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Chapter 2: Space Curves

Section 2.7: Frenet-Serret Formalism

Example 2.7.14

If C is the curve given by Rp=lncosp i+lnsinp j+2p k, p0,π/2, in Example 2.6.3,

a) 

Obtain its Darboux vector d.

b) 

Verify the three identities in Table 2.7.3.

c) 

Show that T×T=κ2d, where primes denote differentiation with respect to arc length s.