Plates - Mechanics of Structures: Variational and Computational Methods - page 758

FIGURE 13.3
Polar coordinate systems.

and

∂ r x

r

∂ r y

r

x =

cos φ =

y =

sin φ =

∂ ∂

(13.7c)

∂φ
∂

1
r

y
r 2

∂φ
∂

1
r

x
r 2 x =−

sin φ =−

y =

cos φ =

These derivatives can be obtained by using the Jacobian (Problem 13.1) or directly from Eq.
(13.7b). As an example of the latter case, observe from r 2 x 2 y 2

= + that

2 r ∂

r

so that ∂

r x

r = x =

2 x

x =

cos φ

∂ ∂