Examples.
-
Input:
trigsimplify(curvature([5*cos(t),5*sin(t)],t))
Output:
- Input:
curvature([2*cos(t),3*sin(t)],t)
Output:
- Input:
curvature([2*cos(t),3*sin(t)],t,pi/2)
Output:
- Input:
curvature(plot(x^2),point(1,1))
(see Section 7.5 and Section 13.6.2.)
Output:
The osculating_circle command
finds and draws the osculating circle of a curve.
To find the osculating circle from a parameterization:
-
osculating_circle takes three arguments:
-
C, a curve.
- t, the parameter of the curve.
- t0, a value of the parameter.
- osculating_circle(C,t,t0) draws and returns the
osculating circle of the curve at the point specified by t0.
To find the osculating circle from a curve object:
-
osculating_circle takes two arguments:
-
C, a curve.
- p, a point on the curve.
- osculating_circle(C,p) draws and returns the
osculating circle of C at the point p.
Examples.
-
Input:
osculating_circle(plot(x^2),point(1,1))
Output:
- Input:
equation(osculating_circle(plot(x^2),point(1,1)))
Output:
⎛
⎝ | x+4 | ⎞
⎠ | 2+ | ⎛
⎜
⎜
⎝ | y− | | ⎞
⎟
⎟
⎠ | | = | |
- Input:
equation(osculating_circle([t^2,t^3],t,1))
Output:
⎛
⎜
⎜
⎝ | x+ | | ⎞
⎟
⎟
⎠ | | + | ⎛
⎜
⎜
⎝ | y− | | ⎞
⎟
⎟
⎠ | | = | |
The evolute command finds and draws the evolute of a curve.
To find the evolute from a parameterization:
-
evolute takes two arguments:
-
C, a curve.
- t, the parameter of the curve.
- evolute(C,t) draws and returns the
evolute of the curve.
To find the evolute from a curve object:
-
evolute takes one argument:
C, a curve.
- evolute(C) draws and returns the
evolute of C.
Examples.
-
Input:
evolute(plot(x^2))
Output:
- Input:
equation(evolute(plot(x^2)))
Output:
27 x2−16 y3+24 y2−12 y+2=0
|
- Input:
equation(evolute([t^2,t],t))
Output:
16 x3−24 x2+12 x−27 y2−2=0
|