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question in helix

Posted on 2012-09-07
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Last Modified: 2012-09-09
i am working on this problem.

All i need is : i need to come up with an equation of helix right ? I know how to find the intrinsic basis but i need to start from the position r of the particle where r is equal to the helix . Am i correct ?
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Question by:c_hockland
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Expert Comment

by:ozo
ID: 38378687
if r is a position, what do you mean by " r is equal to the helix"?
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Author Comment

by:c_hockland
ID: 38378700
r is the position but the position shouyld be a function of helix right ?
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Expert Comment

by:ozo
ID: 38378719
Do you mean a function of the angle θ?
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Author Comment

by:c_hockland
ID: 38378743
yes Sir
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Expert Comment

by:ozo
ID: 38378773
So if by "helix" you mean "the angle θ"
and I interpret your question as:
"i need to start from the position r of the particle where r is equal to the angle θ"
then that does not seem correct, unless you are trying to say "when r and θ are both 0"
and by r you mean something like "the arc-length parameter s"
If you mean "I need to find  position r of the particle as a function of the angle θ"
then that sounds like a useful thing to do, although it may be possible to answer some of the questions in problem 2.8 without need of finding the function.
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Author Comment

by:c_hockland
ID: 38378776
any idea or any tip on how to start working on this then ?
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Expert Comment

by:ozo
ID: 38378783
Finding the position of the bead as a function of the angle θ seems like a reasonable way to start.
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Author Comment

by:c_hockland
ID: 38378790
can i say that r = angle e1 and theta e2   ( e1 and e2 are unti vectors)
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Expert Comment

by:ozo
ID: 38378804
I'm confused.
What is "angle e1 and theta e2"
if e1 is a unit vector, what is "angle e1"
and if theta is an angle, what do you mean by "theta e2"?
Do you mean "the angle between e1 and e2"?
How are you defining the unit vectors e1 and e2?
If r is a position in 3 dimensions, don't you want 3 parameters to describe it?
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Author Comment

by:c_hockland
ID: 38378808
i was thinking to use two reference systems. One fixed to the ground and one fixed to the helix. So the position of the particle can be described as r = cos angle ( in the e1 direction and theta in the e2 direction)
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Expert Comment

by:ozo
ID: 38378820
I thought everything was fixed except for the bead.
If neither the helix nor the ground are moving, then both are fixed to each other.
If by "ground" you mean "the base of the helix", are you trying to say you want the two references to be:
the position of the point on the ground closest to the bead
and, the height of the bead above the ground?
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Author Comment

by:c_hockland
ID: 38378830
i guess we say the same things using different terms. But yes we agree.
since angle and theta are changing is my initial position function r correct ?
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Expert Comment

by:ozo
ID: 38378865
"since angle and theta are changing"
How does "angle" change with "theta"?
If e2 points along the axis of the helix, then the proportionality constant between theta and the projection of r along e2 would depend on R and φ
and you'd still need a third unit vector to describe the position of the bead.
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Accepted Solution

by:
ozo earned 2000 total points
ID: 38378870
If e1 is a unit vector in the O->A direction, then the e1 component of the position would be
R cos theta
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