The effects of orbital dynamics on a velocity distribution from a point source — for example, a fragmentation — may be studied by Housen’s method. This technique permits the computation of a spatial density due to the velocity distribution as the sum over all routes between the source point and any point in space of the velocity density divided by the absolute value of the Jacobian determinant of the propagation map. The determination of all routes constitute finding all Lambert (orbital two point boundary value problem) solutions for the two points over a given elapsed time. In order to understand the observed density structures better, the dynamic admittance is introduced. It is the sum of the reciprocal absolute Jacobian determinants spanning all possible routes and is independent of the initial velocity distribution. The bands, pinch point and other features seen in the dynamic admittance plots are analyzed. The effects of the earth in reducing the number of routes, thereby casting a dynamic shadow, are demonstrated

中文翻译：

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轨道动态导纳与地球阴影

轨道动力学对来自点源的速度分布（例如碎片）的影响可以通过豪恩的方法进行研究。该技术允许计算速度分布引起的空间密度，该速度分布是速度密度的源点和空间中任何点之间的所有路径上的所有路径的总和除以传播图的雅可比行列式的绝对值。所有路径的确定构成了在给定的经过时间上找到两个点的所有Lambert（轨道两点边界值问题）解决方案。为了更好地了解所观察到的密度结构，引入了动态导纳。它是跨越所有可能路径的倒数绝对Jacobian行列式的总和，并且与初始速度分布无关。乐队 分析了在动态导纳图中看到的收缩点和其他特征。演示了地球在减少路线数量上的效果，从而产生了动态阴影