Chapter 2: Space Curves
Section 2.4: Curvature
Example 2.4.5
Obtain and graph the curvature of the catenary defined by y=coshx.
Solution
Type yx=… Context Panel: Assign Function
yx=coshx→assign as functiony
Write the formula for curvature. Press the Enter key.
Context Panel: Simplify≻Assuming Real
y″x1+y′x23/2
coshx1+sinhx23/2
→assuming real
1coshx2
Figure 2.4.5(a) contains a graph of κx, the curvature function for y=x2.
Figure 2.4.5(a) can be obtained interactively via the Context Panel option Plots≻Plot Builder.
Figure 2.4.5(a) Curvature of y=coshx
An alternative route to the curvature is via the Curvature command in the Student VectorCalculus package, provided the curve is represented as a position vector.
Initialize
Tools≻Load Package: Student Vector Calculus
Loading Student:-VectorCalculus
Write R=… as per Table 1.1.1.
Context Panel: Assign Name
R=x,coshx→assign
Obtain the curvature
Apply the simplify command to the result of an application of the Curvature command.
simplifyCurvatureR,x assuming real
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