Deriving maximum velocity in a rotated frame

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  • Thread starter jumbo1985
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  • #1
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rotate%20frame_zps6lbjzvxf.jpg

I have a particle that travels in the cartesian plane with the maximum velocity of A units along the x-axis and B units along the y-axis per unit of time.

How do I go about deriving the maximum velocity of my particle in the rotated uv plane? (the maximum distance the particle can along the u and the v axes in one unit of time)

Any tips greatly appreciated.
 

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  • #2
Buzz Bloom
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Hi jumbo:

I suggest it might help if you add an arrow in the diagram to represent the vector M from the origin to point (x=A,y=B). Then draw perpendiculars from (A,B) to the axes u and v. If you know the angle between x axis and u axis, you can calculate the length of the perpendiculars to the u axis and v axis which represent the M coordinates with respect to the v axis and u axis respectively.

Hope this helps.

Regards,
Buzz
 
  • #3
19
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Thanks Buzz Bloom.

Is this what you mean?

vel_max_zpsuvcup2vg.jpg


Where the length of A' is the maximum distance my particle can travel along the u-axis of the rotated frame in one unit of time. Similarly, the length of B'...
 
Last edited:
  • #4
Buzz Bloom
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Hi jumbo:

I apologize for not expressing my thought more clearly.

You want to draw a line, call it L, from the origin to the point M. M will be on the vertical green line at the height B. L represents the vector corresponding to the maximum velocity of the particle you are describing.

Next draw lines from the point M perpendicular to the u and v axes. These lines will show the coordinates of the vector L in the (u,v) coordinate system. The resulting diagram should help you figure out how to calculate the u and v coordinates of the vector L.

By the way, for the particular example you have drawn, you may want to notice that the v coordinate of L is negative.

Hope this helps.

Regards,
Buzz
 
  • #5
19
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I think I got it. Thanks Buzz

vel_max_2_zpscfsvfczk.jpg
 
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