一种不对称稳性曲线积分计算方法

当有初始横倾时，稳性曲线是不对称的，但负值横倾角区间的函数值与正值横倾角区间的函数值的关系无人探求。当对不对称稳性曲线在始于负值的横倾角区间进行积分计算面积时，以前的做法是直接求出负值横倾角区间的函数值，再进行数值积分。本文经过推导证明，在用数值积分对不对称稳性曲线下的面积进行计算时，自变量为负值的区间的积分可转化到正值区间进行计算，并推导出了转化公式，并且得到结论：不对称稳性曲线是一个奇函数和一个偶函数的线性组合。按照推导出的公式，可在NAPA软件中编程方便地实现美军标DDS079-1破舱稳性衡准的计算。

A numerical integral calculation method of area under unsymmetrical stability curve

When initial heeling is not zero, the stability curve is unsymmetrical, but the relation between the function values in the minus heeling zone and in the positive heeling zone isnot studied by people.When Calculating area under unsymmetrical stability curve in the heeling zone beginning at minus value by numerical integration, The method of before now is calculating out the function value of minus heeling zone and then make numerical integration.This article point out that the integration of stability curve in the minus heeling value zone can be transformed to that in the positive heeling zone, and the transformed formula is deducted, and make a conclusion that the unsymmetrical stability curve is the linear combination of one odd function and one even fuction . As the formula deducted, programming in software NAPA can reach calculating expediently the damage stability criteria of USA military Standard DDS079-1