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V a cosh 2 t sinh 2 t 1 2 cosh t 9 unit binormal

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Unformatted text preview: r B v |v a a| 1 2 cosh t cosh t , sinh t , 1 1 10. unit normal vector î N B 1 2 cosh t T 1 2 cosh 2 t 1 2 cosh 2 t k cosh t 2 sinh t sinh t cosh t î sinh t 1 1 sinh t cosh t cosh t 0, 2 cosh t , 2 sinh t cosh t 0, k cosh t sinh t sinh t cosh t 1 , sinh t cosh t cosh t 11. curvature |v a | |v | 3 2 cosh t 1 2 cosh 2 t 3 2 cosh t 12. torsion 2 vaj 2 |v a | 1 2 cosh 2 t 1 2 cosh t cosh t , sinh t , 1 cosh 2 t cosh t , sinh t , 0 1 2 cosh 2 t sinh 2 t 13. tangential acceleration (compute in 2 ways) aT aT aT d|v | dt d dt 1, 2 sinh t , cosh t , 0 2 cosh t sinh t , 2 cosh t sinh t 2 1 2 cosh t sinh t 2 2 sinh t 2 sinh t 14. normal acceleration (compute in 2 ways) aN aN aN |v | 2 sinh t , cosh t , 0 1 2 cosh 2 t 0, 2 cosh t 15. mass of a wire between t 1 and t sinh 2 ,cosh 2 ,2 1 , sinh t cosh t cosh t 2 1 2 with linear density 2 M r t |v t | dt 1 1 sinh 2 2 2 sinh x 2 cosh t dt 2 1 sinh 2 t 2 2 1 2 sinh 1 16. work to move a bead along the wire from t Frt x 2 ds sinh 1 ,cosh 1 ,1 1 1 to t 2 with the force F 0, y, x 0, cosh t , sinh t sinh 2 ,cosh 2 ,2 W 2 F ds 2 Frt sinh 1 ,cosh 1 ,1 1 2 cosh t sinh t sinh t 1 sinh 2 2 2 cosh 2 v t dt 0, cosh t , sinh t cosh t , sinh t , 1 dt 1 sinh 2 t dt cosh t 2 sinh 2 1 cosh 1 2 2 1 2...
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This note was uploaded on 10/15/2013 for the course MATH 251 taught by Professor Skrypka during the Spring '08 term at Texas A&M.

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