The Coupled Orbit-Attitude Dynamics and Control of Electric Sail in Displaced Solar Orbits

<div>Attitude characteristic index <svg height="11.927pt" id="M110" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 13.2133 11.927" width="13.2133pt" 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="M534 494L526 650H85L77 494H107C123 564 127 582 189 582H423C485 582 488 567 505 494H534ZM472 234V444H443C433 381 426 374 374 374H231C185 374 179 382 169 444H139V234H168C178 297 184 305 237 305H374C426 305 433 297 443 234H472ZM560 171H532C506 91 498 72 417 72H195C113 72 106 93 80 171H51L62 0H550L560 171Z" id="g113-143"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="607" vert-adv-y="607" xpluscharwidth="7.891"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.891,3.132)"><path d="M490 97L476 124C442 96 405 70 398 70C392 70 390 78 396 114C419 243 448 379 463 432L457 436C446 436 431 439 418 442C393 447 368 451 343 451C281 451 204 418 155 381C74 320 24 206 24 107C24 23 59 -12 88 -12C118 -12 155 5 191 34C236 70 290 122 328 177H330L312 84C296 0 311 -12 331 -12C355 -12 425 24 490 97ZM374 387C371 367 360 299 347 264C323 202 187 53 142 53C128 53 113 73 113 120C113 224 157 332 221 380C241 395 274 403 303 403C330 403 360 395 374 387Z" id="g50-98"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="514" vert-adv-y="514" xpluscharwidth="12.56838458"></glyph.data></g></svg> as a function of the angular velocity <svg height="9.25202pt" id="M111" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 13.7483 9.25202" width="13.7483pt" 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="M615 290C615 392 563 448 529 448C511 448 491 441 484 434L483 425C518 400 546 349 546 273C546 158 504 46 417 46C381 46 356 77 356 142C356 184 380 293 392 334L387 340L307 323C305 288 296 228 287 188C265 94 221 52 180 52C144 52 112 89 112 171C112 278 164 372 241 430L226 454C106 394 23 288 23 155C23 40 79 -12 139 -12C184 -12 245 32 285 85C292 31 322 -12 376 -12C423 -12 470 18 501 45C570 104 615 184 615 290Z" id="g113-246"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="638" vert-adv-y="638" xpluscharwidth="8.294"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.969,3.132)"><path d="M538 684C542 703 539 710 529 710C512 710 455 682 363 674L361 644H396C444 644 448 642 438 594L405 438C373 450 347 451 336 451C288 451 200 416 147 374C69 312 24 207 24 113C24 29 60 -12 94 -12C126 -12 156 4 196 30C231 53 296 100 346 166H348L328 81C311 10 325 -12 348 -12C380 -12 450 24 512 98L495 125C466 97 431 70 417 70C408 70 408 80 411 98L538 684ZM390 373L361 240C336 196 210 56 145 56C132 56 113 73 113 131C113 216 156 338 220 379C243 394 266 402 303 402C331 402 375 388 390 373Z" id="g50-101"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="564" vert-adv-y="564" xpluscharwidth="13.101383080000002"></glyph.data></g></svg>.</div>

International Journal of Aerospace Engineering

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Figure 8

Figure 8: The Coupled Orbit-Attitude Dynamics and Control of Electric Sail in Displaced Solar Orbits 