notes001 (3)

notes001 (3) - Curvature Outline of Hass, Weir, Thomas...

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urvature Curvature Outline of Hass, Weir, Thomas – Section 10.4
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nit Tangent Vector Unit Tangent Vector If r t is a smooth curve, then the tangent vector to the curve (as a function of t )is v t d r / dt and the unit tangent vector is T t 1 | v t | v t .
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efinition Definition The curvature of a curve, r t , as a function of t is defined to be t 1 d T t . | v t | dt enotes rc ngth en t 1 | v t | t  dt s d T t d T s If s denotes arc length, then | v t | ds dt ds and thus the curvative is the magnitude of the rate of change f e nit ngent ector ith spect rc ngth of the unit tangent vector with respect to arc length .
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Examples 1) Show that a circle of radius a has curvature 1/ a . 2) Find the curvature function for the parabola y x 2 . 3) Let a and b be positive constants. Show that the helix,
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notes001 (3) - Curvature Outline of Hass, Weir, Thomas...

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