- Controlled by
DIGITSvariable - Numerical integrator keeps estimated relative error low enough
not to affect the first
DIGITSdigits of result
- Section 13.4
- Curvature = k = 1/|v| | dT/dt |
- T = unit tangent vector
- Large dT/ds implies sharper turn
- Circle of curvature at t
- Plane containing circle tangent to r at t
- Radius of curvature = p = 1/k
- Curvature = k = 1/|v| | dT/dt |
- Examples
- r(t) = ⟨ sin(t2/2), 1, cos(t2/2) ⟩
- What is the curvature function? What does it mean?
- What direction is r(t) curving when t = 0?
- Unit normal vector, N, points in direction of curve
- r(t) = ⟨ sin(t2/2), 1, cos(t2/2) ⟩
- Multi-variable functions
- Read section 14.1