VectorCalculus
Curvature
compute the curvature of a curve
Calling Sequence
Parameters
Description
Examples
Curvature(C, t)
C
-
free or position Vector or a Vector valued procedure; specify the components of the curve
t
(optional) name; specify the parameter of the curve
The Curvature(C, t) command computes the curvature of the curve C.
The curve C can be specified as a free or position Vector or a Vector valued procedure. This determines the returned object type.
If t is not specified, the function tries to determine a suitable variable name by using the components of C. To do this, it checks all of the indeterminates of type name in the components of C and removes the ones which are determined to be constants.
If the resulting set has a single entry, that single entry is the variable name. If it has more than one entry, an error is raised.
If a coordinate system attribute is specified on C, it is interpreted in this coordinate system. Otherwise, the curve is interpreted as a curve in the current default coordinate system. If the two are not compatible, an error is raised.
withVectorCalculus:
Curvaturecost,sint,t,t
2cost2+2sint224
CurvaturePositionVectorcost,sint
sint2+cost2
c≔Curvaturet↦t,t2,t3:
simplifyctassumingt::real
29t4+9t2+19t4+4t2+132
Curvatureacost,asint,tassuminga::constant
a2cost2a2+1+a2sint2a2+1a2+1
SetCoordinatespolar
polar
simplifyCurvatureexp−t,tassumingt::real
2ⅇt2
See Also
assuming
VectorCalculus[Binormal]
VectorCalculus[GetCoordinates]
VectorCalculus[PrincipalNormal]
VectorCalculus[RadiusOfCurvature]
VectorCalculus[SetCoordinates]
VectorCalculus[TangentVector]
VectorCalculus[TNBFrame]
VectorCalculus[Torsion]
VectorCalculus[Vector]
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