ENG 102 Study Guide - Midterm Guide: Kinematics, Schauder Basis, Unit Vector
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Converting a vector into unit vector components (cid:1874) =(cid:1874)(cid:2869)(cid:1866)(cid:2869) +(cid:1874)(cid:2870)(cid:1866)(cid:2870) =(cid:4666)(cid:1874)(cid:2869) (cid:1866)(cid:2869) (cid:4667)(cid:1866)(cid:2869) +(cid:4666)(cid:1874)(cid:2870) (cid:1866)(cid:2870) (cid:4667)(cid:1866)(cid:2870) . Method 1: vcos - rotate vector through smaller angle to make it parallel with unit vector. Vsin rotate vector through smaller angle and the turn is cos(90 ) Method 2: use triangle law, signs depend on tip-to-tail position relative to the unit vector basis. Taking derivatives in a ref. frame where vector is fixed will result in a zero. If vector is not fixed but is a fxn of x then the derivative wrt = zero, but wrt to x = nonzero. In ref frame n w/ unit vector basis (cid:1866)(cid:2869) ,(cid:1866)(cid:2870) , we express (cid:1874) as (cid:1874)(cid:2869)(cid:1866)(cid:2869) +(cid:1874)(cid:2870)(cid:1866)(cid:2870) . If v1 and v2 are constants, then (cid:1874) is fixed in n. A vector that is not fixed in a given ref frame is a fxn of one of more scalar variables in that frame (e. g. s, )
