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Unformatted text preview: ~ ~ ~ lu ~ J l~ ~ l :\ .J .j a lL " \II 't lçt $ VI t ~ J-\! " 'l \ ~ ~ 'l ~, 1\ l~ .. t JL rJ (' '- '" \ t- -. ~ .. /'~ 1J I t' 4- -/ .. ~ +- .- .'- \. 0 ~ ,.. .l .. l\ 1\ lLl l~ VI ~ 0 ~ l C- V1 x: )- ~ \iJ l!j -l yJ Q: -4 -- ~ )~ ~u t y. ~ () \I ~ lL V1 () -- 2 /" "' It, ~ )(0 '- )-.0 Li 1 ~i .j (J.i ~ V\ '" V\ 4: t :c o \f ~ Q 1 ~ VI il ~ - il M 't -l ~ t; ~ lU J ~ .. LL l. C' 1- .. Vl .; ~ L F- ~ ~ ~ ~ ~ ~ t 'i \) ~ "' ~ ~ \J () t l ~ (j ~ " \J ~ ~ 2- J- .. r: t " ~ ~ -- .j lI \t 0 1 ~ 't t ~ ~ ~ ~ .r \ ,- .. ~ -- )~ l -- ~ ~ ~\ V -L '3 ,- L\ ~ lU ~\)~ j" 't J \( Q .l 20 Deformation and Flow: Translation, Stretching, Pinching, and Rotating 21 Simple Comments about Velocity Gradient Tensor 22 Simple Example: Expansion/ Contraction Vector Notation 23 Stretching along one Axis 24 Rotation 25 Bending, Distorting, Shearing 26 Example Shearing 27 Simple Example #1 28 Simple Example #1 (from a different point of view) 29 Simple Example #2 30 Simple Example #2 (from a different point of view) - 31 Principal Axes for Symmetric Tensors 32 Example Principal Axes #2 33 Example Principal Axes #1 34 Summary: Cauchy-Stokes Decomposition 35...
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This document was uploaded on 02/28/2014 for the course PHYS 4200 at Columbia.

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