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Rotation of line about rotating axis

  1. Nov 9, 2015 #1
    axis A is always normal to plane of the circle and passes thru centre of circle
    axis B is always parallel to plane of circle and is always parallel to y- axis of lab frame.
    axis B passes thru centre of the circle
    the infinitely long line MN always lies on the plane of the circle and passes thru centre of circle
    the line MN rotates (in plane of circle) about axis A. with angular velo "w1"
    the plane of circle itself rotates about axis B with angular velo "w2"
    if w1 is not equal to w2 and
    w1 is not equal to w2 / 2 and
    w1 /2 is not equal to w2
    then -
    will the line MN (at some point of time) pass thru every point (coordinates defined wrt lab frame) in 3d space?
    (rotations continue forever)

    DSC05749.JPG
     
    Last edited: Nov 9, 2015
  2. jcsd
  3. Nov 9, 2015 #2

    BvU

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    If ##i * \omega_1 = j * \omega_2## (with i, j integers) then it's easy to see that MN sweeps through the xy plane at fixed positions. So it's a matter of common dividers. You only excluded i = 2, j = 1.
     
  4. Nov 9, 2015 #3
    i am adding 3 points to my initial question-
    w1 is not an integral multiple of w2
    w2 is not an integral multiple of w1
    axis B is fixed wrt lab frame

    my question remains unchanged -
     
  5. Nov 10, 2015 #4

    BvU

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    Moving the goalposts while playing, eh ? Do you know about Lissajous figures ? Your casus is analogous in every possible respect if you think of spherical angular coordinates ##\theta## and ##\phi## instead of x and y.
     
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