Reply to thread

Message

<blockquote data-quote="phatcat600" data-source="post: 3425307" data-attributes="member: 555700">We are dealing with arc length and normal and binormal vectors.45) Show that the curvature k is related to the tangent and normal vectors by the equation dT/ds=kN.47) a) show that dB/ds is perpendicular to B.b) show that dB/ds is perpendicular to T.c) Deduce from parts (a) and (b) that dB/ds=-t(s)N for some number t(s) called the torsion of the curve. (the torsion measures the degree of twisting of a curve.)d)Show that for a plane curve the torsion ist(s)=048) The following formulas, called the Frenet-Serret formulas are of fundamental importance in differential geometry.1) dT/ds=kN2) dN/ds=-kT+tB3) dB/ds=-N(Formula 1 comes from excercise 45 and formula 3 comes from excercise 47.) Use the fact that N=BxT to deduce formula 2 from formulas 1 and 3.Im not looking for exact answers but any help would be appreciated. I dont even know where to start these. Thanks a lot. I didnt get any useful responses on yahoo answers //content.invisioncic.com/y282845/emoticons/frown.gif.a3531fa0534503350665a1e957861287.gif</blockquote>

[QUOTE="phatcat600, post: 3425307, member: 555700"] We are dealing with arc length and normal and binormal vectors. 45) Show that the curvature k is related to the tangent and normal vectors by the equation dT/ds=kN. 47) a) show that dB/ds is perpendicular to B. b) show that dB/ds is perpendicular to T. c) Deduce from parts (a) and (b) that dB/ds=-t(s)N for some number t(s) called the torsion of the curve. (the torsion measures the degree of twisting of a curve.) d)Show that for a plane curve the torsion is t(s)=0 48) The following formulas, called the Frenet-Serret formulas are of fundamental importance in differential geometry. 1) dT/ds=kN 2) dN/ds=-kT+tB 3) dB/ds=-N (Formula 1 comes from excercise 45 and formula 3 comes from excercise 47.) Use the fact that N=BxT to deduce formula 2 from formulas 1 and 3. Im not looking for exact answers but any help would be appreciated. I dont even know where to start these. Thanks a lot. I didnt get any useful responses on yahoo answers [IMG]//content.invisioncic.com/y282845/emoticons/frown.gif.a3531fa0534503350665a1e957861287.gif[/IMG] [/QUOTE]

Verification