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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. 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 ...

  5. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    If we condense the skew entries into a vector, (x,y,z), then we produce a 90° rotation around the x-axis for (1, 0, 0), around the y-axis for (0, 1, 0), and around the z-axis for (0, 0, 1). The 180° rotations are just out of reach; for, in the limit as x → ∞ , ( x , 0, 0) does approach a 180° rotation around the x axis, and similarly for ...

  6. 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 ...

  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. Euler angles - Wikipedia

    en.wikipedia.org/wiki/Euler_angles

    There are six possibilities of choosing the rotation axes for proper Euler angles. In all of them, the first and third rotation axes are the same. The six possible sequences are: z 1-x′-z 2 ″ (intrinsic rotations) or z 2-x-z 1 (extrinsic rotations) x 1-y′-x 2 ″ (intrinsic rotations) or x 2-y-x 1 (extrinsic rotations)

  9. Spacecraft flight dynamics - Wikipedia

    en.wikipedia.org/wiki/Spacecraft_flight_dynamics

    Spacecraft flight dynamics is the application of mechanical dynamics to model how the external forces acting on a space vehicle or spacecraft determine its flight path. These forces are primarily of three types: propulsive force provided by the vehicle's engines; gravitational force exerted by the Earth and other celestial bodies; and ...