Low-Thrust Trajectory Design Using Finite Fourier Series Approximation of Pseudoequinoctial Elements

<div><svg height="15.8638pt" id="M218" style="vertical-align:-4.0258pt" version="1.1" viewbox="-0.0498162 -11.838 12.1354 15.8638" width="12.1354pt" 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="M220 349V455C158 436 98 425 38 417V389C85 378 92 374 92 323V104C92 43 83 38 28 32V0H302V32C225 38 220 43 220 104V291C237 330 257 343 276 343C292 343 305 336 322 322C329 316 339 313 353 318C379 328 402 356 402 392C402 426 374 454 335 454C297 454 259 411 222 349H220Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.252,-5.741)"><path d="M514 185C496 134 477 102 459 82C435 55 399 49 360 49C330 49 304 50 285 58C265 66 261 85 261 131V512C261 595 269 601 347 608V650H37V608C114 601 124 595 124 512V138C124 55 114 49 28 42V0H519C528 27 549 127 557 173L514 185Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.252,3.784)"><path d="M628 192C576 88 518 38 435 38C298 38 199 155 199 336C199 483 280 615 423 615C502 615 574 584 609 462L652 469C646 537 638 583 629 638C601 644 527 665 444 665C205 665 43 524 43 317C43 157 156 -15 424 -15C492 -15 587 5 614 12C631 48 657 126 671 173L628 192Z"></path></g></svg> as a function of <svg height="15.672pt" id="M219" style="vertical-align:-3.834pt" version="1.1" viewbox="-0.0498162 -11.838 12.5935 15.672" width="12.5935pt" 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="M483 442H303V410C358 401 362 388 351 355C329 286 296 195 278 149C262 190 226 288 200 358C188 393 193 400 239 410V442H-8V410C40 400 53 388 71 344C120 229 165 113 215 -11H254C315 141 364 261 400 342C421 389 433 400 483 410V442Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.28,-5.741)"><path d="M514 185C496 134 477 102 459 82C435 55 399 49 360 49C330 49 304 50 285 58C265 66 261 85 261 131V512C261 595 269 601 347 608V650H37V608C114 601 124 595 124 512V138C124 55 114 49 28 42V0H519C528 27 549 127 557 173L514 185Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.045,3.784)"><path d="M415 353C483 366 567 404 567 500C567 550 544 592 507 615C467 641 415 650 341 650H45V608C116 601 125 594 125 512V138C125 55 116 49 38 42V0H297C380 0 457 15 508 43C566 74 603 127 603 194C603 290 527 335 415 348V353ZM259 366V549C259 568 261 583 268 590C274 597 290 603 314 603C368 603 422 571 422 482C422 399 375 366 283 366H259ZM259 320H280C391 320 453 275 453 183C453 87 389 48 332 47C278 46 259 68 259 138V320Z"></path></g></svg> and <span class="nowrap"><svg height="11.9805pt" id="M220" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.7741 11.072 11.9805" width="11.072pt" 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="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.331,-5.741)"><path d="M567 167L534 181C505 122 482 94 454 70C428 46 385 42 330 42C288 42 248 44 235 55C216 70 213 91 220 130L295 528C310 609 314 611 401 618L409 650H140L131 618C222 611 224 609 209 528L133 126C118 47 108 41 25 33L18 0H497C514 33 554 126 567 167Z"></path></g></svg>.</span></div>

International Journal of Aerospace Engineering

fig14

Figure 14

Figure 14: Low-Thrust Trajectory Design Using Finite Fourier Series Approximation of Pseudoequinoctial Elements 