Use ihe Frenet-Serret formulas to prove each of the following. (Primes denote derivatives with respect to t . Start as in the proof of Theorem 10.) (a) r ″ = s ″ T + κ ( s r ) 2 N (b) r r × r n = κ ( s r ) 3 B (c) r m = [ s m − κ 2 ( s r ) 3 ] T + [3 κ s′ s″ + κ ′ ( s′ ) 2 ] N + κτ ( s′ ) 3 B (d) τ = ( r ′ × r ″ ) ⋅ r ‴ | r ′ × r ″ | 2
Use ihe Frenet-Serret formulas to prove each of the following. (Primes denote derivatives with respect to t . Start as in the proof of Theorem 10.) (a) r ″ = s ″ T + κ ( s r ) 2 N (b) r r × r n = κ ( s r ) 3 B (c) r m = [ s m − κ 2 ( s r ) 3 ] T + [3 κ s′ s″ + κ ′ ( s′ ) 2 ] N + κτ ( s′ ) 3 B (d) τ = ( r ′ × r ″ ) ⋅ r ‴ | r ′ × r ″ | 2
Solution Summary: The author explains the expression for Frenet-Serret formula.
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