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Orbital Movement

  • IcemanBo

    IcemanBo

    Joined:
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    Orbital Movement

    There is an angle phi that is defined to rotate around z-axis [local system]. When it makes 360°, it will result in one complete rotation. It should be permanently increasing/decreasing, to simulate the motion.

    The motion curve is described by 3 angles:
    • alpha = yaw = rotation around x-axis [global system]
    • beta = pitch = rotation around y-axis [global system]
    • gamma = roll = rotation around z-axis [global system]
    Difference between global and local coordination system
    Global:

    Global system is the world's normal axis system. It is constant, so x,y,z directions are always the same.

    Local:

    In this system the local system describes a 2D simple circle on its x-y-plane, meaning the z-coordinate is always 0.

    Final Rotation + shift:

    The final rotation is obtained by rotating the circle's local coordinate system around the global coordinate system. The shift from global origin is described by defined x/y/z center-coordinates.

    [​IMG]
    [​IMG]

    ... in this system the actual axis rotations can be described by 2 things:
    • Amplitude:
      Describes the axis rotation, between 0° and 360°.
      Technically, with only defining amplitudes you already can get all possible points on the sphere.

    • Frequency Factor:
      The frequency factor will result in pendeling the respective axis rotation between amplitude values.
      Its actual value will always be somewhere from amplitude to -amplitude.
      • Factor = 0 → amplitude/axis rotation is constant
      • Factor = 1 → amplitude/axis rotation equals phi_speed
      • 0 < Factor < 1 → slower curves (with coming closer to 0 it gets slower)
      • 1 < Factor → faster curves
      So the factor only describes how fast the actual angle rotation goes between the amplitudes.

      Example:
      We make alpha_amplitude 50° and make frequency factor 2.
      Now the alpha rotation (x-axis) will go between 50° and -50°, back and forth, with factor 2, leading in 2x speed of a normal sinus curve.
     

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