18.2.1 Curvature of a curve
The curvature
command finds the curvature of a curve.
The curve can be given as an object or by a parameterization.
- To find the curvature from a parameterization,
curvature takes two mandatory arguments and one
optional argument:
- C, a curve.
- t, the parameter of the curve.
- Optionally, t0, a value of the parameter.
- curvature(C,t ⟨,t0⟩) returns the
curvature of the curve; if t0 is
given, the curvature is given at the point it specifies, otherwise
the curvature is given as a function of the parameter.
- To find the curvature from a curve object,
curvature takes two arguments:
- C, a curve.
- p, a point on the curve.
- curvature(C,p) returns the curvature of C at the
point p.
Examples
| trigsimplify(curvature([5*cos(t),5*sin(t)],t)) |
| trigsimplify(curvature([2*cos(t),3*sin(t)],t)) |
|
| |
| |
|
| 260 cos | ⎛
⎝ | 2 t | ⎞
⎠ | +25 cos | ⎛
⎝ | 4 t | ⎞
⎠ | +363 |
|
|
| | | | | | | | | | |
|
| curvature([2*cos(t),3*sin(t)],t,pi/2) |
| curvature(plot(x^2),point(1,1)) |
(see Section 19.2.3 and Section 26.5.2.)