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Arnold's Trivium
1991 Arnold's Trivium
87
Problem 87
Problem 87
Source:
July 1, 2010
calculus
derivative
quadratics
vector
linear algebra
matrix
function
Problem Statement
Find the derivatives of the lengths of the semiaxes of the ellipsoid
x
2
+
y
2
+
z
2
+
x
y
+
y
z
+
z
x
=
1
+
ϵ
x
y
x^2 + y^2 + z^2 + xy + yz + zx = 1 + \epsilon xy
x
2
+
y
2
+
z
2
+
x
y
+
yz
+
z
x
=
1
+
ϵ
x
y
with respect to
ϵ
\epsilon
ϵ
at
ϵ
=
0
\epsilon = 0
ϵ
=
0
.
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