Find expression for dt an where ū, ū, W ae in

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Find
expression for
dt
an
where ū,ū, W an in Ve
Transcribed Image Text:Find expression for dt an where ū,ū, W an in Ve
Expert Solution
Step 1

Formula:

i) ddtut·vt=u't·vt+ut·v't.

ii) ddtut×vt=u't×vt+ut×v't

Properties of cross product and dot product:

i) a·b×c=a×b·c.

ii) a×b=-b×a

Consider ddtut·vt×wt.

ddtut·vt×wt=u't·vt×wt+ut·ddtvt×wt=u't·vt×wt+ut·v't×wt+vt×w't=u't·vt×wt+ut·v't×wt+ut·vt×w't

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