Page 82 - statbility for masters and mates

70 Ship Stability for Masters and Mates
Summary:
A coef®cient of 13 with multipliers of 1, 4, 1 etc.
Simpson's Second Rule
This rule assumes that the equation of the curve is of the third order, i.e. of a curve whose equation, referred to the co-ordinate axes, is of the form y a0 a1x a2x2 a3x3, where a0, a1, a2 and a3 are constants.
Fig. 10.2
In Figure 10.2:
Area of elementary strip ydx
3h O
3h O
a0x 1 a1x2 1 a2x3 1 a3x4 3h 234O
3a0h 9 a1h2 9a2h3 81 a3h4 24
Let the area of the figure Ay1 By2 Cy3 Dy4
Aa0 B a0 a1h a2h2 a3h3
C a0 2a1h 4a2h2 8a3h3
D a0 3a1h 9a2h2 27a3h3 a0 A B C D a1h B 2C 3D
a2h2 B 4C 9D a3h3 B 8C 27D
Area of the figure
ydx
a0 a1x a2x2 a3x3 dx