lib/examples/instant_preview.lyx

   1 #LyX 2.3 created this file. For more info see http://www.lyx.org/
   2 \lyxformat 541
   3 \begin_document
   4 \begin_header
   5 \save_transient_properties true
   6 \origin /systemlyxdir/examples/
   7 \textclass article
   8 \begin_preamble
   9 \usepackage{etex}
  10 \usepackage[all, knot]{xy}
  11 \xyoption{arc}
  12 \usepackage{qtree}
  13 \usepackage{tipa}
  14 \usepackage{pstricks}
  15 \usepackage{pst-plot}
  16 \usepackage{rotating}
  17 \usepackage{tikz}
  18 \usetikzlibrary{scopes}
  19 \end_preamble
  20 \use_default_options false
  21 \maintain_unincluded_children false
  22 \language english
  23 \language_package default
  24 \inputencoding auto
  25 \fontencoding global
  26 \font_roman "lmodern" "default"
  27 \font_sans "default" "default"
  28 \font_typewriter "default" "default"
  29 \font_math "auto" "auto"
  30 \font_default_family default
  31 \use_non_tex_fonts false
  32 \font_sc false
  33 \font_osf false
  34 \font_sf_scale 100 100
  35 \font_tt_scale 100 100
  36 \use_microtype false
  37 \use_dash_ligatures false
  38 \graphics default
  39 \default_output_format pdf
  40 \output_sync 0
  41 \bibtex_command default
  42 \index_command default
  43 \paperfontsize default
  44 \spacing single
  45 \use_hyperref false
  46 \papersize default
  47 \use_geometry false
  48 \use_package amsmath 1
  49 \use_package amssymb 1
  50 \use_package cancel 0
  51 \use_package esint 1
  52 \use_package mathdots 1
  53 \use_package mathtools 0
  54 \use_package mhchem 1
  55 \use_package stackrel 0
  56 \use_package stmaryrd 0
  57 \use_package undertilde 0
  58 \cite_engine basic
  59 \cite_engine_type default
  60 \biblio_style plain
  61 \use_bibtopic false
  62 \use_indices false
  63 \paperorientation portrait
  64 \suppress_date false
  65 \justification true
  66 \use_refstyle 0
  67 \index Index
  68 \shortcut idx
  69 \color #008000
  70 \end_index
  71 \secnumdepth 3
  72 \tocdepth 3
  73 \paragraph_separation indent
  74 \paragraph_indentation default
  75 \is_math_indent 0
  76 \quotes_style english
  77 \papercolumns 1
  78 \papersides 1
  79 \paperpagestyle default
  80 \tracking_changes false
  81 \output_changes false
  82 \html_math_output 0
  83 \html_css_as_file 0
  84 \html_be_strict true
  85 \end_header
  86
  87 \begin_body
  88
  89 \begin_layout Section
  90 Introduction
  91 \end_layout
  92
  93 \begin_layout Standard
  94 In order to properly typeset the document and have instant preview working,
  95  the following packages have to be installed:
  96 \end_layout
  97
  98 \begin_layout LyX-Code
  99 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf, etex
 100 \end_layout
 101
 102 \begin_layout Standard
 103 Due to the use of postscript specials in Section
 104 \begin_inset CommandInset ref
 105 LatexCommand ref
 106 reference "sec:PSTricks"
 107
 108 \end_inset
 109
 110 , only the Postscript or PDF (ps2pdf) output formats will correctly render
 111  the included images.
 112  However, the PDF (Xe\SpecialChar TeX
 113 ) output seems to also work, while trying to typeset
 114  the document with
 115 \family typewriter
 116 pdflatex
 117 \family default
 118  or
 119 \family typewriter
 120 pdflualatex
 121 \family default
 122  will generate errors.
 123 \end_layout
 124
 125 \begin_layout Section
 126 Diagrams by XY(-pic)
 127 \end_layout
 128
 129 \begin_layout Standard
 130 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
 131  examples, see
 132 \begin_inset Flex URL
 133 status collapsed
 134
 135 \begin_layout Plain Layout
 136
 137 https://www.ctan.org/tex-archive/macros/generic/diagrams/xypic/doc/xyguide.pdf
 138 \end_layout
 139
 140 \end_inset
 141
 142 .
 143 \end_layout
 144
 145 \begin_layout Description
 146 Braid
 147 \end_layout
 148
 149 \begin_layout Standard
 150 \begin_inset Preview
 151
 152 \begin_layout Standard
 153 \begin_inset ERT
 154 status collapsed
 155
 156 \begin_layout Plain Layout
 157
 158
 159 \backslash
 160 xy
 161 \end_layout
 162
 163 \begin_layout Plain Layout
 164
 165 (5,10)*{}; (-10,-10)*{} **
 166 \backslash
 167 crv{(6,-2)&(-12,4)}
 168 \end_layout
 169
 170 \begin_layout Plain Layout
 171
 172
 173 \backslash
 174 POS?(.25)*{
 175 \backslash
 176 hole}="x"
 177 \backslash
 178 POS?(.45)*{
 179 \backslash
 180 hole}="y"
 181 \backslash
 182 POS?(.6)*{
 183 \backslash
 184 hole}="z";
 185 \end_layout
 186
 187 \begin_layout Plain Layout
 188
 189 "y"+(0,-1); (2,-10)*{} **
 190 \backslash
 191 crv{}
 192 \backslash
 193 POS?(.2)*{
 194 \backslash
 195 hole}="M";
 196 \end_layout
 197
 198 \begin_layout Plain Layout
 199
 200 (-10,10)*{}; "z" **
 201 \backslash
 202 crv{(-9,0)};
 203 \end_layout
 204
 205 \begin_layout Plain Layout
 206
 207 "z"; "M" **
 208 \backslash
 209 crv{};
 210 \end_layout
 211
 212 \begin_layout Plain Layout
 213
 214 "M"; "x" **
 215 \backslash
 216 crv{(5,0)};
 217 \end_layout
 218
 219 \begin_layout Plain Layout
 220
 221 "x"; "y" **
 222 \backslash
 223 crv{(0,7) & (-5,6)};
 224 \end_layout
 225
 226 \begin_layout Plain Layout
 227
 228
 229 \backslash
 230 endxy
 231 \end_layout
 232
 233 \end_inset
 234
 235
 236 \end_layout
 237
 238 \end_inset
 239
 240
 241 \end_layout
 242
 243 \begin_layout Description
 244 Knots
 245 \end_layout
 246
 247 \begin_layout Standard
 248 \begin_inset Preview
 249
 250 \begin_layout Standard
 251 \begin_inset ERT
 252 status collapsed
 253
 254 \begin_layout Plain Layout
 255
 256
 257 \backslash
 258 xy
 259 \end_layout
 260
 261 \begin_layout Plain Layout
 262
 263 (6,9)*{}="1";
 264 \end_layout
 265
 266 \begin_layout Plain Layout
 267
 268 (-8.5,-1)*{}="2";
 269 \end_layout
 270
 271 \begin_layout Plain Layout
 272
 273 "1";"2" **
 274 \backslash
 275 crv{~*=<.5pt>{.} (0,30)}?(.75)*
 276 \backslash
 277 dir{>}+(-2,2)*{z};
 278 \end_layout
 279
 280 \begin_layout Plain Layout
 281
 282 (-6.5,8)*{}="1";
 283 \end_layout
 284
 285 \begin_layout Plain Layout
 286
 287 (-.5,-9)*{}="2";
 288 \end_layout
 289
 290 \begin_layout Plain Layout
 291
 292 "1";"2" **
 293 \backslash
 294 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
 295 \backslash
 296 dir{>}+(-2,-2)*{u};
 297 \end_layout
 298
 299 \begin_layout Plain Layout
 300
 301 (-9.5,-3.35)*{}="1";
 302 \end_layout
 303
 304 \begin_layout Plain Layout
 305
 306 (8.5,-3)*{}="2";
 307 \end_layout
 308
 309 \begin_layout Plain Layout
 310
 311 "1";"2" **
 312 \backslash
 313 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
 314 \backslash
 315 dir{>}+(-1,-3)*{x};
 316 \end_layout
 317
 318 \begin_layout Plain Layout
 319
 320 (1,-10)*{}="1";
 321 \end_layout
 322
 323 \begin_layout Plain Layout
 324
 325 (6.5,7.13)*{}="2";
 326 \end_layout
 327
 328 \begin_layout Plain Layout
 329
 330 "1";"2" **
 331 \backslash
 332 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
 333 \backslash
 334 dir{>}+(3,-1)*{y};
 335 \end_layout
 336
 337 \begin_layout Plain Layout
 338
 339 (11,-1)*{}="1";
 340 \end_layout
 341
 342 \begin_layout Plain Layout
 343
 344 (-4,8)*{}="2";
 345 \end_layout
 346
 347 \begin_layout Plain Layout
 348
 349 "1";"2" **
 350 \backslash
 351 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
 352 \backslash
 353 dir{>}+(1,2)*{w};
 354 \end_layout
 355
 356 \begin_layout Plain Layout
 357
 358
 359 \backslash
 360 endxy
 361 \end_layout
 362
 363 \end_inset
 364
 365
 366 \end_layout
 367
 368 \end_inset
 369
 370
 371 \end_layout
 372
 373 \begin_layout Description
 374 Circles
 375 \end_layout
 376
 377 \begin_layout Standard
 378 \begin_inset Preview
 379
 380 \begin_layout Standard
 381 \begin_inset ERT
 382 status collapsed
 383
 384 \begin_layout Plain Layout
 385
 386
 387 \backslash
 388 xy
 389 \end_layout
 390
 391 \begin_layout Plain Layout
 392
 393 (0,0)*
 394 \backslash
 395 xycircle(14,8){++
 396 \backslash
 397 dir{<}};
 398 \end_layout
 399
 400 \begin_layout Plain Layout
 401
 402 (0,0)*
 403 \backslash
 404 xycircle<10pt>{{.}};
 405 \end_layout
 406
 407 \begin_layout Plain Layout
 408
 409 (0,0)*
 410 \backslash
 411 xycircle(5,2){:};
 412 \end_layout
 413
 414 \begin_layout Plain Layout
 415
 416 (0,15)*
 417 \backslash
 418 xycircle(10,4){--};
 419 \end_layout
 420
 421 \begin_layout Plain Layout
 422
 423
 424 \backslash
 425 endxy
 426 \end_layout
 427
 428 \end_inset
 429
 430
 431 \end_layout
 432
 433 \end_inset
 434
 435
 436 \end_layout
 437
 438 \begin_layout Description
 439 Cobordism
 440 \end_layout
 441
 442 \begin_layout Standard
 443 \begin_inset Preview
 444
 445 \begin_layout Standard
 446 \begin_inset ERT
 447 status collapsed
 448
 449 \begin_layout Plain Layout
 450
 451
 452 \backslash
 453 xy
 454 \end_layout
 455
 456 \begin_layout Plain Layout
 457
 458 (0,0)*
 459 \backslash
 460 ellipse(3,1){.};
 461 \end_layout
 462
 463 \begin_layout Plain Layout
 464
 465 (0,0)*
 466 \backslash
 467 ellipse(3,1)__,=:a(-180){-};
 468 \end_layout
 469
 470 \begin_layout Plain Layout
 471
 472 (-6,-8)*
 473 \backslash
 474 ellipse(3,1){.};
 475 \end_layout
 476
 477 \begin_layout Plain Layout
 478
 479 (6,-8)*
 480 \backslash
 481 ellipse(3,1){.};
 482 \end_layout
 483
 484 \begin_layout Plain Layout
 485
 486 (0,-8)*
 487 \backslash
 488 ellipse(3,1){.};
 489 \end_layout
 490
 491 \begin_layout Plain Layout
 492
 493 (-6,-8)*
 494 \backslash
 495 ellipse(3,1)__,=:a(-180){-};
 496 \end_layout
 497
 498 \begin_layout Plain Layout
 499
 500 (6,-8)*
 501 \backslash
 502 ellipse(3,1)__,=:a(-180){-};
 503 \end_layout
 504
 505 \begin_layout Plain Layout
 506
 507 (0,-8)*
 508 \backslash
 509 ellipse(3,1)__,=:a(180){-};
 510 \end_layout
 511
 512 \begin_layout Plain Layout
 513
 514 (-3,6)*
 515 \backslash
 516 ellipse(3,1){-};
 517 \end_layout
 518
 519 \begin_layout Plain Layout
 520
 521 (3,6)*
 522 \backslash
 523 ellipse(3,1){-};
 524 \end_layout
 525
 526 \begin_layout Plain Layout
 527
 528 (-3,12)*{}="1";
 529 \end_layout
 530
 531 \begin_layout Plain Layout
 532
 533 (3,12)*{}="2";
 534 \end_layout
 535
 536 \begin_layout Plain Layout
 537
 538 (-9,12)*{}="A2";
 539 \end_layout
 540
 541 \begin_layout Plain Layout
 542
 543 (9,12)*{}="B2";
 544 \end_layout
 545
 546 \begin_layout Plain Layout
 547
 548 "1";"2" **
 549 \backslash
 550 crv{(-3,7) & (3,7)};
 551 \end_layout
 552
 553 \begin_layout Plain Layout
 554
 555 (-3,0)*{}="A";
 556 \end_layout
 557
 558 \begin_layout Plain Layout
 559
 560 (3,0)*{}="B";
 561 \end_layout
 562
 563 \begin_layout Plain Layout
 564
 565 (-3,1)*{}="A1";
 566 \end_layout
 567
 568 \begin_layout Plain Layout
 569
 570 (3,1)*{}="B1";
 571 \end_layout
 572
 573 \begin_layout Plain Layout
 574
 575 "A";"A1" **
 576 \backslash
 577 dir{-};
 578 \end_layout
 579
 580 \begin_layout Plain Layout
 581
 582 "B";"B1" **
 583 \backslash
 584 dir{-};
 585 \end_layout
 586
 587 \begin_layout Plain Layout
 588
 589 "B2";"B1" **
 590 \backslash
 591 crv{(8,7) & (3,5)};
 592 \end_layout
 593
 594 \begin_layout Plain Layout
 595
 596 "A2";"A1" **
 597 \backslash
 598 crv{(-8,7) & (-3,5)};
 599 \end_layout
 600
 601 \begin_layout Plain Layout
 602
 603 %REFLECT
 604 \end_layout
 605
 606 \begin_layout Plain Layout
 607
 608 (3,-16)*{}="1";
 609 \end_layout
 610
 611 \begin_layout Plain Layout
 612
 613 (9,-16)*{}="2";
 614 \end_layout
 615
 616 \begin_layout Plain Layout
 617
 618 "1";"2" **
 619 \backslash
 620 crv{(3,-10) & (9,-10)};
 621 \end_layout
 622
 623 \begin_layout Plain Layout
 624
 625 (-3,-16)*{}="1";
 626 \end_layout
 627
 628 \begin_layout Plain Layout
 629
 630 (-9,-16)*{}="2";
 631 \end_layout
 632
 633 \begin_layout Plain Layout
 634
 635 "1";"2" **
 636 \backslash
 637 crv{(-3,-10) & (-9,-10)};
 638 \end_layout
 639
 640 \begin_layout Plain Layout
 641
 642 (-15,-16)*{}="A2";
 643 \end_layout
 644
 645 \begin_layout Plain Layout
 646
 647 (15,-16)*{}="B2";
 648 \end_layout
 649
 650 \begin_layout Plain Layout
 651
 652 (-3,0)*{}="A";
 653 \end_layout
 654
 655 \begin_layout Plain Layout
 656
 657 (3,0)*{}="B";
 658 \end_layout
 659
 660 \begin_layout Plain Layout
 661
 662 (-3,-1)*{}="A1";
 663 \end_layout
 664
 665 \begin_layout Plain Layout
 666
 667 (3,-1)*{}="B1";
 668 \end_layout
 669
 670 \begin_layout Plain Layout
 671
 672 "A";"A1" **
 673 \backslash
 674 dir{-};
 675 \end_layout
 676
 677 \begin_layout Plain Layout
 678
 679 "B";"B1" **
 680 \backslash
 681 dir{-};
 682 \end_layout
 683
 684 \begin_layout Plain Layout
 685
 686 "B2";"B1" **
 687 \backslash
 688 crv{(13,-6) & (2,-8)};
 689 \end_layout
 690
 691 \begin_layout Plain Layout
 692
 693 "A2";"A1" **
 694 \backslash
 695 crv{(-13,-6) & (-2,-8)};
 696 \end_layout
 697
 698 \begin_layout Plain Layout
 699
 700
 701 \backslash
 702 endxy
 703 \end_layout
 704
 705 \end_inset
 706
 707
 708 \end_layout
 709
 710 \end_inset
 711
 712
 713 \begin_inset Preview
 714
 715 \begin_layout Standard
 716 \begin_inset ERT
 717 status collapsed
 718
 719 \begin_layout Plain Layout
 720
 721
 722 \backslash
 723 xy 0;/r.18pc/:
 724 \end_layout
 725
 726 \begin_layout Plain Layout
 727
 728 (20,2)*{
 729 \backslash
 730 bullet}="RU"+(1,3)*{x^{
 731 \backslash
 732 ast}};
 733 \end_layout
 734
 735 \begin_layout Plain Layout
 736
 737 (16,-3)*{
 738 \backslash
 739 bullet}="RD"+(2.5,2)*{x^{
 740 \backslash
 741 ast}};
 742 \end_layout
 743
 744 \begin_layout Plain Layout
 745
 746 (-16,2)*{
 747 \backslash
 748 bullet}="LU"+(-1,2)*{x};
 749 \end_layout
 750
 751 \begin_layout Plain Layout
 752
 753 (-20,-3)*{
 754 \backslash
 755 bullet}="LD"+(-1,2)*{x};
 756 \end_layout
 757
 758 \begin_layout Plain Layout
 759
 760 "RU";"RD" **
 761 \backslash
 762 crv{(4,2) & (4,-1)}; ?(.1)*
 763 \backslash
 764 dir{<}; ?(.85)*
 765 \backslash
 766 dir{<};
 767 \end_layout
 768
 769 \begin_layout Plain Layout
 770
 771 "LD";"LU" **
 772 \backslash
 773 crv{(-4,-2) & (-4,1)};
 774 \end_layout
 775
 776 \begin_layout Plain Layout
 777
 778 ?(.08)*
 779 \backslash
 780 dir{<}; ?(.85)*
 781 \backslash
 782 dir{<};
 783 \end_layout
 784
 785 \begin_layout Plain Layout
 786
 787 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
 788 \end_layout
 789
 790 \begin_layout Plain Layout
 791
 792 "x1"; "x2" **
 793 \backslash
 794 crv{(7,-10) & (-7,-10)};
 795 \end_layout
 796
 797 \begin_layout Plain Layout
 798
 799 (16,-20)*{
 800 \backslash
 801 bullet}="RDD"+(2.5,-1)*{x^{
 802 \backslash
 803 ast}};
 804 \end_layout
 805
 806 \begin_layout Plain Layout
 807
 808 (-20,-20)*{
 809 \backslash
 810 bullet}="LDD"+(-1,-3)*{x};
 811 \end_layout
 812
 813 \begin_layout Plain Layout
 814
 815 (20,-12.5)*{
 816 \backslash
 817 bullet}="RUD"+(3.5,1)*{x^{
 818 \backslash
 819 ast}};
 820 \end_layout
 821
 822 \begin_layout Plain Layout
 823
 824 (-16,-15)*{
 825 \backslash
 826 bullet}="LUD";
 827 \end_layout
 828
 829 \begin_layout Plain Layout
 830
 831 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
 832 \end_layout
 833
 834 \begin_layout Plain Layout
 835
 836 "RD"; "RDD" **
 837 \backslash
 838 dir{-};
 839 \end_layout
 840
 841 \begin_layout Plain Layout
 842
 843 "LD"; "LDD" **
 844 \backslash
 845 dir{-};
 846 \end_layout
 847
 848 \begin_layout Plain Layout
 849
 850 "A"; "LUD" **
 851 \backslash
 852 dir{.};
 853 \end_layout
 854
 855 \begin_layout Plain Layout
 856
 857 "RDD"; "LDD" **
 858 \backslash
 859 crv{(0,-17)}; ?(.57)*
 860 \backslash
 861 dir{>};
 862 \end_layout
 863
 864 \begin_layout Plain Layout
 865
 866 "RU"; "RUD" **
 867 \backslash
 868 dir{-};
 869 \end_layout
 870
 871 \begin_layout Plain Layout
 872
 873 "LU"; "A" **
 874 \backslash
 875 dir{-};
 876 \end_layout
 877
 878 \begin_layout Plain Layout
 879
 880 "B"; "RUD" **
 881 \backslash
 882 crv{(18,-14.15)};
 883 \end_layout
 884
 885 \begin_layout Plain Layout
 886
 887 "B"; "LUD" **
 888 \backslash
 889 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
 890 \backslash
 891 dir{<};
 892 \end_layout
 893
 894 \begin_layout Plain Layout
 895
 896
 897 \backslash
 898 endxy
 899 \end_layout
 900
 901 \end_inset
 902
 903
 904 \end_layout
 905
 906 \end_inset
 907
 908
 909 \end_layout
 910
 911 \begin_layout Description
 912 Strings
 913 \end_layout
 914
 915 \begin_layout Standard
 916 \begin_inset Preview
 917
 918 \begin_layout Standard
 919 \begin_inset ERT
 920 status open
 921
 922 \begin_layout Plain Layout
 923
 924
 925 \backslash
 926 xy (-15,0)*{};(15,0)*{};
 927 \end_layout
 928
 929 \begin_layout Plain Layout
 930
 931
 932 \backslash
 933 endxy
 934 \end_layout
 935
 936 \begin_layout Plain Layout
 937
 938
 939 \backslash
 940 qquad =
 941 \backslash
 942 qquad
 943 \backslash
 944 xy
 945 \end_layout
 946
 947 \begin_layout Plain Layout
 948
 949 (-10,12)*{}; (-10,-12)*{}; **
 950 \backslash
 951 dir{-}?(.5)*
 952 \backslash
 953 dir{<}+(-4,0)*{F(x)};
 954 \end_layout
 955
 956 \begin_layout Plain Layout
 957
 958 (-2,12)*{}="1";
 959 \end_layout
 960
 961 \begin_layout Plain Layout
 962
 963 (6,-7) *{}="2";
 964 \end_layout
 965
 966 \begin_layout Plain Layout
 967
 968 (14,-7) *{}="3";
 969 \end_layout
 970
 971 \begin_layout Plain Layout
 972
 973 (14,-13)*{}="3'";
 974 \end_layout
 975
 976 \begin_layout Plain Layout
 977
 978 (18,0) *={}="";
 979 \end_layout
 980
 981 \begin_layout Plain Layout
 982
 983 "1";"2" **
 984 \backslash
 985 crv{(-4,-21)&(5,-15)};
 986 \end_layout
 987
 988 \begin_layout Plain Layout
 989
 990 ?(.15)*
 991 \backslash
 992 dir{<}+(5,10)*{
 993 \backslash
 994 overline{F(x)}};
 995 \end_layout
 996
 997 \begin_layout Plain Layout
 998
 999 "2";"3" **
1000 \backslash
1001 crv{(6,1)&(14,1)};
1002 \end_layout
1003
1004 \begin_layout Plain Layout
1005
1006 ?(0)*
1007 \backslash
1008 dir{<}+(4,8)*{
1009 \backslash
1010 widetilde{F(i_x)}} ;
1011 \end_layout
1012
1013 \begin_layout Plain Layout
1014
1015 ?(.95)*
1016 \backslash
1017 dir{<}+(5,-2)*{F(
1018 \backslash
1019 overline x)};
1020 \end_layout
1021
1022 \begin_layout Plain Layout
1023
1024 "3";"3'" **
1025 \backslash
1026 dir{-};
1027 \end_layout
1028
1029 \begin_layout Plain Layout
1030
1031 (-2,6)*{}="X1";
1032 \end_layout
1033
1034 \begin_layout Plain Layout
1035
1036 (-10,6)*{}="X2";
1037 \end_layout
1038
1039 \begin_layout Plain Layout
1040
1041 "X1";"X2" **
1042 \backslash
1043 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1044 \end_layout
1045
1046 \begin_layout Plain Layout
1047
1048 (-2,-6)*{}="XA";
1049 \end_layout
1050
1051 \begin_layout Plain Layout
1052
1053 (-10,-6)*{}="XB";
1054 \end_layout
1055
1056 \begin_layout Plain Layout
1057
1058 "XA";"XB" **
1059 \backslash
1060 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1061 \end_layout
1062
1063 \begin_layout Plain Layout
1064
1065
1066 \backslash
1067 endxy
1068 \end_layout
1069
1070 \end_inset
1071
1072
1073 \end_layout
1074
1075 \end_inset
1076
1077
1078 \end_layout
1079
1080 \begin_layout Description
1081 Categories
1082 \end_layout
1083
1084 \begin_layout Standard
1085 \begin_inset Preview
1086
1087 \begin_layout Standard
1088 \begin_inset ERT
1089 status collapsed
1090
1091 \begin_layout Plain Layout
1092
1093
1094 \backslash
1095 xymatrix{
1096 \end_layout
1097
1098 \begin_layout Plain Layout
1099
1100 (x
1101 \backslash
1102 otimes 1)
1103 \backslash
1104 otimes y
1105 \end_layout
1106
1107 \begin_layout Plain Layout
1108
1109
1110 \backslash
1111 ar[rr]^{a_{x,1,y}}
1112 \end_layout
1113
1114 \begin_layout Plain Layout
1115
1116
1117 \backslash
1118 ar[dr]_{r_x
1119 \backslash
1120 otimes 1_y}
1121 \end_layout
1122
1123 \begin_layout Plain Layout
1124
1125 && x
1126 \backslash
1127 otimes(1
1128 \backslash
1129 otimes y)
1130 \end_layout
1131
1132 \begin_layout Plain Layout
1133
1134
1135 \backslash
1136 ar[dl]^{1_x
1137 \backslash
1138 otimes
1139 \backslash
1140 ell_y }
1141 \backslash
1142
1143 \backslash
1144
1145 \end_layout
1146
1147 \begin_layout Plain Layout
1148
1149 & x
1150 \backslash
1151 otimes y }
1152 \end_layout
1153
1154 \end_inset
1155
1156
1157 \end_layout
1158
1159 \end_inset
1160
1161
1162 \begin_inset Preview
1163
1164 \begin_layout Standard
1165 \begin_inset ERT
1166 status collapsed
1167
1168 \begin_layout Plain Layout
1169
1170
1171 \backslash
1172 xy
1173 \end_layout
1174
1175 \begin_layout Plain Layout
1176
1177 (-9,0)*+{
1178 \backslash
1179 bullet}="1";
1180 \end_layout
1181
1182 \begin_layout Plain Layout
1183
1184 (0,0)*+{
1185 \backslash
1186 bullet}="2";
1187 \end_layout
1188
1189 \begin_layout Plain Layout
1190
1191 {
1192 \backslash
1193 ar@/^.9pc/ "1";"2"};
1194 \end_layout
1195
1196 \begin_layout Plain Layout
1197
1198 {
1199 \backslash
1200 ar@/_.9pc/ "1";"2"};
1201 \end_layout
1202
1203 \begin_layout Plain Layout
1204
1205 {
1206 \backslash
1207 ar@/^2pc/ "1";"2"};
1208 \end_layout
1209
1210 \begin_layout Plain Layout
1211
1212 {
1213 \backslash
1214 ar@/_2pc/ "1";"2"};
1215 \end_layout
1216
1217 \begin_layout Plain Layout
1218
1219 {
1220 \backslash
1221 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1222 \end_layout
1223
1224 \begin_layout Plain Layout
1225
1226 {
1227 \backslash
1228 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1229 \end_layout
1230
1231 \begin_layout Plain Layout
1232
1233 {
1234 \backslash
1235 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1236 \end_layout
1237
1238 \begin_layout Plain Layout
1239
1240 (0,0)*+{
1241 \backslash
1242 bullet}="1";
1243 \end_layout
1244
1245 \begin_layout Plain Layout
1246
1247 (9,0)*+{
1248 \backslash
1249 bullet}="2";
1250 \end_layout
1251
1252 \begin_layout Plain Layout
1253
1254 (18,0)*+{
1255 \backslash
1256 bullet}="3";
1257 \end_layout
1258
1259 \begin_layout Plain Layout
1260
1261 {
1262 \backslash
1263 ar "1";"2"};
1264 \end_layout
1265
1266 \begin_layout Plain Layout
1267
1268 {
1269 \backslash
1270 ar "2";"3"};
1271 \end_layout
1272
1273 \begin_layout Plain Layout
1274
1275 {
1276 \backslash
1277 ar@/^1pc/ "1";"2"};
1278 \end_layout
1279
1280 \begin_layout Plain Layout
1281
1282 {
1283 \backslash
1284 ar@/_1pc/ "1";"2"};
1285 \end_layout
1286
1287 \begin_layout Plain Layout
1288
1289 {
1290 \backslash
1291 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1292 \end_layout
1293
1294 \begin_layout Plain Layout
1295
1296 {
1297 \backslash
1298 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1299 \end_layout
1300
1301 \begin_layout Plain Layout
1302
1303
1304 \backslash
1305 endxy
1306 \end_layout
1307
1308 \end_inset
1309
1310
1311 \end_layout
1312
1313 \end_inset
1314
1315
1316 \end_layout
1317
1318 \begin_layout Description
1319 Transformations
1320 \end_layout
1321
1322 \begin_layout Standard
1323 \begin_inset Preview
1324
1325 \begin_layout Standard
1326 \begin_inset ERT
1327 status collapsed
1328
1329 \begin_layout Plain Layout
1330
1331
1332 \backslash
1333 xy %FIG.19.
1334  Natural transformation between functors.
1335 \end_layout
1336
1337 \begin_layout Plain Layout
1338
1339 (-26,-2)*+{
1340 \backslash
1341 bullet}="a";
1342 \end_layout
1343
1344 \begin_layout Plain Layout
1345
1346 (-12,3)*+{
1347 \backslash
1348 bullet}="b";
1349 \end_layout
1350
1351 \begin_layout Plain Layout
1352
1353 (-16,-5)*+{
1354 \backslash
1355 bullet}="c";
1356 \end_layout
1357
1358 \begin_layout Plain Layout
1359
1360 {
1361 \backslash
1362 ar@/^.25pc/ "a";"b"};
1363 \end_layout
1364
1365 \begin_layout Plain Layout
1366
1367 {
1368 \backslash
1369 ar@/_.25pc/"a";"c"};
1370 \end_layout
1371
1372 \begin_layout Plain Layout
1373
1374 {
1375 \backslash
1376 ar@/_.15pc/ "b";"c"};
1377 \end_layout
1378
1379 \begin_layout Plain Layout
1380
1381 %START TOP
1382 \end_layout
1383
1384 \begin_layout Plain Layout
1385
1386 (12,10)*+{
1387 \backslash
1388 bullet}="ta";
1389 \end_layout
1390
1391 \begin_layout Plain Layout
1392
1393 (26,15)*+{
1394 \backslash
1395 bullet}="tb";
1396 \end_layout
1397
1398 \begin_layout Plain Layout
1399
1400 (22,8)*+{
1401 \backslash
1402 bullet}="tc";
1403 \end_layout
1404
1405 \begin_layout Plain Layout
1406
1407 {
1408 \backslash
1409 ar@/^.25pc/ "ta";"tb"};
1410 \end_layout
1411
1412 \begin_layout Plain Layout
1413
1414 {
1415 \backslash
1416 ar@/_.25pc/ "ta";"tc"};
1417 \end_layout
1418
1419 \begin_layout Plain Layout
1420
1421 {
1422 \backslash
1423 ar@/_.15pc/ "tb";"tc"};
1424 \end_layout
1425
1426 \begin_layout Plain Layout
1427
1428 %START bottom
1429 \end_layout
1430
1431 \begin_layout Plain Layout
1432
1433 (12,-10)*+{
1434 \backslash
1435 bullet}="ba";
1436 \end_layout
1437
1438 \begin_layout Plain Layout
1439
1440 (26,-5)*+{
1441 \backslash
1442 bullet}="bb";
1443 \end_layout
1444
1445 \begin_layout Plain Layout
1446
1447 (22,-12)*+{
1448 \backslash
1449 bullet}="bc";
1450 \end_layout
1451
1452 \begin_layout Plain Layout
1453
1454 {
1455 \backslash
1456 ar@/^.25pc/@{.>} "ba";"bb"};
1457 \end_layout
1458
1459 \begin_layout Plain Layout
1460
1461 {
1462 \backslash
1463 ar@/_.25pc/ "ba";"bc"};
1464 \end_layout
1465
1466 \begin_layout Plain Layout
1467
1468 {
1469 \backslash
1470 ar@/_.15pc/ "bb";"bc"};
1471 \end_layout
1472
1473 \begin_layout Plain Layout
1474
1475 %START CONNECT
1476 \end_layout
1477
1478 \begin_layout Plain Layout
1479
1480 {
1481 \backslash
1482 ar@/_.15pc/ "ta";"ba"};
1483 \end_layout
1484
1485 \begin_layout Plain Layout
1486
1487 {
1488 \backslash
1489 ar@/_.15pc/ "tb";"bb"};
1490 \end_layout
1491
1492 \begin_layout Plain Layout
1493
1494 {
1495 \backslash
1496 ar@/_.15pc/ "tc";"bc"};
1497 \end_layout
1498
1499 \begin_layout Plain Layout
1500
1501 %START ARROWS AND LABELS
1502 \end_layout
1503
1504 \begin_layout Plain Layout
1505
1506 (-12,6)*{}="DF";
1507 \end_layout
1508
1509 \begin_layout Plain Layout
1510
1511 (6,10)*{}="CF";
1512 \end_layout
1513
1514 \begin_layout Plain Layout
1515
1516 {
1517 \backslash
1518 ar@/^.35pc/^F "DF";"CF"};
1519 \end_layout
1520
1521 \begin_layout Plain Layout
1522
1523 (-12,-6)*{}="DF";
1524 \end_layout
1525
1526 \begin_layout Plain Layout
1527
1528 (6,-10)*{}="CF";
1529 \end_layout
1530
1531 \begin_layout Plain Layout
1532
1533 {
1534 \backslash
1535 ar@/_.35pc/_G "DF";"CF"};
1536 \end_layout
1537
1538 \begin_layout Plain Layout
1539
1540 (-2,5)*{}="DF";
1541 \end_layout
1542
1543 \begin_layout Plain Layout
1544
1545 (-2,-5)*{}="CF";
1546 \end_layout
1547
1548 \begin_layout Plain Layout
1549
1550 {
1551 \backslash
1552 ar@{=>}^{
1553 \backslash
1554 alpha} "DF";"CF"};
1555 \end_layout
1556
1557 \begin_layout Plain Layout
1558
1559 (29,3)*{D};
1560 \end_layout
1561
1562 \begin_layout Plain Layout
1563
1564 (-23,3)*{C};
1565 \end_layout
1566
1567 \begin_layout Plain Layout
1568
1569
1570 \backslash
1571 endxy
1572 \end_layout
1573
1574 \end_inset
1575
1576
1577 \end_layout
1578
1579 \end_inset
1580
1581
1582 \end_layout
1583
1584 \begin_layout Section
1585 IPA
1586 \end_layout
1587
1588 \begin_layout Standard
1589 \begin_inset Preview
1590
1591 \begin_layout Standard
1592 \begin_inset ERT
1593 status collapsed
1594
1595 \begin_layout Plain Layout
1596
1597
1598 \backslash
1599 textipa{Ekspl@"neIS@n}
1600 \end_layout
1601
1602 \end_inset
1603
1604
1605 \end_layout
1606
1607 \end_inset
1608
1609
1610 \end_layout
1611
1612 \begin_layout Section
1613 QTree
1614 \end_layout
1615
1616 \begin_layout Standard
1617 \begin_inset Preview
1618
1619 \begin_layout Standard
1620 \begin_inset ERT
1621 status collapsed
1622
1623 \begin_layout Plain Layout
1624
1625
1626 \backslash
1627 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1628 \end_layout
1629
1630 \end_inset
1631
1632
1633 \end_layout
1634
1635 \end_inset
1636
1637
1638 \begin_inset Preview
1639
1640 \begin_layout Standard
1641 \begin_inset ERT
1642 status collapsed
1643
1644 \begin_layout Plain Layout
1645
1646
1647 \backslash
1648 Tree [.$
1649 \backslash
1650 sigma$ $
1651 \backslash
1652 mu$ $
1653 \backslash
1654 mu$ ]
1655 \end_layout
1656
1657 \end_inset
1658
1659
1660 \end_layout
1661
1662 \end_inset
1663
1664
1665 \end_layout
1666
1667 \begin_layout Section
1668 PSTricks
1669 \begin_inset CommandInset label
1670 LatexCommand label
1671 name "sec:PSTricks"
1672
1673 \end_inset
1674
1675
1676 \end_layout
1677
1678 \begin_layout Standard
1679 Some simple graphing examples.
1680 \end_layout
1681
1682 \begin_layout Subsection
1683 Function plotting
1684 \end_layout
1685
1686 \begin_layout Standard
1687 \begin_inset Preview
1688
1689 \begin_layout Standard
1690 \begin_inset ERT
1691 status open
1692
1693 \begin_layout Plain Layout
1694
1695
1696 \backslash
1697 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1698 \end_layout
1699
1700 \begin_layout Plain Layout
1701
1702
1703 \backslash
1704 psaxes{->}(0,0)(0,-3)(10,3)
1705 \end_layout
1706
1707 \begin_layout Plain Layout
1708
1709
1710 \backslash
1711 uput[-90](10,0){$x$}
1712 \backslash
1713 uput[0](0,3){$f(x)$}
1714 \end_layout
1715
1716 \begin_layout Plain Layout
1717
1718
1719 \backslash
1720 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1721 \end_layout
1722
1723 \begin_layout Plain Layout
1724
1725
1726 \backslash
1727 end{pspicture*}
1728 \end_layout
1729
1730 \end_inset
1731
1732
1733 \end_layout
1734
1735 \end_inset
1736
1737
1738 \end_layout
1739
1740 \begin_layout Subsection
1741 Inline data plotting
1742 \end_layout
1743
1744 \begin_layout Standard
1745 \align center
1746 \begin_inset Preview
1747
1748 \begin_layout Standard
1749 \align center
1750 \begin_inset ERT
1751 status open
1752
1753 \begin_layout Plain Layout
1754
1755
1756 \backslash
1757 begin{pspicture*}(-1.5,-1.5)(11,5)
1758 \end_layout
1759
1760 \begin_layout Plain Layout
1761
1762
1763 \backslash
1764 psaxes{->}(0,0)(0,0)(10,5)
1765 \end_layout
1766
1767 \begin_layout Plain Layout
1768
1769
1770 \backslash
1771 psset{linewidth=2.5pt}
1772 \end_layout
1773
1774 \begin_layout Plain Layout
1775
1776
1777 \backslash
1778 rput(5.0,-1.0){Speed [MPH]}
1779 \end_layout
1780
1781 \begin_layout Plain Layout
1782
1783
1784 \backslash
1785 rput(-1.0,1.0){
1786 \backslash
1787 begin{rotate}{90}Cost [Dollars]
1788 \backslash
1789 end{rotate}}
1790 \end_layout
1791
1792 \begin_layout Plain Layout
1793
1794
1795 \backslash
1796 savedata{
1797 \backslash
1798 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1799 \end_layout
1800
1801 \begin_layout Plain Layout
1802
1803
1804 \backslash
1805 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1806 \backslash
1807 mydata}
1808 \end_layout
1809
1810 \begin_layout Plain Layout
1811
1812
1813 \backslash
1814 end{pspicture*}
1815 \end_layout
1816
1817 \end_inset
1818
1819
1820 \end_layout
1821
1822 \end_inset
1823
1824
1825 \end_layout
1826
1827 \begin_layout Subsection
1828 Lissajous curves
1829 \end_layout
1830
1831 \begin_layout Standard
1832 \begin_inset Preview
1833
1834 \begin_layout Standard
1835 \begin_inset ERT
1836 status open
1837
1838 \begin_layout Plain Layout
1839
1840
1841 \backslash
1842 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1843 \end_layout
1844
1845 \begin_layout Plain Layout
1846
1847
1848 \backslash
1849 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1850  cos 100 t mul sin}
1851 \end_layout
1852
1853 \begin_layout Plain Layout
1854
1855
1856 \backslash
1857 end{pspicture*}
1858 \end_layout
1859
1860 \end_inset
1861
1862
1863 \end_layout
1864
1865 \end_inset
1866
1867
1868 \begin_inset space \hfill{}
1869 \end_inset
1870
1871
1872 \begin_inset Preview
1873
1874 \begin_layout Standard
1875 \begin_inset ERT
1876 status open
1877
1878 \begin_layout Plain Layout
1879
1880
1881 \backslash
1882 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1883 \end_layout
1884
1885 \begin_layout Plain Layout
1886
1887
1888 \backslash
1889 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1890  mul cos 100 t mul sin}
1891 \end_layout
1892
1893 \begin_layout Plain Layout
1894
1895
1896 \backslash
1897 end{pspicture*}
1898 \end_layout
1899
1900 \end_inset
1901
1902
1903 \end_layout
1904
1905 \end_inset
1906
1907
1908 \begin_inset space \hfill{}
1909 \end_inset
1910
1911
1912 \begin_inset Preview
1913
1914 \begin_layout Standard
1915 \begin_inset ERT
1916 status open
1917
1918 \begin_layout Plain Layout
1919
1920
1921 \backslash
1922 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1923 \end_layout
1924
1925 \begin_layout Plain Layout
1926
1927
1928 \backslash
1929 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1930  mul cos 200 t mul sin}
1931 \end_layout
1932
1933 \begin_layout Plain Layout
1934
1935
1936 \backslash
1937 end{pspicture*}
1938 \end_layout
1939
1940 \end_inset
1941
1942
1943 \end_layout
1944
1945 \end_inset
1946
1947
1948 \begin_inset space \hfill{}
1949 \end_inset
1950
1951
1952 \begin_inset Preview
1953
1954 \begin_layout Standard
1955 \begin_inset ERT
1956 status open
1957
1958 \begin_layout Plain Layout
1959
1960
1961 \backslash
1962 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1963 \end_layout
1964
1965 \begin_layout Plain Layout
1966
1967
1968 \backslash
1969 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1970  mul cos 200 t mul sin}
1971 \end_layout
1972
1973 \begin_layout Plain Layout
1974
1975
1976 \backslash
1977 end{pspicture*}
1978 \end_layout
1979
1980 \end_inset
1981
1982
1983 \end_layout
1984
1985 \end_inset
1986
1987
1988 \end_layout
1989
1990 \begin_layout Section
1991 TikZ
1992 \end_layout
1993
1994 \begin_layout Standard
1995 \begin_inset Flex URL
1996 status collapsed
1997
1998 \begin_layout Plain Layout
1999
2000 http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
2001 \end_layout
2002
2003 \end_inset
2004
2005
2006 \end_layout
2007
2008 \begin_layout Standard
2009 \begin_inset Preview
2010
2011 \begin_layout Standard
2012 \begin_inset ERT
2013 status collapsed
2014
2015 \begin_layout Plain Layout
2016
2017
2018 \backslash
2019 def
2020 \backslash
2021 iangle{35} % Angle of the inclined plane
2022 \end_layout
2023
2024 \begin_layout Plain Layout
2025
2026
2027 \backslash
2028 def
2029 \backslash
2030 down{-90}
2031 \end_layout
2032
2033 \begin_layout Plain Layout
2034
2035
2036 \backslash
2037 def
2038 \backslash
2039 arcr{0.5cm} % Radius of the arc used to indicate angles
2040 \end_layout
2041
2042 \begin_layout Plain Layout
2043
2044 \end_layout
2045
2046 \begin_layout Plain Layout
2047
2048
2049 \backslash
2050 begin{tikzpicture}[
2051 \end_layout
2052
2053 \begin_layout Plain Layout
2054
2055     force/.style={>=latex,draw=blue,fill=blue},
2056 \end_layout
2057
2058 \begin_layout Plain Layout
2059
2060     axis/.style={densely dashed,gray,font=
2061 \backslash
2062 small},
2063 \end_layout
2064
2065 \begin_layout Plain Layout
2066
2067     M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2068 \end_layout
2069
2070 \begin_layout Plain Layout
2071
2072     m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2073 \end_layout
2074
2075 \begin_layout Plain Layout
2076
2077     plane/.style={draw=black,fill=blue!10},
2078 \end_layout
2079
2080 \begin_layout Plain Layout
2081
2082     string/.style={draw=red, thick},
2083 \end_layout
2084
2085 \begin_layout Plain Layout
2086
2087     pulley/.style={thick},
2088 \end_layout
2089
2090 \begin_layout Plain Layout
2091
2092 ]
2093 \end_layout
2094
2095 \begin_layout Plain Layout
2096
2097 \end_layout
2098
2099 \begin_layout Plain Layout
2100
2101
2102 \backslash
2103 matrix[column sep=1cm] {
2104 \end_layout
2105
2106 \begin_layout Plain Layout
2107
2108     %% Sketch
2109 \end_layout
2110
2111 \begin_layout Plain Layout
2112
2113
2114 \backslash
2115 draw[plane] (0,-1) coordinate (base)
2116 \end_layout
2117
2118 \begin_layout Plain Layout
2119
2120                      -- coordinate[pos=0.5] (mid) ++(
2121 \backslash
2122 iangle:3) coordinate (top)
2123 \end_layout
2124
2125 \begin_layout Plain Layout
2126
2127                      |- (base) -- cycle;
2128 \end_layout
2129
2130 \begin_layout Plain Layout
2131
2132
2133 \backslash
2134 path (mid) node[M,rotate=
2135 \backslash
2136 iangle,yshift=0.25cm] (M) {};
2137 \end_layout
2138
2139 \begin_layout Plain Layout
2140
2141
2142 \backslash
2143 draw[pulley] (top) -- ++(
2144 \backslash
2145 iangle:0.25) circle (0.25cm)
2146 \end_layout
2147
2148 \begin_layout Plain Layout
2149
2150                    ++ (90-
2151 \backslash
2152 iangle:0.5) coordinate (pulley);
2153 \end_layout
2154
2155 \begin_layout Plain Layout
2156
2157
2158 \backslash
2159 draw[string] (M.east) -- ++(
2160 \backslash
2161 iangle:1.5cm) arc (90+
2162 \backslash
2163 iangle:0:0.25)
2164 \end_layout
2165
2166 \begin_layout Plain Layout
2167
2168                   -- ++(0,-1) node[m] {};
2169 \end_layout
2170
2171 \begin_layout Plain Layout
2172
2173 \end_layout
2174
2175 \begin_layout Plain Layout
2176
2177
2178 \backslash
2179 draw[->] (base)++(
2180 \backslash
2181 arcr,0) arc (0:
2182 \backslash
2183 iangle:
2184 \backslash
2185 arcr);
2186 \end_layout
2187
2188 \begin_layout Plain Layout
2189
2190
2191 \backslash
2192 path (base)++(
2193 \backslash
2194 iangle*0.5:
2195 \backslash
2196 arcr+5pt) node {$
2197 \backslash
2198 alpha$};
2199 \end_layout
2200
2201 \begin_layout Plain Layout
2202
2203     %%
2204 \end_layout
2205
2206 \begin_layout Plain Layout
2207
2208 \end_layout
2209
2210 \begin_layout Plain Layout
2211
2212 &
2213 \end_layout
2214
2215 \begin_layout Plain Layout
2216
2217     %% Free body diagram of M
2218 \end_layout
2219
2220 \begin_layout Plain Layout
2221
2222
2223 \backslash
2224 begin{scope}[rotate=
2225 \backslash
2226 iangle]
2227 \end_layout
2228
2229 \begin_layout Plain Layout
2230
2231
2232 \backslash
2233 node[M,transform shape] (M) {};
2234 \end_layout
2235
2236 \begin_layout Plain Layout
2237
2238         % Draw axes and help lines
2239 \end_layout
2240
2241 \begin_layout Plain Layout
2242
2243 \end_layout
2244
2245 \begin_layout Plain Layout
2246
2247         {[axis,->]
2248 \end_layout
2249
2250 \begin_layout Plain Layout
2251
2252
2253 \backslash
2254 draw (0,-1) -- (0,2) node[right] {$+y$};
2255 \end_layout
2256
2257 \begin_layout Plain Layout
2258
2259
2260 \backslash
2261 draw (M) -- ++(2,0) node[right] {$+x$};
2262 \end_layout
2263
2264 \begin_layout Plain Layout
2265
2266             % Indicate angle.
2267  The code is a bit awkward.
2268 \end_layout
2269
2270 \begin_layout Plain Layout
2271
2272 \end_layout
2273
2274 \begin_layout Plain Layout
2275
2276
2277 \backslash
2278 draw[solid,shorten >=0.5pt] (
2279 \backslash
2280 down-
2281 \backslash
2282 iangle:
2283 \backslash
2284 arcr)
2285 \end_layout
2286
2287 \begin_layout Plain Layout
2288
2289                 arc(
2290 \backslash
2291 down-
2292 \backslash
2293 iangle:
2294 \backslash
2295 down:
2296 \backslash
2297 arcr);
2298 \end_layout
2299
2300 \begin_layout Plain Layout
2301
2302
2303 \backslash
2304 node at (
2305 \backslash
2306 down-0.5*
2307 \backslash
2308 iangle:1.3*
2309 \backslash
2310 arcr) {$
2311 \backslash
2312 alpha$};
2313 \end_layout
2314
2315 \begin_layout Plain Layout
2316
2317         }
2318 \end_layout
2319
2320 \begin_layout Plain Layout
2321
2322 \end_layout
2323
2324 \begin_layout Plain Layout
2325
2326         % Forces
2327 \end_layout
2328
2329 \begin_layout Plain Layout
2330
2331         {[force,->]
2332 \end_layout
2333
2334 \begin_layout Plain Layout
2335
2336             % Assuming that Mg = 1.
2337  The normal force will therefore be cos(alpha)
2338 \end_layout
2339
2340 \begin_layout Plain Layout
2341
2342
2343 \backslash
2344 draw (M.center) -- ++(0,{cos(
2345 \backslash
2346 iangle)}) node[above right] {$N$};
2347 \end_layout
2348
2349 \begin_layout Plain Layout
2350
2351
2352 \backslash
2353 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2354 \end_layout
2355
2356 \begin_layout Plain Layout
2357
2358
2359 \backslash
2360 draw (M.east) -- ++(1,0) node[above] {$T$};
2361 \end_layout
2362
2363 \begin_layout Plain Layout
2364
2365         }
2366 \end_layout
2367
2368 \begin_layout Plain Layout
2369
2370 \end_layout
2371
2372 \begin_layout Plain Layout
2373
2374
2375 \backslash
2376 end{scope}
2377 \end_layout
2378
2379 \begin_layout Plain Layout
2380
2381     % Draw gravity force.
2382  The code is put outside the rotated
2383 \end_layout
2384
2385 \begin_layout Plain Layout
2386
2387     % scope for simplicity.
2388  No need to do any angle calculations.
2389
2390 \end_layout
2391
2392 \begin_layout Plain Layout
2393
2394
2395 \backslash
2396 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2397 \end_layout
2398
2399 \begin_layout Plain Layout
2400
2401     %%
2402 \end_layout
2403
2404 \begin_layout Plain Layout
2405
2406 \end_layout
2407
2408 \begin_layout Plain Layout
2409
2410 &
2411 \end_layout
2412
2413 \begin_layout Plain Layout
2414
2415     %%%
2416 \end_layout
2417
2418 \begin_layout Plain Layout
2419
2420     % Free body diagram of m
2421 \end_layout
2422
2423 \begin_layout Plain Layout
2424
2425
2426 \backslash
2427 node[m] (m) {};
2428 \end_layout
2429
2430 \begin_layout Plain Layout
2431
2432
2433 \backslash
2434 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2435 \end_layout
2436
2437 \begin_layout Plain Layout
2438
2439     {[force,->]
2440 \end_layout
2441
2442 \begin_layout Plain Layout
2443
2444
2445 \backslash
2446 draw (m.north) -- ++(0,1) node[above] {$T'$};
2447 \end_layout
2448
2449 \begin_layout Plain Layout
2450
2451
2452 \backslash
2453 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2454 \end_layout
2455
2456 \begin_layout Plain Layout
2457
2458     }
2459 \end_layout
2460
2461 \begin_layout Plain Layout
2462
2463 \end_layout
2464
2465 \begin_layout Plain Layout
2466
2467
2468 \backslash
2469
2470 \backslash
2471
2472 \end_layout
2473
2474 \begin_layout Plain Layout
2475
2476 };
2477 \end_layout
2478
2479 \begin_layout Plain Layout
2480
2481
2482 \backslash
2483 end{tikzpicture}
2484 \end_layout
2485
2486 \begin_layout Plain Layout
2487
2488 \end_layout
2489
2490 \end_inset
2491
2492
2493 \end_layout
2494
2495 \end_inset
2496
2497
2498 \end_layout
2499
2500 \end_body
2501 \end_document