Semianalytical Solutions of Relative Motions with Applications to Periodic Orbits about a Nominal Circular Orbit

<div>Planar periodic configurations with amplitudes <svg height="9.92533pt" id="M133" style="vertical-align:-1.57651pt" version="1.1" viewbox="-0.0498162 -8.34882 99.9049 9.92533" width="99.9049pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z" id="g113-223"></path></g><g transform="matrix(.013,0,0,-0.013,11.017,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,22.28,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 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coordinate system. These periodic orbits are determined by the analytical solutions truncated at the 15th order.</div>

Mathematical Problems in Engineering

fig2

Figure 2

Figure 2: Semianalytical Solutions of Relative Motions with Applications to Periodic Orbits about a Nominal Circular Orbit 