ENME361 Quiz 1 Solution

ENME361 Quiz 1 Solution - B. Balachandran ENME361 Fall 2008...

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B. Balachandran ENME361 Fall 2008 Solution to Quiz #1 (September 4, 2008; 10 minutes) 1) (a) Determine the vector velocity v for the following position vector r () s in () cos () ri j θθ =+ (t) x t d t d t where d is a constant. In your result, use the compact notation / x dx dt = ± and / dd t = ± . s s (c o s ) s i n vi j i j ij θ ⎛⎞ == + = + ⎜⎟ ⎝⎠ + ±± ± dr t d d d d tx t d t d t x t d t d t dt dt dt dt dt xd d (b) Based on the result obtained in (a), determine the dot product v · v and express it in its simplest form. ( ) 2 22 2 2 o s ) s i n o s ) s i n ( cos ) sin 2 cos vv i j i j •= + + • + + + + ± ± ± d d d x d 2) By using the results obtained in (1), determine expressions for the partial derivatives , , and Tx Tx T
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This note was uploaded on 02/13/2011 for the course ENME 361 taught by Professor Yoo during the Spring '11 term at Maryland.

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