A SYSTEMATIC APPROACH FOR SOLVING THE GREAT CIRCLE TRACK PROBLEMS BASED ON VECTOR ALGEBRA
A SYSTEMATIC APPROACH FOR SOLVING THE GREAT CIRCLE TRACK PROBLEMS BASED ON VECTOR ALGEBRA
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DOI：
10.1515/pomr-2016-0014
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发表时间：
2016-04-01
影响因子：
2
通讯作者：
Chen, Chih-Li
中科院分区：
文献类型：
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作者：
Chen, Chih-Li
提出了一种基于向量代数多重积（S-VA）的球面三角形公式求解大圆轨迹（GCT）问题的系统方法。由于几何和代数的数学性质都嵌入在S-VA方法中，与使用向量基的复杂线性组合的方法相比，球面三角形公式的推导变得更容易理解和更直接。此外，S-VA方法可以处理所有给定的初始条件，以更简单，更清晰地解决GCT问题，并避免了传统方法中存在的冗余公式。通过将地球经纬度坐标系转换为笛卡尔坐标系，并采用相对经度概念，可以方便、直接地导出S-VA法的简明控制方程。由于S-VA方法的优点，它使实际的导航仪快速调整，以解决GCT问题。在S-VA方法的基础上，编制了GCTPro_VA程序，方便了导航仪的使用。几个验证的例子表明，S-VA方法是简单和通用的解决GCT问题。
A systematic approach, based on multiple products of the vector algebra (S-VA), is proposed to derive the spherical triangle formulae for solving the great circle track (GCT) problems. Because the mathematical properties of the geometry and algebra are both embedded in the S-VA approach, derivations of the spherical triangle formulae become more understandable and more straightforward as compared with those approaches which use the complex linear combination of a vector basis. In addition, the S-VA approach can handle all given initial conditions for solving the GCT problems simpler, clearer and avoid redundant formulae existing in the conventional approaches. With the technique of transforming the Earth coordinates system of latitudes and longitudes into the Cartesian one and adopting the relative longitude concept, the concise governing equations of the S-VA approach can be easily and directly derived. Owing to the advantage of the S-VA approach, it makes the practical navigator quickly adjust to solve the GCT problems. Based on the S-VA approach, a program namely GCTPro_VA is developed for friendly use of the navigator. Several validation examples are provided to show the S-VA approach is simple and versatile to solve the GCT problems.