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Math Help - Helix

  1. #1
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    Helix

    Show that \mathbf{R} = \cos{t} (\mathbf{i} - \mathbf{j}) + \sin{t} (\mathbf{i} + \mathbf{j}) + \frac{1}{2}t\mathbf{k} is a helix

    I'm not sure what I have to show. I've already computed \mathbf{R}'(t), \mathbf{R}''(t), \mathbf{T}(t) and \kappa
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  2. #2
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    You're on the wrong track. You need to transform the equations you have into a set of equations that clearly define a helix.

    Try rotating the coordinate axes clockwise by 45^\circ around the z-axis.

    The substitution is:

    \mathbf{i}=\frac{\sqrt{2}}{2}\mathbf{i}'+\frac{\sq  rt{2}}{2}\mathbf{j}'

    \mathbf{j}=-\frac{\sqrt{2}}{2}\mathbf{i}'+\frac{\sqrt{2}}{2}\m  athbf{j}'

    and of course \mathbf{k}=\mathbf{k}'.

    And you'll need to know that a helix is defined by a particle traveling at a constant rate in the z direction, and around a circle with constant angular speed in the x-y direction.

    Post again if you're still having trouble.
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