Motion_and_Curvature9-2&3

Rt rt a n kv 2 v rt v

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Unformatted text preview: o C dt dt r ˆ dv ˆ ˆ ˆ ∴ a(t ) = κv 2 N + T = a N N + aT T dt Using the definitions of dot and cross products of v & a, one can show that the tangential (aT) and normal (aN) components of a are: 21 The Binormal dv || v • a || || r′(t ) • r′′(t ) || = = || v || || r′(t ) || dt || v × a || || r′(t ) × r′′(t ) || || v × a || || r′(t ) × r′′(t ) || a N = kv 2 = &κ= = = || v || || r′(t ) || || v ||3 || r′(t ) ||3 aT = dT / dt ˆ ˆ = T' ∴Unit normal: N =...
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