Exercises P1 ( Pathline):
Find the pathline for the given vector field through the given point P.
G
G
G
a) V = (1 − y )i + ( 2 + x ) j , P=(0,1)
G
G
G
b) V = (1 + 2 y )i + ( 2 − x ) j , P=(0,2)
G
G
G
c) V = (t − y )i + ( 2 + x ) j , P=(0,1)
G
G
G
d) V = (sin(t ) + x )i + (1 − y ) j , P=(0,0)
Answers:
a)
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Thus
x (t ) = 2 cos(t ) − 2 ,
y (t ) = 2 sin(t ) + 1
The pathline is defined by
( x (t ), y (t )) = ( 2 cos(t ) − 2, 2 sin(t ) + 1)
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b)
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c)
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d)
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