how are u
i want to know i can compute the volume of ship by triple integrations
if i have three equations ( e.g y = ax2 + bx + c ,
z = dy2 + ey + f ,
x = gz2 + hz + i)
i mean how can i do tripple integrations to this eqs
Yes - we're all here. But most of us are sailors, boatbuilders, yacht designers and naval architects, and we don't do that many triple integrations! Whenever we have to calculate volumes by hand, we tend to use Simpson integration or anything similar. Mainly because the shape of our designs cannot be described using polynomials like yours.
Maybe you should ask a mathematician instead?
NOTE: This post is a natural product. The slight variations in spelling and grammar enhance its individual character and beauty and are in no way to be considered flaws or defects.
I'm not quite sure but I think it works like this:
First you need a funktion that describes the volume of whatever it is. If you have single functions in x, y, z then you have to multiply them.
V = x * y * z In your case:
V = (gz2 + hz + i)*(ax2 + bx + c)*(dy2 + ey + f)
To calculate the volume you have to do the tripple integration. I think you will also have a problem defining the boundaries of your integration. It's not going to be from -1 to +1. I think you will end up with a funktion for the boundaries for at least one coordinate direction. I the side direction you only want to integrate to the point where the waterline meets the hull. The coordinates of that point depend on the forward - aft coordinate.
Your Highness Caesar it is impossible for someone to calculate the triple integral if u don't tell him which are the boundaries (boundary of x= length, boundary of y= depth, boundary of z=beam).U also have to define the values of the coefficients a,b,c,d, etc.Why don't u try to find the offsets of 10 tranverse sections of same distance each one, then the area of each transverse section and then integrate using Simpson rule or trapezoidal rule ??
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