Dynamics of the Space Tug System with a Short Tether

<div>The components of the tension force (<svg height="11.7574pt" id="M292" style="vertical-align:-3.16066pt" version="1.1" viewbox="-0.0498162 -8.59674 12.7109 11.7574" width="12.7109pt" 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="M606 650H137L129 618C217 609 221 609 203 518L129 129C115 46 106 40 26 32L18 0H300L307 32C210 40 203 45 218 129L249 305H358C454 305 455 296 457 219H491L531 425H497C465 353 463 350 366 350H259L300 569C306 605 310 611 346 611H444C522 611 535 598 541 578C550 557 553 519 552 485L588 489L606 650Z" id="g50-71"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="630" vert-adv-y="630"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.89,3.001)"><path d="M545 403C545 425 527 451 498 451C448 451 400 404 312 286L290 341C262 412 246 451 219 451C182 451 138 404 92 345L112 323C152 368 169 378 181 378C192 378 201 359 216 321L257 214C184 115 142 69 113 69C102 69 93 73 88 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609 221 609 203 518L129 129C115 46 106 40 26 32L18 0H300L307 32C210 40 203 45 218 129L249 305H358C454 305 455 296 457 219H491L531 425H497C465 353 463 350 366 350H259L300 569C306 605 310 611 346 611H444C522 611 535 598 541 578C550 557 553 519 552 485L588 489L606 650Z" id="g50-71"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="630" vert-adv-y="630"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.89,3.001)"><path d="M481 445L456 468C426 437 403 427 388 427C372 427 356 428 302 438C256 447 221 451 187 451C159 451 130 428 105 384C93 363 80 340 65 305L96 290C122 342 149 381 193 381C216 381 267 377 294 374S346 372 365 376L75 105C37 70 24 35 24 16C24 2 30 -5 35 -8C42 -8 46 -6 48 -2C58 14 75 35 90 41C102 46 116 46 147 32C200 8 267 -21 298 -21C347 -21 390 12 448 126L420 151C369 77 338 56 311 56C287 56 249 68 212 81C180 92 149 100 127 98C212 172 353 308 413 372L481 445Z" id="g50-123"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="505" vert-adv-y="505"></glyph.data></g></svg>) and the disturbing torque (<svg height="11.9661pt" id="M295" style="vertical-align:-3.16057pt" version="1.1" viewbox="-0.0498162 -8.80553 13.1024 11.9661" width="13.1024pt" 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="M655 676H628C608 656 600 650 571 650H156C118 650 114 651 102 676H77C63 615 45 548 24 485L60 486C81 531 97 562 114 580C134 603 148 611 252 611H308L217 127C201 41 196 38 105 32L98 0H384L393 32C300 38 288 41 304 127L393 611H466C553 611 571 604 582 580C592 559 597 530 595 485L630 489C636 548 645 624 655 676Z" id="g50-85"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="673" vert-adv-y="673"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.28,3.001)"><path d="M545 403C545 425 527 451 498 451C448 451 400 404 312 286L290 341C262 412 246 451 219 451C182 451 138 404 92 345L112 323C152 368 169 378 181 378C192 378 201 359 216 321L257 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id="g50-123"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="505" vert-adv-y="505"></glyph.data></g></svg>) in <svg height="9.05107pt" id="M298" style="vertical-align:-3.05102pt" version="1.1" viewbox="-0.0498162 -6.00005 14.6082 9.05107" width="14.6082pt" 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="M583 449L551 460C535 436 529 433 494 433C409 433 311 438 228 438C97 438 53 381 24 341L44 316C85 355 124 372 183 372C161 259 87 53 26 5L34 -12C53 -12 94 -4 118 12C166 92 211 256 236 371L394 369C375 301 352 212 334 121C329 96 326 75 326 58C326 5 349 -12 381 -12C431 -12 482 25 519 66L504 97C480 80 448 64 432 64C419 64 410 80 422 154C432 217 450 303 466 365C499 365 536 366 546 369C557 384 570 409 583 449Z" id="g50-238"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="601" vert-adv-y="601"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.488,3.001)"><path d="M722 32C646 41 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International Journal of Aerospace Engineering

Dynamics of the Space Tug System with a Short Tether

Figure 20