飞越北极  

Fly over the Arctic Cirell

作　　者：何永强[1] 陆新根[1] 沈重欢[1] 数模组 

机构地区：[1]浙江万里学院,,宁波315101

出　　处：《数学的实践与认识》2001年第1期110-113,共4页Mathematics in Practice and Theory

摘　　要：本文对“飞机从北京出发、飞越北极直达底特律的所需时间 ,可比原航线节省多少时间”的问题进行讨论 ,并将航线选择归结为寻求曲面上的最短弧 .应用“曲面上最短弧为测地线”的事实进行了讨论 .模型 (一 )假设地球是球体 ,我们可通过单位向量的点乘与夹角的关系 ,加以解决 ;对于模型 (二 )设地球是旋转椭球体 ,我们利用微分几何学中测地线方程加以解决 ,并且把球面的纬度转化为旋转椭球面纬度 .对于 4组较特殊的点 ,纬度几乎相等或相近 ,或者两者之间的经度差过大时 ,用测地线计算比较困难 ,我们用椭圆弧 (长 )代替测地线长 ,结合数学软件 Mathematica的数值积分功能 。As to the problem of the time needed for an airplane to start from Beijing,fly over arctic pole,and reach Detroit,this article discusses how much time can be saved in the models that established in the article in comparison with the original flight route.And it summarizes selection of the flight route for searching the shortest arc in the surface.Discussion is based on the fact that the shortest arc on surface is geodesic.Model 1 is on the assumption that the Earth is a sphere.It can be solved by the relation between inner- product and included angle of two unitvectors.Model2 is on the assumption thatthe Earth is a revolving ellipsoid.Itcan be solved by the geodesic equation in differential geometry,which turns latitude of the Earth into thatof ellipsoid.For the4pairs of special points,their latitudes or longitudes are too close to calculate geodesic,so we replace geodesic with ellipse arc,and use software Mathematica to obtain the length

关 键 词：“飞越北极” 微分几何 航线选择 测地线 数学模型 

分 类 号：O29[理学—应用数学]