d. Evaluate the second time derivative of the unit vectors êp. e. Given that i = rê, + rể,, show that i = rê, + rôê, +r sin0 bê, f. Given that ā = rê, + 2řể, + rể, show that a = ( -r sin? 0 4² – ro?)ê, + (rë + 2ř0 - r sin e cos o p²)êo + (r sin 0 ở + 2r cos e 04 + 2r¢ sin 0)ês
d. Evaluate the second time derivative of the unit vectors êp. e. Given that i = rê, + rể,, show that i = rê, + rôê, +r sin0 bê, f. Given that ā = rê, + 2řể, + rể, show that a = ( -r sin? 0 4² – ro?)ê, + (rë + 2ř0 - r sin e cos o p²)êo + (r sin 0 ở + 2r cos e 04 + 2r¢ sin 0)ês
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Transcribed Image Text:d. Evaluate the second time derivative of the unit vectors êp.
e. Given that i = rê, + rể,, show that i = rê, + rôê, +r sin0 bê,
f. Given that ä = řê, + 2řể, + rể, show that a = ( -r sin? 0 4² – ro?)ê, +
(rë + 2r0 - r sin e cos o 4²)êo + (r sin 0 + 2r cos 0 04 + 2r¢ sin 0 )ê̟
Transcribed Image Text:(b)
Sphericals
x=r sine coso
y=r sine sino
z=r cose
Consider spherical coordinates as defined by their relationships to the Cartesian
coordinates:
x =r sin 8 cos p
X2 =r sin 0 cos
X3 =r cos 0
r2 = [xỉ + x3 + x
e = tan-(x? + x3)x3
$ = tan-(x2/x1)
or
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