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Pursuit curve

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186: 223: 277: 20: 450: 175: 443: 436: 382: 460: 623: 374: 55: 214:, having traced such accounts as far back as the late 19th century, indicates that these anecdotes are unfounded. 204:, Bouguer defined a curve of pursuit to explore the way in which one ship might maneuver while pursuing another. 588: 597: 109: 535: 323: 242: 51:
or points representing pursuers and pursuees; the curve of pursuit is the curve traced by the pursuers.
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Typical drawings of curves of pursuit have each point acting as both pursuer and pursuee, inside a
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Mémoires de mathématique et de physique tirés des registres de l'Académie royale des sciences
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The path followed by a single pursuer, following a pursuee that moves at constant speed on a
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has occasionally been credited with first exploring curves of pursuit. However
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Class of curves traced by a point which follows another moving point
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Chases and Escapes: The Mathematics of Pursuits and Evasion
112: 587: 563: 544: 510: 467: 169: 154: 324:Circles of Apollonius#Apollonius pursuit problem 58:in time, the pursuee is always on the pursuer's 444: 8: 404:, with a slightly narrower definition that | 226:Curves of pursuit with different parameters 451: 437: 429: 54:With the paths of the pursuer and pursuee 111: 275: 340: 196:The pursuit curve was first studied by 192:'s 1732 article studying pursuit curves 7: 170:{\displaystyle L(t)=F(t)+xF'\!(t).} 47:constructed by analogy to having a 280:Curve of pursuit of vertices of a 84:, the pursued (leader), for every 14: 23:A simple pursuit curve in which 521:Pedal & Contrapedal curves 161: 155: 137: 131: 122: 116: 73:, the pursuer (follower), and 1: 459:Differential transforms of 640: 375:Princeton University Press 200:in 1732. In an article on 241:It is a solution of the 246:1 +   424:MacTutor Pursuit curve 293: 227: 193: 171: 32: 591:on a family of curves 548:defined by two points 279: 243:differential equation 225: 188: 172: 22: 526:Negative pedal curve 110: 27:is the pursuer and 567:defined by a point 514:defined by a point 377:. pp. 27–28. 355:(in French): 1–15. 314:Logarithmic spiral 294: 228: 194: 167: 33: 606: 605: 565:Binary operations 384:978-0-691-12514-5 272:Multiple pursuers 208:Leonardo da Vinci 62:. That is, given 631: 546:Unary operations 512:Unary operations 469:Unary operations 453: 446: 439: 430: 389: 388: 363: 357: 356: 345: 267: 176: 174: 173: 168: 153: 102: 98: 87: 83: 72: 41:curve of pursuit 30: 26: 639: 638: 634: 633: 632: 630: 629: 628: 624:Pursuit–evasion 609: 608: 607: 602: 583: 559: 540: 506: 463: 457: 420:)| are constant 398: 393: 392: 385: 365: 364: 360: 349:Bouguer, Pierre 347: 346: 342: 337: 329:Pursuit–evasion 310: 274: 258: −  245: 220: 183: 146: 108: 107: 100: 89: 85: 74: 63: 28: 24: 17: 12: 11: 5: 637: 635: 627: 626: 621: 611: 610: 604: 603: 601: 600: 594: 592: 585: 584: 582: 581: 576: 570: 568: 561: 560: 558: 557: 551: 549: 542: 541: 539: 538: 533: 528: 523: 517: 515: 508: 507: 505: 504: 499: 497:Parallel curve 494: 489: 484: 479: 473: 471: 465: 464: 458: 456: 455: 448: 441: 433: 427: 426: 421: 397: 396:External links 394: 391: 390: 383: 367:Nahin, Paul J. 358: 339: 338: 336: 333: 332: 331: 326: 321: 316: 309: 306: 273: 270: 219: 218:Single pursuer 216: 198:Pierre Bouguer 190:Pierre Bouguer 182: 179: 178: 177: 166: 163: 160: 157: 152: 149: 145: 142: 139: 136: 133: 130: 127: 124: 121: 118: 115: 31:is the pursuee 15: 13: 10: 9: 6: 4: 3: 2: 636: 625: 622: 620: 617: 616: 614: 599: 596: 595: 593: 590: 586: 580: 577: 575: 572: 571: 569: 566: 562: 556: 553: 552: 550: 547: 543: 537: 534: 532: 531:Pursuit curve 529: 527: 524: 522: 519: 518: 516: 513: 509: 503: 500: 498: 495: 493: 492:Inverse curve 490: 488: 485: 483: 480: 478: 475: 474: 472: 470: 466: 462: 454: 449: 447: 442: 440: 435: 434: 431: 425: 422: 419: 415: 411: 407: 403: 400: 399: 395: 386: 380: 376: 372: 368: 362: 359: 354: 350: 344: 341: 334: 330: 327: 325: 322: 320: 317: 315: 312: 311: 307: 305: 303: 299: 291: 287: 283: 278: 271: 269: 265: 261: 257: 253: 249: 244: 239: 237: 233: 224: 217: 215: 213: 212:Paul J. Nahin 209: 205: 203: 199: 191: 187: 180: 164: 158: 150: 147: 143: 140: 134: 128: 125: 119: 113: 106: 105: 104: 96: 92: 81: 77: 70: 66: 61: 57: 56:parameterized 52: 50: 46: 42: 38: 21: 530: 461:plane curves 417: 413: 409: 405: 370: 361: 352: 343: 302:mice problem 295: 289: 286:mice problem 263: 259: 255: 251: 247: 240: 229: 206: 195: 99:there is an 94: 90: 79: 75: 68: 64: 53: 40: 34: 613:Categories 589:Operations 487:Dual curve 335:References 250:  = 236:radiodrome 202:navigation 103:such that 555:Strophoid 402:Mathworld 254:  ( 598:Envelope 574:Roulette 482:Involute 416:′( 412:)| and | 408:′( 369:(2007). 319:Tractrix 308:See also 151:′ 93: ( 37:geometry 579:Cissoid 536:Caustic 502:Isoptic 477:Evolute 298:polygon 266:  234:, is a 181:History 60:tangent 619:Curves 381:  282:square 284:(the 97:) ≠ 0 88:with 49:point 45:curve 43:is a 379:ISBN 292:=4). 288:for 232:line 39:, a 264:y′′ 238:. 35:In 615:: 373:. 304:. 268:. 262:) 248:y′ 91:F′ 452:e 445:t 438:v 418:t 414:F 410:t 406:L 387:. 290:n 260:x 256:a 252:k 165:. 162:) 159:t 156:( 148:F 144:x 141:+ 138:) 135:t 132:( 129:F 126:= 123:) 120:t 117:( 114:L 101:x 95:t 86:t 82:) 80:t 78:( 76:L 71:) 69:t 67:( 65:F 29:A 25:P

Index


geometry
curve
point
parameterized
tangent

Pierre Bouguer
Pierre Bouguer
navigation
Leonardo da Vinci
Paul J. Nahin

line
radiodrome
differential equation

square
mice problem
polygon
mice problem
Logarithmic spiral
Tractrix
Circles of Apollonius#Apollonius pursuit problem
Pursuit–evasion
Bouguer, Pierre
Nahin, Paul J.
Princeton University Press
ISBN
978-0-691-12514-5

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