lib/examples/instant_preview.lyx

   1 #LyX 2.1 created this file. For more info see http://www.lyx.org/
   2 \lyxformat 474
   3 \begin_document
   4 \begin_header
   5 \textclass article
   6 \begin_preamble
   7 \usepackage{etex}
   8 \usepackage[all, knot]{xy}
   9 \xyoption{arc}
  10 \usepackage{qtree}
  11 \usepackage{tipa}
  12 \usepackage{pstricks}
  13 \usepackage{pst-plot}
  14 \usepackage{rotating}
  15 \usepackage{tikz}
  16 \usetikzlibrary{scopes}
  17 \end_preamble
  18 \use_default_options false
  19 \maintain_unincluded_children false
  20 \language english
  21 \language_package default
  22 \inputencoding auto
  23 \fontencoding global
  24 \font_roman lmodern
  25 \font_sans default
  26 \font_typewriter default
  27 \font_math auto
  28 \font_default_family default
  29 \use_non_tex_fonts false
  30 \font_sc false
  31 \font_osf false
  32 \font_sf_scale 100
  33 \font_tt_scale 100
  34 \graphics default
  35 \default_output_format pdf
  36 \output_sync 0
  37 \bibtex_command default
  38 \index_command default
  39 \paperfontsize default
  40 \spacing single
  41 \use_hyperref false
  42 \papersize default
  43 \use_geometry false
  44 \use_package amsmath 1
  45 \use_package amssymb 1
  46 \use_package cancel 0
  47 \use_package esint 1
  48 \use_package mathdots 1
  49 \use_package mathtools 0
  50 \use_package mhchem 1
  51 \use_package stackrel 0
  52 \use_package stmaryrd 0
  53 \use_package undertilde 0
  54 \cite_engine basic
  55 \cite_engine_type default
  56 \biblio_style plain
  57 \use_bibtopic false
  58 \use_indices false
  59 \paperorientation portrait
  60 \suppress_date false
  61 \justification true
  62 \use_refstyle 0
  63 \index Index
  64 \shortcut idx
  65 \color #008000
  66 \end_index
  67 \secnumdepth 3
  68 \tocdepth 3
  69 \paragraph_separation indent
  70 \paragraph_indentation default
  71 \quotes_language english
  72 \papercolumns 1
  73 \papersides 1
  74 \paperpagestyle default
  75 \tracking_changes false
  76 \output_changes false
  77 \html_math_output 0
  78 \html_css_as_file 0
  79 \html_be_strict true
  80 \end_header
  81
  82 \begin_body
  83
  84 \begin_layout Section
  85 Introduction
  86 \end_layout
  87
  88 \begin_layout Standard
  89 In order to properly typeset the document and have instant preview working,
  90  the following packages have to be installed:
  91 \end_layout
  92
  93 \begin_layout LyX-Code
  94 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf, etex
  95 \end_layout
  96
  97 \begin_layout Standard
  98 Due to the use of postscript specials in Section
  99 \begin_inset CommandInset ref
 100 LatexCommand ref
 101 reference "sec:PSTricks"
 102
 103 \end_inset
 104
 105 , only the Postscript or PDF (ps2pdf) output formats will correctly render
 106  the included images.
 107  However, the PDF (XeTeX) output seems to also work, while trying to typeset
 108  the document with
 109 \family typewriter
 110 pdflatex
 111 \family default
 112  or
 113 \family typewriter
 114 pdflualatex
 115 \family default
 116  will generate errors.
 117 \end_layout
 118
 119 \begin_layout Section
 120 Diagrams by XY(-pic)
 121 \end_layout
 122
 123 \begin_layout Standard
 124 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
 125  examples, see
 126 \begin_inset Flex URL
 127 status collapsed
 128
 129 \begin_layout Plain Layout
 130
 131 http://www.math.columbia.edu/~lauda/xy/
 132 \end_layout
 133
 134 \end_inset
 135
 136 .
 137 \end_layout
 138
 139 \begin_layout Description
 140 Braid
 141 \end_layout
 142
 143 \begin_layout Standard
 144 \begin_inset Preview
 145
 146 \begin_layout Standard
 147 \begin_inset ERT
 148 status collapsed
 149
 150 \begin_layout Plain Layout
 151
 152
 153 \backslash
 154 xy
 155 \end_layout
 156
 157 \begin_layout Plain Layout
 158
 159 (5,10)*{}; (-10,-10)*{} **
 160 \backslash
 161 crv{(6,-2)&(-12,4)}
 162 \end_layout
 163
 164 \begin_layout Plain Layout
 165
 166
 167 \backslash
 168 POS?(.25)*{
 169 \backslash
 170 hole}="x"
 171 \backslash
 172 POS?(.45)*{
 173 \backslash
 174 hole}="y"
 175 \backslash
 176 POS?(.6)*{
 177 \backslash
 178 hole}="z";
 179 \end_layout
 180
 181 \begin_layout Plain Layout
 182
 183 "y"+(0,-1); (2,-10)*{} **
 184 \backslash
 185 crv{}
 186 \backslash
 187 POS?(.2)*{
 188 \backslash
 189 hole}="M";
 190 \end_layout
 191
 192 \begin_layout Plain Layout
 193
 194 (-10,10)*{}; "z" **
 195 \backslash
 196 crv{(-9,0)};
 197 \end_layout
 198
 199 \begin_layout Plain Layout
 200
 201 "z"; "M" **
 202 \backslash
 203 crv{};
 204 \end_layout
 205
 206 \begin_layout Plain Layout
 207
 208 "M"; "x" **
 209 \backslash
 210 crv{(5,0)};
 211 \end_layout
 212
 213 \begin_layout Plain Layout
 214
 215 "x"; "y" **
 216 \backslash
 217 crv{(0,7) & (-5,6)};
 218 \end_layout
 219
 220 \begin_layout Plain Layout
 221
 222
 223 \backslash
 224 endxy
 225 \end_layout
 226
 227 \end_inset
 228
 229
 230 \end_layout
 231
 232 \end_inset
 233
 234
 235 \end_layout
 236
 237 \begin_layout Description
 238 Knots
 239 \end_layout
 240
 241 \begin_layout Standard
 242 \begin_inset Preview
 243
 244 \begin_layout Standard
 245 \begin_inset ERT
 246 status collapsed
 247
 248 \begin_layout Plain Layout
 249
 250
 251 \backslash
 252 xy
 253 \end_layout
 254
 255 \begin_layout Plain Layout
 256
 257 (6,9)*{}="1";
 258 \end_layout
 259
 260 \begin_layout Plain Layout
 261
 262 (-8.5,-1)*{}="2";
 263 \end_layout
 264
 265 \begin_layout Plain Layout
 266
 267 "1";"2" **
 268 \backslash
 269 crv{~*=<.5pt>{.} (0,30)}?(.75)*
 270 \backslash
 271 dir{>}+(-2,2)*{z};
 272 \end_layout
 273
 274 \begin_layout Plain Layout
 275
 276 (-6.5,8)*{}="1";
 277 \end_layout
 278
 279 \begin_layout Plain Layout
 280
 281 (-.5,-9)*{}="2";
 282 \end_layout
 283
 284 \begin_layout Plain Layout
 285
 286 "1";"2" **
 287 \backslash
 288 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
 289 \backslash
 290 dir{>}+(-2,-2)*{u};
 291 \end_layout
 292
 293 \begin_layout Plain Layout
 294
 295 (-9.5,-3.35)*{}="1";
 296 \end_layout
 297
 298 \begin_layout Plain Layout
 299
 300 (8.5,-3)*{}="2";
 301 \end_layout
 302
 303 \begin_layout Plain Layout
 304
 305 "1";"2" **
 306 \backslash
 307 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
 308 \backslash
 309 dir{>}+(-1,-3)*{x};
 310 \end_layout
 311
 312 \begin_layout Plain Layout
 313
 314 (1,-10)*{}="1";
 315 \end_layout
 316
 317 \begin_layout Plain Layout
 318
 319 (6.5,7.13)*{}="2";
 320 \end_layout
 321
 322 \begin_layout Plain Layout
 323
 324 "1";"2" **
 325 \backslash
 326 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
 327 \backslash
 328 dir{>}+(3,-1)*{y};
 329 \end_layout
 330
 331 \begin_layout Plain Layout
 332
 333 (11,-1)*{}="1";
 334 \end_layout
 335
 336 \begin_layout Plain Layout
 337
 338 (-4,8)*{}="2";
 339 \end_layout
 340
 341 \begin_layout Plain Layout
 342
 343 "1";"2" **
 344 \backslash
 345 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
 346 \backslash
 347 dir{>}+(1,2)*{w};
 348 \end_layout
 349
 350 \begin_layout Plain Layout
 351
 352
 353 \backslash
 354 endxy
 355 \end_layout
 356
 357 \end_inset
 358
 359
 360 \end_layout
 361
 362 \end_inset
 363
 364
 365 \end_layout
 366
 367 \begin_layout Description
 368 Circles
 369 \end_layout
 370
 371 \begin_layout Standard
 372 \begin_inset Preview
 373
 374 \begin_layout Standard
 375 \begin_inset ERT
 376 status collapsed
 377
 378 \begin_layout Plain Layout
 379
 380
 381 \backslash
 382 xy
 383 \end_layout
 384
 385 \begin_layout Plain Layout
 386
 387 (0,0)*
 388 \backslash
 389 xycircle(14,8){++
 390 \backslash
 391 dir{<}};
 392 \end_layout
 393
 394 \begin_layout Plain Layout
 395
 396 (0,0)*
 397 \backslash
 398 xycircle<10pt>{{.}};
 399 \end_layout
 400
 401 \begin_layout Plain Layout
 402
 403 (0,0)*
 404 \backslash
 405 xycircle(5,2){:};
 406 \end_layout
 407
 408 \begin_layout Plain Layout
 409
 410 (0,15)*
 411 \backslash
 412 xycircle(10,4){--};
 413 \end_layout
 414
 415 \begin_layout Plain Layout
 416
 417
 418 \backslash
 419 endxy
 420 \end_layout
 421
 422 \end_inset
 423
 424
 425 \end_layout
 426
 427 \end_inset
 428
 429
 430 \end_layout
 431
 432 \begin_layout Description
 433 Cobordism
 434 \end_layout
 435
 436 \begin_layout Standard
 437 \begin_inset Preview
 438
 439 \begin_layout Standard
 440 \begin_inset ERT
 441 status collapsed
 442
 443 \begin_layout Plain Layout
 444
 445
 446 \backslash
 447 xy
 448 \end_layout
 449
 450 \begin_layout Plain Layout
 451
 452 (0,0)*
 453 \backslash
 454 ellipse(3,1){.};
 455 \end_layout
 456
 457 \begin_layout Plain Layout
 458
 459 (0,0)*
 460 \backslash
 461 ellipse(3,1)__,=:a(-180){-};
 462 \end_layout
 463
 464 \begin_layout Plain Layout
 465
 466 (-6,-8)*
 467 \backslash
 468 ellipse(3,1){.};
 469 \end_layout
 470
 471 \begin_layout Plain Layout
 472
 473 (6,-8)*
 474 \backslash
 475 ellipse(3,1){.};
 476 \end_layout
 477
 478 \begin_layout Plain Layout
 479
 480 (0,-8)*
 481 \backslash
 482 ellipse(3,1){.};
 483 \end_layout
 484
 485 \begin_layout Plain Layout
 486
 487 (-6,-8)*
 488 \backslash
 489 ellipse(3,1)__,=:a(-180){-};
 490 \end_layout
 491
 492 \begin_layout Plain Layout
 493
 494 (6,-8)*
 495 \backslash
 496 ellipse(3,1)__,=:a(-180){-};
 497 \end_layout
 498
 499 \begin_layout Plain Layout
 500
 501 (0,-8)*
 502 \backslash
 503 ellipse(3,1)__,=:a(180){-};
 504 \end_layout
 505
 506 \begin_layout Plain Layout
 507
 508 (-3,6)*
 509 \backslash
 510 ellipse(3,1){-};
 511 \end_layout
 512
 513 \begin_layout Plain Layout
 514
 515 (3,6)*
 516 \backslash
 517 ellipse(3,1){-};
 518 \end_layout
 519
 520 \begin_layout Plain Layout
 521
 522 (-3,12)*{}="1";
 523 \end_layout
 524
 525 \begin_layout Plain Layout
 526
 527 (3,12)*{}="2";
 528 \end_layout
 529
 530 \begin_layout Plain Layout
 531
 532 (-9,12)*{}="A2";
 533 \end_layout
 534
 535 \begin_layout Plain Layout
 536
 537 (9,12)*{}="B2";
 538 \end_layout
 539
 540 \begin_layout Plain Layout
 541
 542 "1";"2" **
 543 \backslash
 544 crv{(-3,7) & (3,7)};
 545 \end_layout
 546
 547 \begin_layout Plain Layout
 548
 549 (-3,0)*{}="A";
 550 \end_layout
 551
 552 \begin_layout Plain Layout
 553
 554 (3,0)*{}="B";
 555 \end_layout
 556
 557 \begin_layout Plain Layout
 558
 559 (-3,1)*{}="A1";
 560 \end_layout
 561
 562 \begin_layout Plain Layout
 563
 564 (3,1)*{}="B1";
 565 \end_layout
 566
 567 \begin_layout Plain Layout
 568
 569 "A";"A1" **
 570 \backslash
 571 dir{-};
 572 \end_layout
 573
 574 \begin_layout Plain Layout
 575
 576 "B";"B1" **
 577 \backslash
 578 dir{-};
 579 \end_layout
 580
 581 \begin_layout Plain Layout
 582
 583 "B2";"B1" **
 584 \backslash
 585 crv{(8,7) & (3,5)};
 586 \end_layout
 587
 588 \begin_layout Plain Layout
 589
 590 "A2";"A1" **
 591 \backslash
 592 crv{(-8,7) & (-3,5)};
 593 \end_layout
 594
 595 \begin_layout Plain Layout
 596
 597 %REFLECT
 598 \end_layout
 599
 600 \begin_layout Plain Layout
 601
 602 (3,-16)*{}="1";
 603 \end_layout
 604
 605 \begin_layout Plain Layout
 606
 607 (9,-16)*{}="2";
 608 \end_layout
 609
 610 \begin_layout Plain Layout
 611
 612 "1";"2" **
 613 \backslash
 614 crv{(3,-10) & (9,-10)};
 615 \end_layout
 616
 617 \begin_layout Plain Layout
 618
 619 (-3,-16)*{}="1";
 620 \end_layout
 621
 622 \begin_layout Plain Layout
 623
 624 (-9,-16)*{}="2";
 625 \end_layout
 626
 627 \begin_layout Plain Layout
 628
 629 "1";"2" **
 630 \backslash
 631 crv{(-3,-10) & (-9,-10)};
 632 \end_layout
 633
 634 \begin_layout Plain Layout
 635
 636 (-15,-16)*{}="A2";
 637 \end_layout
 638
 639 \begin_layout Plain Layout
 640
 641 (15,-16)*{}="B2";
 642 \end_layout
 643
 644 \begin_layout Plain Layout
 645
 646 (-3,0)*{}="A";
 647 \end_layout
 648
 649 \begin_layout Plain Layout
 650
 651 (3,0)*{}="B";
 652 \end_layout
 653
 654 \begin_layout Plain Layout
 655
 656 (-3,-1)*{}="A1";
 657 \end_layout
 658
 659 \begin_layout Plain Layout
 660
 661 (3,-1)*{}="B1";
 662 \end_layout
 663
 664 \begin_layout Plain Layout
 665
 666 "A";"A1" **
 667 \backslash
 668 dir{-};
 669 \end_layout
 670
 671 \begin_layout Plain Layout
 672
 673 "B";"B1" **
 674 \backslash
 675 dir{-};
 676 \end_layout
 677
 678 \begin_layout Plain Layout
 679
 680 "B2";"B1" **
 681 \backslash
 682 crv{(13,-6) & (2,-8)};
 683 \end_layout
 684
 685 \begin_layout Plain Layout
 686
 687 "A2";"A1" **
 688 \backslash
 689 crv{(-13,-6) & (-2,-8)};
 690 \end_layout
 691
 692 \begin_layout Plain Layout
 693
 694
 695 \backslash
 696 endxy
 697 \end_layout
 698
 699 \end_inset
 700
 701
 702 \end_layout
 703
 704 \end_inset
 705
 706
 707 \begin_inset Preview
 708
 709 \begin_layout Standard
 710 \begin_inset ERT
 711 status collapsed
 712
 713 \begin_layout Plain Layout
 714
 715
 716 \backslash
 717 xy 0;/r.18pc/:
 718 \end_layout
 719
 720 \begin_layout Plain Layout
 721
 722 (20,2)*{
 723 \backslash
 724 bullet}="RU"+(1,3)*{x^{
 725 \backslash
 726 ast}};
 727 \end_layout
 728
 729 \begin_layout Plain Layout
 730
 731 (16,-3)*{
 732 \backslash
 733 bullet}="RD"+(2.5,2)*{x^{
 734 \backslash
 735 ast}};
 736 \end_layout
 737
 738 \begin_layout Plain Layout
 739
 740 (-16,2)*{
 741 \backslash
 742 bullet}="LU"+(-1,2)*{x};
 743 \end_layout
 744
 745 \begin_layout Plain Layout
 746
 747 (-20,-3)*{
 748 \backslash
 749 bullet}="LD"+(-1,2)*{x};
 750 \end_layout
 751
 752 \begin_layout Plain Layout
 753
 754 "RU";"RD" **
 755 \backslash
 756 crv{(4,2) & (4,-1)}; ?(.1)*
 757 \backslash
 758 dir{<}; ?(.85)*
 759 \backslash
 760 dir{<};
 761 \end_layout
 762
 763 \begin_layout Plain Layout
 764
 765 "LD";"LU" **
 766 \backslash
 767 crv{(-4,-2) & (-4,1)};
 768 \end_layout
 769
 770 \begin_layout Plain Layout
 771
 772 ?(.08)*
 773 \backslash
 774 dir{<}; ?(.85)*
 775 \backslash
 776 dir{<};
 777 \end_layout
 778
 779 \begin_layout Plain Layout
 780
 781 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
 782 \end_layout
 783
 784 \begin_layout Plain Layout
 785
 786 "x1"; "x2" **
 787 \backslash
 788 crv{(7,-10) & (-7,-10)};
 789 \end_layout
 790
 791 \begin_layout Plain Layout
 792
 793 (16,-20)*{
 794 \backslash
 795 bullet}="RDD"+(2.5,-1)*{x^{
 796 \backslash
 797 ast}};
 798 \end_layout
 799
 800 \begin_layout Plain Layout
 801
 802 (-20,-20)*{
 803 \backslash
 804 bullet}="LDD"+(-1,-3)*{x};
 805 \end_layout
 806
 807 \begin_layout Plain Layout
 808
 809 (20,-12.5)*{
 810 \backslash
 811 bullet}="RUD"+(3.5,1)*{x^{
 812 \backslash
 813 ast}};
 814 \end_layout
 815
 816 \begin_layout Plain Layout
 817
 818 (-16,-15)*{
 819 \backslash
 820 bullet}="LUD";
 821 \end_layout
 822
 823 \begin_layout Plain Layout
 824
 825 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
 826 \end_layout
 827
 828 \begin_layout Plain Layout
 829
 830 "RD"; "RDD" **
 831 \backslash
 832 dir{-};
 833 \end_layout
 834
 835 \begin_layout Plain Layout
 836
 837 "LD"; "LDD" **
 838 \backslash
 839 dir{-};
 840 \end_layout
 841
 842 \begin_layout Plain Layout
 843
 844 "A"; "LUD" **
 845 \backslash
 846 dir{.};
 847 \end_layout
 848
 849 \begin_layout Plain Layout
 850
 851 "RDD"; "LDD" **
 852 \backslash
 853 crv{(0,-17)}; ?(.57)*
 854 \backslash
 855 dir{>};
 856 \end_layout
 857
 858 \begin_layout Plain Layout
 859
 860 "RU"; "RUD" **
 861 \backslash
 862 dir{-};
 863 \end_layout
 864
 865 \begin_layout Plain Layout
 866
 867 "LU"; "A" **
 868 \backslash
 869 dir{-};
 870 \end_layout
 871
 872 \begin_layout Plain Layout
 873
 874 "B"; "RUD" **
 875 \backslash
 876 crv{(18,-14.15)};
 877 \end_layout
 878
 879 \begin_layout Plain Layout
 880
 881 "B"; "LUD" **
 882 \backslash
 883 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
 884 \backslash
 885 dir{<};
 886 \end_layout
 887
 888 \begin_layout Plain Layout
 889
 890
 891 \backslash
 892 endxy
 893 \end_layout
 894
 895 \end_inset
 896
 897
 898 \end_layout
 899
 900 \end_inset
 901
 902
 903 \end_layout
 904
 905 \begin_layout Description
 906 Strings
 907 \end_layout
 908
 909 \begin_layout Standard
 910 \begin_inset Preview
 911
 912 \begin_layout Standard
 913 \begin_inset ERT
 914 status open
 915
 916 \begin_layout Plain Layout
 917
 918
 919 \backslash
 920 xy (-15,0)*{};(15,0)*{};
 921 \end_layout
 922
 923 \begin_layout Plain Layout
 924
 925
 926 \backslash
 927 endxy
 928 \end_layout
 929
 930 \begin_layout Plain Layout
 931
 932
 933 \backslash
 934 qquad =
 935 \backslash
 936 qquad
 937 \backslash
 938 xy
 939 \end_layout
 940
 941 \begin_layout Plain Layout
 942
 943 (-10,12)*{}; (-10,-12)*{}; **
 944 \backslash
 945 dir{-}?(.5)*
 946 \backslash
 947 dir{<}+(-4,0)*{F(x)};
 948 \end_layout
 949
 950 \begin_layout Plain Layout
 951
 952 (-2,12)*{}="1";
 953 \end_layout
 954
 955 \begin_layout Plain Layout
 956
 957 (6,-7) *{}="2";
 958 \end_layout
 959
 960 \begin_layout Plain Layout
 961
 962 (14,-7) *{}="3";
 963 \end_layout
 964
 965 \begin_layout Plain Layout
 966
 967 (14,-13)*{}="3'";
 968 \end_layout
 969
 970 \begin_layout Plain Layout
 971
 972 (18,0) *={}="";
 973 \end_layout
 974
 975 \begin_layout Plain Layout
 976
 977 "1";"2" **
 978 \backslash
 979 crv{(-4,-21)&(5,-15)};
 980 \end_layout
 981
 982 \begin_layout Plain Layout
 983
 984 ?(.15)*
 985 \backslash
 986 dir{<}+(5,10)*{
 987 \backslash
 988 overline{F(x)}};
 989 \end_layout
 990
 991 \begin_layout Plain Layout
 992
 993 "2";"3" **
 994 \backslash
 995 crv{(6,1)&(14,1)};
 996 \end_layout
 997
 998 \begin_layout Plain Layout
 999
1000 ?(0)*
1001 \backslash
1002 dir{<}+(4,8)*{
1003 \backslash
1004 widetilde{F(i_x)}} ;
1005 \end_layout
1006
1007 \begin_layout Plain Layout
1008
1009 ?(.95)*
1010 \backslash
1011 dir{<}+(5,-2)*{F(
1012 \backslash
1013 overline x)};
1014 \end_layout
1015
1016 \begin_layout Plain Layout
1017
1018 "3";"3'" **
1019 \backslash
1020 dir{-};
1021 \end_layout
1022
1023 \begin_layout Plain Layout
1024
1025 (-2,6)*{}="X1";
1026 \end_layout
1027
1028 \begin_layout Plain Layout
1029
1030 (-10,6)*{}="X2";
1031 \end_layout
1032
1033 \begin_layout Plain Layout
1034
1035 "X1";"X2" **
1036 \backslash
1037 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1038 \end_layout
1039
1040 \begin_layout Plain Layout
1041
1042 (-2,-6)*{}="XA";
1043 \end_layout
1044
1045 \begin_layout Plain Layout
1046
1047 (-10,-6)*{}="XB";
1048 \end_layout
1049
1050 \begin_layout Plain Layout
1051
1052 "XA";"XB" **
1053 \backslash
1054 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1055 \end_layout
1056
1057 \begin_layout Plain Layout
1058
1059
1060 \backslash
1061 endxy
1062 \end_layout
1063
1064 \end_inset
1065
1066
1067 \end_layout
1068
1069 \end_inset
1070
1071
1072 \end_layout
1073
1074 \begin_layout Description
1075 Categories
1076 \end_layout
1077
1078 \begin_layout Standard
1079 \begin_inset Preview
1080
1081 \begin_layout Standard
1082 \begin_inset ERT
1083 status collapsed
1084
1085 \begin_layout Plain Layout
1086
1087
1088 \backslash
1089 xymatrix{
1090 \end_layout
1091
1092 \begin_layout Plain Layout
1093
1094 (x
1095 \backslash
1096 otimes 1)
1097 \backslash
1098 otimes y
1099 \end_layout
1100
1101 \begin_layout Plain Layout
1102
1103
1104 \backslash
1105 ar[rr]^{a_{x,1,y}}
1106 \end_layout
1107
1108 \begin_layout Plain Layout
1109
1110
1111 \backslash
1112 ar[dr]_{r_x
1113 \backslash
1114 otimes 1_y}
1115 \end_layout
1116
1117 \begin_layout Plain Layout
1118
1119 && x
1120 \backslash
1121 otimes(1
1122 \backslash
1123 otimes y)
1124 \end_layout
1125
1126 \begin_layout Plain Layout
1127
1128
1129 \backslash
1130 ar[dl]^{1_x
1131 \backslash
1132 otimes
1133 \backslash
1134 ell_y }
1135 \backslash
1136
1137 \backslash
1138
1139 \end_layout
1140
1141 \begin_layout Plain Layout
1142
1143 & x
1144 \backslash
1145 otimes y }
1146 \end_layout
1147
1148 \end_inset
1149
1150
1151 \end_layout
1152
1153 \end_inset
1154
1155
1156 \begin_inset Preview
1157
1158 \begin_layout Standard
1159 \begin_inset ERT
1160 status collapsed
1161
1162 \begin_layout Plain Layout
1163
1164
1165 \backslash
1166 xy
1167 \end_layout
1168
1169 \begin_layout Plain Layout
1170
1171 (-9,0)*+{
1172 \backslash
1173 bullet}="1";
1174 \end_layout
1175
1176 \begin_layout Plain Layout
1177
1178 (0,0)*+{
1179 \backslash
1180 bullet}="2";
1181 \end_layout
1182
1183 \begin_layout Plain Layout
1184
1185 {
1186 \backslash
1187 ar@/^.9pc/ "1";"2"};
1188 \end_layout
1189
1190 \begin_layout Plain Layout
1191
1192 {
1193 \backslash
1194 ar@/_.9pc/ "1";"2"};
1195 \end_layout
1196
1197 \begin_layout Plain Layout
1198
1199 {
1200 \backslash
1201 ar@/^2pc/ "1";"2"};
1202 \end_layout
1203
1204 \begin_layout Plain Layout
1205
1206 {
1207 \backslash
1208 ar@/_2pc/ "1";"2"};
1209 \end_layout
1210
1211 \begin_layout Plain Layout
1212
1213 {
1214 \backslash
1215 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1216 \end_layout
1217
1218 \begin_layout Plain Layout
1219
1220 {
1221 \backslash
1222 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1223 \end_layout
1224
1225 \begin_layout Plain Layout
1226
1227 {
1228 \backslash
1229 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1230 \end_layout
1231
1232 \begin_layout Plain Layout
1233
1234 (0,0)*+{
1235 \backslash
1236 bullet}="1";
1237 \end_layout
1238
1239 \begin_layout Plain Layout
1240
1241 (9,0)*+{
1242 \backslash
1243 bullet}="2";
1244 \end_layout
1245
1246 \begin_layout Plain Layout
1247
1248 (18,0)*+{
1249 \backslash
1250 bullet}="3";
1251 \end_layout
1252
1253 \begin_layout Plain Layout
1254
1255 {
1256 \backslash
1257 ar "1";"2"};
1258 \end_layout
1259
1260 \begin_layout Plain Layout
1261
1262 {
1263 \backslash
1264 ar "2";"3"};
1265 \end_layout
1266
1267 \begin_layout Plain Layout
1268
1269 {
1270 \backslash
1271 ar@/^1pc/ "1";"2"};
1272 \end_layout
1273
1274 \begin_layout Plain Layout
1275
1276 {
1277 \backslash
1278 ar@/_1pc/ "1";"2"};
1279 \end_layout
1280
1281 \begin_layout Plain Layout
1282
1283 {
1284 \backslash
1285 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1286 \end_layout
1287
1288 \begin_layout Plain Layout
1289
1290 {
1291 \backslash
1292 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1293 \end_layout
1294
1295 \begin_layout Plain Layout
1296
1297
1298 \backslash
1299 endxy
1300 \end_layout
1301
1302 \end_inset
1303
1304
1305 \end_layout
1306
1307 \end_inset
1308
1309
1310 \end_layout
1311
1312 \begin_layout Description
1313 Transformations
1314 \end_layout
1315
1316 \begin_layout Standard
1317 \begin_inset Preview
1318
1319 \begin_layout Standard
1320 \begin_inset ERT
1321 status collapsed
1322
1323 \begin_layout Plain Layout
1324
1325
1326 \backslash
1327 xy %FIG.19.
1328  Natural transformation between functors.
1329 \end_layout
1330
1331 \begin_layout Plain Layout
1332
1333 (-26,-2)*+{
1334 \backslash
1335 bullet}="a";
1336 \end_layout
1337
1338 \begin_layout Plain Layout
1339
1340 (-12,3)*+{
1341 \backslash
1342 bullet}="b";
1343 \end_layout
1344
1345 \begin_layout Plain Layout
1346
1347 (-16,-5)*+{
1348 \backslash
1349 bullet}="c";
1350 \end_layout
1351
1352 \begin_layout Plain Layout
1353
1354 {
1355 \backslash
1356 ar@/^.25pc/ "a";"b"};
1357 \end_layout
1358
1359 \begin_layout Plain Layout
1360
1361 {
1362 \backslash
1363 ar@/_.25pc/"a";"c"};
1364 \end_layout
1365
1366 \begin_layout Plain Layout
1367
1368 {
1369 \backslash
1370 ar@/_.15pc/ "b";"c"};
1371 \end_layout
1372
1373 \begin_layout Plain Layout
1374
1375 %START TOP
1376 \end_layout
1377
1378 \begin_layout Plain Layout
1379
1380 (12,10)*+{
1381 \backslash
1382 bullet}="ta";
1383 \end_layout
1384
1385 \begin_layout Plain Layout
1386
1387 (26,15)*+{
1388 \backslash
1389 bullet}="tb";
1390 \end_layout
1391
1392 \begin_layout Plain Layout
1393
1394 (22,8)*+{
1395 \backslash
1396 bullet}="tc";
1397 \end_layout
1398
1399 \begin_layout Plain Layout
1400
1401 {
1402 \backslash
1403 ar@/^.25pc/ "ta";"tb"};
1404 \end_layout
1405
1406 \begin_layout Plain Layout
1407
1408 {
1409 \backslash
1410 ar@/_.25pc/ "ta";"tc"};
1411 \end_layout
1412
1413 \begin_layout Plain Layout
1414
1415 {
1416 \backslash
1417 ar@/_.15pc/ "tb";"tc"};
1418 \end_layout
1419
1420 \begin_layout Plain Layout
1421
1422 %START bottom
1423 \end_layout
1424
1425 \begin_layout Plain Layout
1426
1427 (12,-10)*+{
1428 \backslash
1429 bullet}="ba";
1430 \end_layout
1431
1432 \begin_layout Plain Layout
1433
1434 (26,-5)*+{
1435 \backslash
1436 bullet}="bb";
1437 \end_layout
1438
1439 \begin_layout Plain Layout
1440
1441 (22,-12)*+{
1442 \backslash
1443 bullet}="bc";
1444 \end_layout
1445
1446 \begin_layout Plain Layout
1447
1448 {
1449 \backslash
1450 ar@/^.25pc/@{.>} "ba";"bb"};
1451 \end_layout
1452
1453 \begin_layout Plain Layout
1454
1455 {
1456 \backslash
1457 ar@/_.25pc/ "ba";"bc"};
1458 \end_layout
1459
1460 \begin_layout Plain Layout
1461
1462 {
1463 \backslash
1464 ar@/_.15pc/ "bb";"bc"};
1465 \end_layout
1466
1467 \begin_layout Plain Layout
1468
1469 %START CONNECT
1470 \end_layout
1471
1472 \begin_layout Plain Layout
1473
1474 {
1475 \backslash
1476 ar@/_.15pc/ "ta";"ba"};
1477 \end_layout
1478
1479 \begin_layout Plain Layout
1480
1481 {
1482 \backslash
1483 ar@/_.15pc/ "tb";"bb"};
1484 \end_layout
1485
1486 \begin_layout Plain Layout
1487
1488 {
1489 \backslash
1490 ar@/_.15pc/ "tc";"bc"};
1491 \end_layout
1492
1493 \begin_layout Plain Layout
1494
1495 %START ARROWS AND LABELS
1496 \end_layout
1497
1498 \begin_layout Plain Layout
1499
1500 (-12,6)*{}="DF";
1501 \end_layout
1502
1503 \begin_layout Plain Layout
1504
1505 (6,10)*{}="CF";
1506 \end_layout
1507
1508 \begin_layout Plain Layout
1509
1510 {
1511 \backslash
1512 ar@/^.35pc/^F "DF";"CF"};
1513 \end_layout
1514
1515 \begin_layout Plain Layout
1516
1517 (-12,-6)*{}="DF";
1518 \end_layout
1519
1520 \begin_layout Plain Layout
1521
1522 (6,-10)*{}="CF";
1523 \end_layout
1524
1525 \begin_layout Plain Layout
1526
1527 {
1528 \backslash
1529 ar@/_.35pc/_G "DF";"CF"};
1530 \end_layout
1531
1532 \begin_layout Plain Layout
1533
1534 (-2,5)*{}="DF";
1535 \end_layout
1536
1537 \begin_layout Plain Layout
1538
1539 (-2,-5)*{}="CF";
1540 \end_layout
1541
1542 \begin_layout Plain Layout
1543
1544 {
1545 \backslash
1546 ar@{=>}^{
1547 \backslash
1548 alpha} "DF";"CF"};
1549 \end_layout
1550
1551 \begin_layout Plain Layout
1552
1553 (29,3)*{D};
1554 \end_layout
1555
1556 \begin_layout Plain Layout
1557
1558 (-23,3)*{C};
1559 \end_layout
1560
1561 \begin_layout Plain Layout
1562
1563
1564 \backslash
1565 endxy
1566 \end_layout
1567
1568 \end_inset
1569
1570
1571 \end_layout
1572
1573 \end_inset
1574
1575
1576 \end_layout
1577
1578 \begin_layout Section
1579 IPA
1580 \end_layout
1581
1582 \begin_layout Standard
1583 \begin_inset Preview
1584
1585 \begin_layout Standard
1586 \begin_inset ERT
1587 status collapsed
1588
1589 \begin_layout Plain Layout
1590
1591
1592 \backslash
1593 textipa{Ekspl@"neIS@n}
1594 \end_layout
1595
1596 \end_inset
1597
1598
1599 \end_layout
1600
1601 \end_inset
1602
1603
1604 \end_layout
1605
1606 \begin_layout Section
1607 QTree
1608 \end_layout
1609
1610 \begin_layout Standard
1611 \begin_inset Preview
1612
1613 \begin_layout Standard
1614 \begin_inset ERT
1615 status collapsed
1616
1617 \begin_layout Plain Layout
1618
1619
1620 \backslash
1621 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1622 \end_layout
1623
1624 \end_inset
1625
1626
1627 \end_layout
1628
1629 \end_inset
1630
1631
1632 \begin_inset Preview
1633
1634 \begin_layout Standard
1635 \begin_inset ERT
1636 status collapsed
1637
1638 \begin_layout Plain Layout
1639
1640
1641 \backslash
1642 Tree [.$
1643 \backslash
1644 sigma$ $
1645 \backslash
1646 mu$ $
1647 \backslash
1648 mu$ ]
1649 \end_layout
1650
1651 \end_inset
1652
1653
1654 \end_layout
1655
1656 \end_inset
1657
1658
1659 \end_layout
1660
1661 \begin_layout Section
1662 PSTricks
1663 \begin_inset CommandInset label
1664 LatexCommand label
1665 name "sec:PSTricks"
1666
1667 \end_inset
1668
1669
1670 \end_layout
1671
1672 \begin_layout Standard
1673 Some simple graphing examples.
1674 \end_layout
1675
1676 \begin_layout Subsection
1677 Function plotting
1678 \end_layout
1679
1680 \begin_layout Standard
1681 \begin_inset Preview
1682
1683 \begin_layout Standard
1684 \begin_inset ERT
1685 status open
1686
1687 \begin_layout Plain Layout
1688
1689
1690 \backslash
1691 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1692 \end_layout
1693
1694 \begin_layout Plain Layout
1695
1696
1697 \backslash
1698 psaxes{->}(0,0)(0,-3)(10,3)
1699 \end_layout
1700
1701 \begin_layout Plain Layout
1702
1703
1704 \backslash
1705 uput[-90](10,0){$x$}
1706 \backslash
1707 uput[0](0,3){$f(x)$}
1708 \end_layout
1709
1710 \begin_layout Plain Layout
1711
1712
1713 \backslash
1714 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1715 \end_layout
1716
1717 \begin_layout Plain Layout
1718
1719
1720 \backslash
1721 end{pspicture*}
1722 \end_layout
1723
1724 \end_inset
1725
1726
1727 \end_layout
1728
1729 \end_inset
1730
1731
1732 \end_layout
1733
1734 \begin_layout Subsection
1735 Inline data plotting
1736 \end_layout
1737
1738 \begin_layout Standard
1739 \align center
1740 \begin_inset Preview
1741
1742 \begin_layout Standard
1743 \align center
1744 \begin_inset ERT
1745 status open
1746
1747 \begin_layout Plain Layout
1748
1749
1750 \backslash
1751 begin{pspicture*}(-1.5,-1.5)(11,5)
1752 \end_layout
1753
1754 \begin_layout Plain Layout
1755
1756
1757 \backslash
1758 psaxes{->}(0,0)(0,0)(10,5)
1759 \end_layout
1760
1761 \begin_layout Plain Layout
1762
1763
1764 \backslash
1765 psset{linewidth=2.5pt}
1766 \end_layout
1767
1768 \begin_layout Plain Layout
1769
1770
1771 \backslash
1772 rput(5.0,-1.0){Speed [MPH]}
1773 \end_layout
1774
1775 \begin_layout Plain Layout
1776
1777
1778 \backslash
1779 rput(-1.0,1.0){
1780 \backslash
1781 begin{rotate}{90}Cost [Dollars]
1782 \backslash
1783 end{rotate}}
1784 \end_layout
1785
1786 \begin_layout Plain Layout
1787
1788
1789 \backslash
1790 savedata{
1791 \backslash
1792 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1793 \end_layout
1794
1795 \begin_layout Plain Layout
1796
1797
1798 \backslash
1799 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1800 \backslash
1801 mydata}
1802 \end_layout
1803
1804 \begin_layout Plain Layout
1805
1806
1807 \backslash
1808 end{pspicture*}
1809 \end_layout
1810
1811 \end_inset
1812
1813
1814 \end_layout
1815
1816 \end_inset
1817
1818
1819 \end_layout
1820
1821 \begin_layout Subsection
1822 Lissajous curves
1823 \end_layout
1824
1825 \begin_layout Standard
1826 \begin_inset Preview
1827
1828 \begin_layout Standard
1829 \begin_inset ERT
1830 status open
1831
1832 \begin_layout Plain Layout
1833
1834
1835 \backslash
1836 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1837 \end_layout
1838
1839 \begin_layout Plain Layout
1840
1841
1842 \backslash
1843 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1844  cos 100 t mul sin}
1845 \end_layout
1846
1847 \begin_layout Plain Layout
1848
1849
1850 \backslash
1851 end{pspicture*}
1852 \end_layout
1853
1854 \end_inset
1855
1856
1857 \end_layout
1858
1859 \end_inset
1860
1861
1862 \begin_inset space \hfill{}
1863 \end_inset
1864
1865
1866 \begin_inset Preview
1867
1868 \begin_layout Standard
1869 \begin_inset ERT
1870 status open
1871
1872 \begin_layout Plain Layout
1873
1874
1875 \backslash
1876 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1877 \end_layout
1878
1879 \begin_layout Plain Layout
1880
1881
1882 \backslash
1883 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1884  mul cos 100 t mul sin}
1885 \end_layout
1886
1887 \begin_layout Plain Layout
1888
1889
1890 \backslash
1891 end{pspicture*}
1892 \end_layout
1893
1894 \end_inset
1895
1896
1897 \end_layout
1898
1899 \end_inset
1900
1901
1902 \begin_inset space \hfill{}
1903 \end_inset
1904
1905
1906 \begin_inset Preview
1907
1908 \begin_layout Standard
1909 \begin_inset ERT
1910 status open
1911
1912 \begin_layout Plain Layout
1913
1914
1915 \backslash
1916 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1917 \end_layout
1918
1919 \begin_layout Plain Layout
1920
1921
1922 \backslash
1923 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1924  mul cos 200 t mul sin}
1925 \end_layout
1926
1927 \begin_layout Plain Layout
1928
1929
1930 \backslash
1931 end{pspicture*}
1932 \end_layout
1933
1934 \end_inset
1935
1936
1937 \end_layout
1938
1939 \end_inset
1940
1941
1942 \begin_inset space \hfill{}
1943 \end_inset
1944
1945
1946 \begin_inset Preview
1947
1948 \begin_layout Standard
1949 \begin_inset ERT
1950 status open
1951
1952 \begin_layout Plain Layout
1953
1954
1955 \backslash
1956 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1957 \end_layout
1958
1959 \begin_layout Plain Layout
1960
1961
1962 \backslash
1963 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1964  mul cos 200 t mul sin}
1965 \end_layout
1966
1967 \begin_layout Plain Layout
1968
1969
1970 \backslash
1971 end{pspicture*}
1972 \end_layout
1973
1974 \end_inset
1975
1976
1977 \end_layout
1978
1979 \end_inset
1980
1981
1982 \end_layout
1983
1984 \begin_layout Section
1985 TikZ
1986 \end_layout
1987
1988 \begin_layout Standard
1989 \begin_inset Flex URL
1990 status collapsed
1991
1992 \begin_layout Plain Layout
1993
1994 http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
1995 \end_layout
1996
1997 \end_inset
1998
1999
2000 \end_layout
2001
2002 \begin_layout Standard
2003 \begin_inset Preview
2004
2005 \begin_layout Standard
2006 \begin_inset ERT
2007 status collapsed
2008
2009 \begin_layout Plain Layout
2010
2011
2012 \backslash
2013 def
2014 \backslash
2015 iangle{35} % Angle of the inclined plane
2016 \end_layout
2017
2018 \begin_layout Plain Layout
2019
2020
2021 \backslash
2022 def
2023 \backslash
2024 down{-90}
2025 \end_layout
2026
2027 \begin_layout Plain Layout
2028
2029
2030 \backslash
2031 def
2032 \backslash
2033 arcr{0.5cm} % Radius of the arc used to indicate angles
2034 \end_layout
2035
2036 \begin_layout Plain Layout
2037
2038 \end_layout
2039
2040 \begin_layout Plain Layout
2041
2042
2043 \backslash
2044 begin{tikzpicture}[
2045 \end_layout
2046
2047 \begin_layout Plain Layout
2048
2049     force/.style={>=latex,draw=blue,fill=blue},
2050 \end_layout
2051
2052 \begin_layout Plain Layout
2053
2054     axis/.style={densely dashed,gray,font=
2055 \backslash
2056 small},
2057 \end_layout
2058
2059 \begin_layout Plain Layout
2060
2061     M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2062 \end_layout
2063
2064 \begin_layout Plain Layout
2065
2066     m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2067 \end_layout
2068
2069 \begin_layout Plain Layout
2070
2071     plane/.style={draw=black,fill=blue!10},
2072 \end_layout
2073
2074 \begin_layout Plain Layout
2075
2076     string/.style={draw=red, thick},
2077 \end_layout
2078
2079 \begin_layout Plain Layout
2080
2081     pulley/.style={thick},
2082 \end_layout
2083
2084 \begin_layout Plain Layout
2085
2086 ]
2087 \end_layout
2088
2089 \begin_layout Plain Layout
2090
2091 \end_layout
2092
2093 \begin_layout Plain Layout
2094
2095
2096 \backslash
2097 matrix[column sep=1cm] {
2098 \end_layout
2099
2100 \begin_layout Plain Layout
2101
2102     %% Sketch
2103 \end_layout
2104
2105 \begin_layout Plain Layout
2106
2107
2108 \backslash
2109 draw[plane] (0,-1) coordinate (base)
2110 \end_layout
2111
2112 \begin_layout Plain Layout
2113
2114                      -- coordinate[pos=0.5] (mid) ++(
2115 \backslash
2116 iangle:3) coordinate (top)
2117 \end_layout
2118
2119 \begin_layout Plain Layout
2120
2121                      |- (base) -- cycle;
2122 \end_layout
2123
2124 \begin_layout Plain Layout
2125
2126
2127 \backslash
2128 path (mid) node[M,rotate=
2129 \backslash
2130 iangle,yshift=0.25cm] (M) {};
2131 \end_layout
2132
2133 \begin_layout Plain Layout
2134
2135
2136 \backslash
2137 draw[pulley] (top) -- ++(
2138 \backslash
2139 iangle:0.25) circle (0.25cm)
2140 \end_layout
2141
2142 \begin_layout Plain Layout
2143
2144                    ++ (90-
2145 \backslash
2146 iangle:0.5) coordinate (pulley);
2147 \end_layout
2148
2149 \begin_layout Plain Layout
2150
2151
2152 \backslash
2153 draw[string] (M.east) -- ++(
2154 \backslash
2155 iangle:1.5cm) arc (90+
2156 \backslash
2157 iangle:0:0.25)
2158 \end_layout
2159
2160 \begin_layout Plain Layout
2161
2162                   -- ++(0,-1) node[m] {};
2163 \end_layout
2164
2165 \begin_layout Plain Layout
2166
2167 \end_layout
2168
2169 \begin_layout Plain Layout
2170
2171
2172 \backslash
2173 draw[->] (base)++(
2174 \backslash
2175 arcr,0) arc (0:
2176 \backslash
2177 iangle:
2178 \backslash
2179 arcr);
2180 \end_layout
2181
2182 \begin_layout Plain Layout
2183
2184
2185 \backslash
2186 path (base)++(
2187 \backslash
2188 iangle*0.5:
2189 \backslash
2190 arcr+5pt) node {$
2191 \backslash
2192 alpha$};
2193 \end_layout
2194
2195 \begin_layout Plain Layout
2196
2197     %%
2198 \end_layout
2199
2200 \begin_layout Plain Layout
2201
2202 \end_layout
2203
2204 \begin_layout Plain Layout
2205
2206 &
2207 \end_layout
2208
2209 \begin_layout Plain Layout
2210
2211     %% Free body diagram of M
2212 \end_layout
2213
2214 \begin_layout Plain Layout
2215
2216
2217 \backslash
2218 begin{scope}[rotate=
2219 \backslash
2220 iangle]
2221 \end_layout
2222
2223 \begin_layout Plain Layout
2224
2225
2226 \backslash
2227 node[M,transform shape] (M) {};
2228 \end_layout
2229
2230 \begin_layout Plain Layout
2231
2232         % Draw axes and help lines
2233 \end_layout
2234
2235 \begin_layout Plain Layout
2236
2237 \end_layout
2238
2239 \begin_layout Plain Layout
2240
2241         {[axis,->]
2242 \end_layout
2243
2244 \begin_layout Plain Layout
2245
2246
2247 \backslash
2248 draw (0,-1) -- (0,2) node[right] {$+y$};
2249 \end_layout
2250
2251 \begin_layout Plain Layout
2252
2253
2254 \backslash
2255 draw (M) -- ++(2,0) node[right] {$+x$};
2256 \end_layout
2257
2258 \begin_layout Plain Layout
2259
2260             % Indicate angle.
2261  The code is a bit awkward.
2262 \end_layout
2263
2264 \begin_layout Plain Layout
2265
2266 \end_layout
2267
2268 \begin_layout Plain Layout
2269
2270
2271 \backslash
2272 draw[solid,shorten >=0.5pt] (
2273 \backslash
2274 down-
2275 \backslash
2276 iangle:
2277 \backslash
2278 arcr)
2279 \end_layout
2280
2281 \begin_layout Plain Layout
2282
2283                 arc(
2284 \backslash
2285 down-
2286 \backslash
2287 iangle:
2288 \backslash
2289 down:
2290 \backslash
2291 arcr);
2292 \end_layout
2293
2294 \begin_layout Plain Layout
2295
2296
2297 \backslash
2298 node at (
2299 \backslash
2300 down-0.5*
2301 \backslash
2302 iangle:1.3*
2303 \backslash
2304 arcr) {$
2305 \backslash
2306 alpha$};
2307 \end_layout
2308
2309 \begin_layout Plain Layout
2310
2311         }
2312 \end_layout
2313
2314 \begin_layout Plain Layout
2315
2316 \end_layout
2317
2318 \begin_layout Plain Layout
2319
2320         % Forces
2321 \end_layout
2322
2323 \begin_layout Plain Layout
2324
2325         {[force,->]
2326 \end_layout
2327
2328 \begin_layout Plain Layout
2329
2330             % Assuming that Mg = 1.
2331  The normal force will therefore be cos(alpha)
2332 \end_layout
2333
2334 \begin_layout Plain Layout
2335
2336
2337 \backslash
2338 draw (M.center) -- ++(0,{cos(
2339 \backslash
2340 iangle)}) node[above right] {$N$};
2341 \end_layout
2342
2343 \begin_layout Plain Layout
2344
2345
2346 \backslash
2347 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2348 \end_layout
2349
2350 \begin_layout Plain Layout
2351
2352
2353 \backslash
2354 draw (M.east) -- ++(1,0) node[above] {$T$};
2355 \end_layout
2356
2357 \begin_layout Plain Layout
2358
2359         }
2360 \end_layout
2361
2362 \begin_layout Plain Layout
2363
2364 \end_layout
2365
2366 \begin_layout Plain Layout
2367
2368
2369 \backslash
2370 end{scope}
2371 \end_layout
2372
2373 \begin_layout Plain Layout
2374
2375     % Draw gravity force.
2376  The code is put outside the rotated
2377 \end_layout
2378
2379 \begin_layout Plain Layout
2380
2381     % scope for simplicity.
2382  No need to do any angle calculations.
2383
2384 \end_layout
2385
2386 \begin_layout Plain Layout
2387
2388
2389 \backslash
2390 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2391 \end_layout
2392
2393 \begin_layout Plain Layout
2394
2395     %%
2396 \end_layout
2397
2398 \begin_layout Plain Layout
2399
2400 \end_layout
2401
2402 \begin_layout Plain Layout
2403
2404 &
2405 \end_layout
2406
2407 \begin_layout Plain Layout
2408
2409     %%%
2410 \end_layout
2411
2412 \begin_layout Plain Layout
2413
2414     % Free body diagram of m
2415 \end_layout
2416
2417 \begin_layout Plain Layout
2418
2419
2420 \backslash
2421 node[m] (m) {};
2422 \end_layout
2423
2424 \begin_layout Plain Layout
2425
2426
2427 \backslash
2428 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2429 \end_layout
2430
2431 \begin_layout Plain Layout
2432
2433     {[force,->]
2434 \end_layout
2435
2436 \begin_layout Plain Layout
2437
2438
2439 \backslash
2440 draw (m.north) -- ++(0,1) node[above] {$T'$};
2441 \end_layout
2442
2443 \begin_layout Plain Layout
2444
2445
2446 \backslash
2447 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2448 \end_layout
2449
2450 \begin_layout Plain Layout
2451
2452     }
2453 \end_layout
2454
2455 \begin_layout Plain Layout
2456
2457 \end_layout
2458
2459 \begin_layout Plain Layout
2460
2461
2462 \backslash
2463
2464 \backslash
2465
2466 \end_layout
2467
2468 \begin_layout Plain Layout
2469
2470 };
2471 \end_layout
2472
2473 \begin_layout Plain Layout
2474
2475
2476 \backslash
2477 end{tikzpicture}
2478 \end_layout
2479
2480 \begin_layout Plain Layout
2481
2482 \end_layout
2483
2484 \end_inset
2485
2486
2487 \end_layout
2488
2489 \end_inset
2490
2491
2492 \end_layout
2493
2494 \end_body
2495 \end_document