(4.75)

At a radial distance v from the origin,

constant

(4.76)

(4.77)

To solve the Eq.(4.75) subject to the constraint of the equation (4.64), Lagrange’s method of undetermined multipliers is applied. Multiplying Eq.(4.77) by λ and adding to Eq.(4.75),

(4.78)

where λ is called the Lagrange’s  multipliers.

 Since v_x, v_y and v_z are now independent variables, the coefficients of dv_x, dv_y and dv_z are individually equated to zero.

(4.79)

(4.80)

(4.81)

From Eq.(4.79),

(4.82)

(4.83)

(4.84)

or,            

(4.85)

Similarly,

(4.86)