The availability of devices that track moving objects has led to an explosive growth in trajectory data. When exploring the resulting large trajectory collections, visual summaries are a useful tool to identify time intervals of interest. A typical approach is to represent the spatial positions of the tracked objects at each time step via a one-dimensional ordering; visualizations of such orderings can then be placed in temporal order along a time line. There are two main criteria to assess the quality of the resulting visual summary: spatial quality -- how well does the ordering capture the structure of the data at each time step, and stability -- how coherent are the orderings over consecutive time steps or temporal ranges? In this paper we introduce a new Stable Principal Component (SPC) method to compute such orderings, which is explicitly parameterized for stability, allowing a trade-off between the spatial quality and stability. We conduct extensive computational experiments that quantitatively compare the orderings produced by ours and other stable dimensionality-reduction methods to various state-of-the-art approaches using a set of well-established quality metrics that capture spatial quality and stability. We conclude that stable dimensionality reduction outperforms existing methods on stability, without sacrificing spatial quality or efficiency; in particular, our new SPC method does so at a fraction of the computational costs.