最近30从www.hoelymoley.com 2023 - 07 - 10 - t05:57:13z //www.hoelymoley.com/feeds/question/19487 https://creativecommons.org/licenses/by-sa/4.0/rdf //www.hoelymoley.com/q/19487 26 Toivo Sawen //www.hoelymoley.com/users/13314 2020 - 03 - 22 - t11:17:03z 2020 - 03 - 26 - t11:33:13z

< p >有一个大圆,纬度和经度的名称是平等的吗?我有尝试谷歌搜索但只有赤道和本初子午线是我能找到定义的来源。(在开发地图应用程序相关的跟踪的纬度和经度)。< / p >

//www.hoelymoley.com/questions/19487/-/19489 # 19489 54 user18801 //www.hoelymoley.com/users/0 2020 - 03 - 22 - t13:54:00z 2020 - 03 - 26 - t11:33:13z

< p >经度和纬度的曲线是平等不是一个大圆。但随着乔khool写在他的< a href = " //www.hoelymoley.com/a/19502/18801 " >优秀回答< / >,叫做<强>曲线Viviani < / >强壮!很容易看到曲线不是一个大圆,因为,用天真的球坐标(弧度)< span class = " math-container " >(\φ,\λ)美元< / span >与< span class = " math-container " > \λ< / span >美元是经度和<跨类= " math-container " > \φ< / span >被美元纬度在赤道(零),这条曲线通过< span class = " math-container " >(0, 0)美元< / span >,并通过< span class = " math-container " >美元(\π/ 2,\π/ 2)< / span >这是北极美元(<跨类= " math-container " > $美元(\π/ 2 \λ)< / span >是北极任何<跨类= " math-container " > \λ< / span >美元),但它也经过,说,< span class = " math-container " >(1, 1)美元< / span >这不是前两个点之间在大圆。< / p > < p >事实上你得到的曲线是这样的:< / p > < p > < a href = " https://i.stack.imgur.com/iF0y2.png " rel = " noreferrer " > < img src = " https://i.stack.imgur.com/iF0y2.png " alt = "不是一个大圆" > < / > < / p > <人力资源> < p > <强>注意。< /强>我策划这个明显的方式通过定义笛卡尔坐标:< / p > < p > <跨类= " math-container " > $ $ \{对齐}开始x,λ= R \ cosφ\ \因为\ \ \ y,λ= R \ cosφ\ \罪\ \ \ z,φ= R \罪\ \结束{对齐}$ $ < / span > < / p > < p >,然后策划类< span = " math-container " > (x, y, z)美元< / span >为<跨类= " math-container " > \φ= \λ美元< / span >和<跨类= " math-container " > $ \λ\[- \π/ 2 \π/ 2)< / span >美元。< / p > < p >早期版本的这个答案策划类< span = " math-container " > (x, y, z)美元< / span >为<跨类= " math-container " > \φ= \λ美元< / span >和<跨类= " math-container " > $ \λ\[- \ππ\]$ < / span >。这意味着< span class = " math-container " > \φ< / span >美元中不需要值<跨类= " math-container " >美元[\π/ 2,\π/ 2)< / span >当然美元。我曾以为,这些点会在地球的背面:你会得到一种“S”席卷地球,但事实上它最终又在前面:< / p > < p > < a href = " https://i.stack.imgur.com/z34C2.png " rel = " noreferrer " > < img src = " https://i.stack.imgur.com/z34C2.png " alt = "也不是一个大圆" > < / > < / p > < p >这让我吃惊! < / p >

//www.hoelymoley.com/questions/19487/-/19502 # 19502 19 乔khool //www.hoelymoley.com/users/19184 2020 - 03 - 24 - t07:16:00z 2020 - 03 - 24 - t07:22:38z

< p >如果地球是一个球体,然后最后一张照片中的曲线tfb的回答是< a href = " https://en.wikipedia.org/wiki/Viviani%27s_curve # Parametric_representation”rel = " noreferrer " >曲线Viviani < / >;否则,如果你让扁球面的假设,你有轻微的扭曲版本的曲线。< / p > < p >更普遍的是,一个< a href = " https://en.wikipedia.org/wiki/Cl%C3%A9lie " rel = " noreferrer " > < em > clelie < / em > < / >是经度的名称给任何球面曲线类< span = " math-container " > \ varphi < / span >美元和余纬度<跨类= " math-container " > \θ< / span >有美元的关系< span class = " math-container " > \ varphi = c \θ,美元\四c> 0 < / span >美元和Viviani曲线对应于地球同步轨道的轨迹,< span class = " math-container " > c = 1美元< / span >。< / p >

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