamics. Flight dynamics is the science of air vehicle orientation and control in three dimensions. The three critical flight dynamics parameters are the angles of rotation in three dimensions about the vehicle's center of gravity (cg), known as pitch, roll and yaw. These are collectively known as aircraft attitude, often ...

  9. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    Every rotation in three dimensions is defined by its axis (a vector along this axis is unchanged by the rotation), and its angle — the amount of rotation about that axis (Euler rotation theorem). There are several methods to compute the axis and angle from a rotation matrix (see also axis–angle representation ).