Introduction and theoretical background - Earth Dynamics: Deformations and Oscillations of the Rotating Earth - page 92

The supporting polynomials are quintics that can be defined in terms of the canon-
ical quadratics by

0 (ζ 2 )

z
z 2

3
2 ψ

L L L

η

2 ( z )

= η

0 (ζ 2 )

+ , (1.605)

z
2 ψ

R R L L

ψ

1 ( z )

= z η

0 (ζ 1 ), ψ 2 ( z )

=

0 (ζ 2 ).

(1.606)

Their derivatives are

⎝

z 2 ψ 0 (ζ 2 ) ⎠ ,

z
z 2

1
z η

2 z

3
2 z ψ

3 z η 2 ( z )

0 (ζ 2 )

z 2 η 0 (ζ 2 )

0 (ζ 2 )

= + + + (1.607)

and

2 z 2

z 2 1

2 ψ

ψ 1 ( z )

R

z 2 η 0 (ζ 1 ), ψ 2 ( z )

L

z 2 ψ 0 (ζ 2 ).

= η

0 (ζ 1 )

+ =

0 (ζ 2 )

+ (1.608)