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在最佳航线数值计算中,除使用最普遍的动态规划方法外,还有变分法和基于光折射原理的方法。 变分法 是通过求解欧拉方程式计算两点间最佳航线的一种方法。 假设船沿最少航时轨迹C以速度V完成两点间的航渡,在这中间耗费时间T,则经线性积分求得该时间: 这里ψ=1/V,是时间、地点和航向的函数,并可用参数形式来表示,通过取代(1)式中的ds(园点表示该参数对时间t微分),求得: 这里的符号“＇”表示对x微分。若x为独立变量,则(2)可改为
In the calculation of optimal course values, in addition to the most common dynamic programming methods, there are variational methods and methods based on the principle of light refraction. Variational method is a method of calculating the best course between two points by solving Euler equations. Assuming that the ship completes the voyage between two points along the least-time trajectory C at velocity V, consuming time T in between, the time is obtained by linear integral: where ψ = 1 / V as a function of time, place and heading , And can be expressed in the form of a parameter. By substituting ds in the formula (1), which indicates that the parameter is differentiated with respect to time t, the symbol “’” here indicates x differential. If x is an independent variable, then (2) can be changed to