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Curvature - Three Dimensional Space
In this part we want to briefly discuss the curvature of a smooth curve (remind that for a smooth curve we require →r′ (t) is continuous and →r′ (t) ≠ 0 ). The curvature measures how fast a curve is changing direction at a specific point.
There are various formulas for finding out the curvature for a curve. The formal definition of curvature is,
k = |d T→/ ds|
in which T→ stands for the unit tangent and s is the arc length. Remind that we saw in a preceding section how to reparameterize a curve to acquire it into terms of the arc length.
Generally the formal definition of the curvature is not simple to use so there are two alternate formulas that we can utilize. Here they are.
Κ = ||→T' (t)|| /|| →r' (t)||
Κ = || →r' (t) * →r''(t)|| /|| →r' (t)||3
These may not be particularly simple to deal with either, although at least we don't need to reparameterize the unit tangent.
How will you write this in words 216.9805
In the earlier section we introduced the Wronskian to assist us find out whether two solutions were a fundamental set of solutions. Under this section we will look at the other app
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