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FIGURE 19. Schematic of anatomy and geometry in the vicinity of a sea-urchin
spine.
H = cosy
and
RL
Df
= sin
y
.
(53)
Introducing a dimensionless paremeter m which combines physiological and
anatomical constants:
m= kR ,
the differential equation (52) can be rewritten with the aid of (53) to read:
d
d o
sin
y
(
)
=-
m
1
-
cos
y
,
(54)
f
which can readily be solved to yield a transcendental equation in y:
1
2
1
2
Ê
Ë
ˆ
¯ += + Ê
ˆ
¯ +
cot
yy f
cot
y y
,
(55)
o
Ë
o
o
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