Curvilinear coordinate
, Introduction
• Let the rectangular Cartesian coordinates (x,
y,z) of any point P in space be expressed in
terms of three independent, single values and
continuously differentiable scalar point
functions such that
x x (u1 , u 2 , u 3 ), y y (u1 , u 2 , u 3 ), x z (u1 , u 2 , u 3 ) (1)
x, y, z
Suppose J 0 Then the transforma tion (1) can be inverted .
u , u
1 2 3, u
Thus we can say that with each pt in space , there exists unique triad
of numbers u1 , u 2 , u 3 and to each such triad there is a definite pt .
, Introduction
• Let the rectangular Cartesian coordinates (x,
y,z) of any point P in space be expressed in
terms of three independent, single values and
continuously differentiable scalar point
functions such that
x x (u1 , u 2 , u 3 ), y y (u1 , u 2 , u 3 ), x z (u1 , u 2 , u 3 ) (1)
x, y, z
Suppose J 0 Then the transforma tion (1) can be inverted .
u , u
1 2 3, u
Thus we can say that with each pt in space , there exists unique triad
of numbers u1 , u 2 , u 3 and to each such triad there is a definite pt .
