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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. 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 ...

  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. Right-hand rule - Wikipedia

    en.wikipedia.org/wiki/Right-hand_rule

    Right-hand rule. In mathematics and physics, the right-hand rule is a convention and a mnemonic, utilized to define the orientation of axes in three-dimensional space and to determine the direction of the cross product of two vectors, as well as to establish the direction of the force on a current-carrying conductor in a magnetic field.

  7. Flight control surfaces - Wikipedia

    en.wikipedia.org/wiki/Flight_control_surfaces

    The controls (stick and rudder) for rotary wing aircraft (helicopter or autogyro) accomplish the same motions about the three axes of rotation, but manipulate the rotating flight controls (main rotor disk and tail rotor disk) in a completely different manner. Flight control surfaces are operated by aircraft flight control systems.

  8. 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.

  9. Gyroscope - Wikipedia

    en.wikipedia.org/wiki/Gyroscope

    The rotor will maintain its spin axis direction regardless of the orientation of the outer frame. A gyroscope (from Ancient Greek γῦρος gŷros, "round" and σκοπέω skopéō, "to look") is a device used for measuring or maintaining orientation and angular velocity. [ 1 ][ 2 ] It is a spinning wheel or disc in which the axis of ...