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Unformatted text preview: [Return HW; hand out time sheets] Prof. Tibor Beke will substitute for me on Thursday and Friday of this week. Another perspective on the  v ( t ) =  v ( t ) for all t problem we discussed last time: What values can the left hand side take? What about the right hand side? Section 10.8: Arc length and curvature Three formulas for the curvature of a space curve: =  d T / ds  (the definition; requires the arclength parametrization) ( t ) =  T ( t )/ r ( t ) (any parametrization will do) ( t ) =  r ( t ) r ( t ) /  r ( t ) 3 An intuitive description of =  T ( t )/ r ( t ): Since the length of T ( t ) is constant,  T ( t ) is the rate of change of direction, or turning, of the unit tangent, and  r ( t ) measures the speed along the curve. So is the rate of turning of the unit tangent divided by the speed along the curve. For a circle in the plane parametrized in the standard way, r ( t ) = a...
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 Fall '11
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