Calculus III: Section 13 - Shippensburg University of...
Transcript of Calculus III: Section 13 - Shippensburg University of...
Calculus III: Section 13.4
Professor Ensley
Ship Math
September 30, 2011
Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 1 / 6
Curvature
Curvature
Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 2 / 6
Curvature
Curvature
Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 2 / 6
Curvature
Curvature
Example. Find the curvature of the circle with vector parameterizationr(s) = 〈cos (s/R), sin (s/R)〉.
Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 2 / 6
Curvature
Curvature
Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 2 / 6
Curvature
Curvature
Use ParametricPlot3D to visualize.
Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 3 / 6
Curvature
Curvature
Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 3 / 6
Unit normal vector
Unit normal vector
Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 4 / 6
Unit normal vector
Unit normal vector
this
Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 4 / 6
Osculating circles
Osculating circles
Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 5 / 6
Osculating circles
Osculating circles
Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 5 / 6
Osculating circles
Osculating circles
Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 5 / 6
Osculating circles
Osculating circles in 3D
Professor Ensley (Ship Math) Calculus III: Section 13.4 September 30, 2011 6 / 6