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

<div>Coupled-system characteristic indexes <svg height="11.927pt" id="M118" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 12.2725 11.927" width="12.2725pt" 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="M387 400C387 425 348 451 303 451C247 451 176 414 132 376C69 322 24 228 24 148C24 43 74 -12 147 -12C211 -12 301 33 363 103L346 128C319 99 249 51 193 51C148 51 112 84 112 165C112 230 130 287 154 330C170 359 199 400 243 400C277 400 304 383 326 354C333 345 343 343 354 348C378 360 387 382 387 400Z" id="g50-100"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="411" vert-adv-y="411" xpluscharwidth="11.63108767"></glyph.data></g></svg> as a function of the angular velocity <svg height="9.25202pt" id="M119" 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

fig9

Figure 9

Figure 9: The Coupled Orbit-Attitude Dynamics and Control of Electric Sail in Displaced Solar Orbits 