Suppose |||| = a, so that the tip of r is on a sphere of radius a with center at O. (a) Show that r = aN+BB, where a and 3 are related to p and 7 by -p and BT: -de the equations a = - = ds (b) If 7 = 0, show that the tip of r moves on a circle about the line of B as an axis. (c) If 70, show that p² + 1/2 (de) ds 2 =a².

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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(21) Suppose ||r||
center at O.
=
a, so that the tip of r is on a sphere of radius a with
(a) Show that r = = aN + BB, where a and ß are related to p and 7 by
the equations a = -p and BT
dp
ds
(b) If 7 = 0, show that the tip of r moves on a circle about the line of
B as an axis.
=
2
1
(c) If 70, show that p² + - (2) ²-
dp
=a².
7² ds
Transcribed Image Text:(21) Suppose ||r|| center at O. = a, so that the tip of r is on a sphere of radius a with (a) Show that r = = aN + BB, where a and ß are related to p and 7 by the equations a = -p and BT dp ds (b) If 7 = 0, show that the tip of r moves on a circle about the line of B as an axis. = 2 1 (c) If 70, show that p² + - (2) ²- dp =a². 7² ds
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