A Simple Time Domain Collocation Method to Precisely Search for the Periodic Orbits of Satellite Relative Motion

<table>The selection of collocation points. Blue solid line: the unbounded orbit in a time period <svg height="9.38774pt" id="M139" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -9.33792 8.76219 9.38774" width="8.76219pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z" id="g113-85"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="637" vert-adv-y="637"></glyph.data></g></svg>; red circles: the collocation points.</table>

Mathematical Problems in Engineering

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Figure 2

Figure 2: A Simple Time Domain Collocation Method to Precisely Search for the Periodic Orbits of Satellite Relative Motion 