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