lib/examples/Graphics_and_Insets/Instant_Preview.lyx

   1 #LyX 2.4 created this file. For more info see https://www.lyx.org/
   2 \lyxformat 600
   3 \begin_document
   4 \begin_header
   5 \save_transient_properties true
   6 \origin /systemlyxdir/examples/Graphics_and_Insets/
   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 no
  22 \language english
  23 \language_package default
  24 \inputencoding utf8
  25 \fontencoding auto
  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_sans_osf false
  34 \font_typewriter_osf false
  35 \font_roman_osf false
  36 \font_sf_scale 100 100
  37 \font_tt_scale 100 100
  38 \use_microtype false
  39 \use_dash_ligatures false
  40 \graphics default
  41 \default_output_format pdf
  42 \output_sync 0
  43 \bibtex_command default
  44 \index_command default
  45 \paperfontsize default
  46 \spacing single
  47 \use_hyperref false
  48 \papersize default
  49 \use_geometry false
  50 \use_package amsmath 1
  51 \use_package amssymb 1
  52 \use_package cancel 1
  53 \use_package esint 1
  54 \use_package mathdots 1
  55 \use_package mathtools 1
  56 \use_package mhchem 1
  57 \use_package stackrel 1
  58 \use_package stmaryrd 1
  59 \use_package undertilde 1
  60 \cite_engine basic
  61 \cite_engine_type default
  62 \biblio_style plain
  63 \use_bibtopic false
  64 \use_indices false
  65 \paperorientation portrait
  66 \suppress_date false
  67 \justification true
  68 \use_refstyle 0
  69 \use_minted 0
  70 \use_lineno 0
  71 \index Index
  72 \shortcut idx
  73 \color #008000
  74 \end_index
  75 \secnumdepth 3
  76 \tocdepth 3
  77 \paragraph_separation indent
  78 \paragraph_indentation default
  79 \is_math_indent 0
  80 \math_numbering_side default
  81 \quotes_style english
  82 \dynamic_quotes 0
  83 \papercolumns 1
  84 \papersides 1
  85 \paperpagestyle default
  86 \tracking_changes false
  87 \postpone_fragile_content false
  88 \output_changes false
  89 \html_math_output 0
  90 \html_css_as_file 0
  91 \html_be_strict true
  92 \end_header
  93
  94 \begin_body
  95
  96 \begin_layout Section
  97 Introduction
  98 \end_layout
  99
 100 \begin_layout Standard
 101 In order to properly typeset the document and have instant preview working,
 102  the following packages have to be installed:
 103 \end_layout
 104
 105 \begin_layout LyX-Code
 106 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf, etex
 107 \end_layout
 108
 109 \begin_layout Standard
 110 Due to the use of postscript specials in Section
 111 \begin_inset CommandInset ref
 112 LatexCommand ref
 113 reference "sec:PSTricks"
 114
 115 \end_inset
 116
 117 , only the Postscript or PDF (ps2pdf) output formats will correctly render
 118  the included images.
 119  Starting with TeX Live 2021, you may need to add the flag
 120 \family typewriter
 121 -dALLOWPSTRANSPARENCY
 122 \family default
 123  to the
 124 \family typewriter
 125 ps2pdf
 126 \family default
 127  converter.
 128  The PDF (Xe\SpecialChar TeX
 129 ) output seems to also work, while trying to typeset the document
 130  with
 131 \family typewriter
 132 pdflatex
 133 \family default
 134  or
 135 \family typewriter
 136 pdflualatex
 137 \family default
 138  will generate errors.
 139 \end_layout
 140
 141 \begin_layout Section
 142 Diagrams by XY(-pic)
 143 \end_layout
 144
 145 \begin_layout Standard
 146 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
 147  examples, see
 148 \begin_inset Flex URL
 149 status collapsed
 150
 151 \begin_layout Plain Layout
 152
 153 https://www.ctan.org/tex-archive/macros/generic/diagrams/xypic/doc/xyguide.pdf
 154 \end_layout
 155
 156 \end_inset
 157
 158 .
 159 \end_layout
 160
 161 \begin_layout Description
 162 Braid
 163 \end_layout
 164
 165 \begin_layout Standard
 166 \begin_inset Preview
 167
 168 \begin_layout Standard
 169 \begin_inset ERT
 170 status collapsed
 171
 172 \begin_layout Plain Layout
 173
 174
 175 \backslash
 176 xy
 177 \end_layout
 178
 179 \begin_layout Plain Layout
 180
 181 (5,10)*{}; (-10,-10)*{} **
 182 \backslash
 183 crv{(6,-2)&(-12,4)}
 184 \end_layout
 185
 186 \begin_layout Plain Layout
 187
 188
 189 \backslash
 190 POS?(.25)*{
 191 \backslash
 192 hole}="x"
 193 \backslash
 194 POS?(.45)*{
 195 \backslash
 196 hole}="y"
 197 \backslash
 198 POS?(.6)*{
 199 \backslash
 200 hole}="z";
 201 \end_layout
 202
 203 \begin_layout Plain Layout
 204
 205 "y"+(0,-1); (2,-10)*{} **
 206 \backslash
 207 crv{}
 208 \backslash
 209 POS?(.2)*{
 210 \backslash
 211 hole}="M";
 212 \end_layout
 213
 214 \begin_layout Plain Layout
 215
 216 (-10,10)*{}; "z" **
 217 \backslash
 218 crv{(-9,0)};
 219 \end_layout
 220
 221 \begin_layout Plain Layout
 222
 223 "z"; "M" **
 224 \backslash
 225 crv{};
 226 \end_layout
 227
 228 \begin_layout Plain Layout
 229
 230 "M"; "x" **
 231 \backslash
 232 crv{(5,0)};
 233 \end_layout
 234
 235 \begin_layout Plain Layout
 236
 237 "x"; "y" **
 238 \backslash
 239 crv{(0,7) & (-5,6)};
 240 \end_layout
 241
 242 \begin_layout Plain Layout
 243
 244
 245 \backslash
 246 endxy
 247 \end_layout
 248
 249 \end_inset
 250
 251
 252 \end_layout
 253
 254 \end_inset
 255
 256
 257 \end_layout
 258
 259 \begin_layout Description
 260 Knots
 261 \end_layout
 262
 263 \begin_layout Standard
 264 \begin_inset Preview
 265
 266 \begin_layout Standard
 267 \begin_inset ERT
 268 status collapsed
 269
 270 \begin_layout Plain Layout
 271
 272
 273 \backslash
 274 xy
 275 \end_layout
 276
 277 \begin_layout Plain Layout
 278
 279 (6,9)*{}="1";
 280 \end_layout
 281
 282 \begin_layout Plain Layout
 283
 284 (-8.5,-1)*{}="2";
 285 \end_layout
 286
 287 \begin_layout Plain Layout
 288
 289 "1";"2" **
 290 \backslash
 291 crv{~*=<.5pt>{.} (0,30)}?(.75)*
 292 \backslash
 293 dir{>}+(-2,2)*{z};
 294 \end_layout
 295
 296 \begin_layout Plain Layout
 297
 298 (-6.5,8)*{}="1";
 299 \end_layout
 300
 301 \begin_layout Plain Layout
 302
 303 (-.5,-9)*{}="2";
 304 \end_layout
 305
 306 \begin_layout Plain Layout
 307
 308 "1";"2" **
 309 \backslash
 310 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
 311 \backslash
 312 dir{>}+(-2,-2)*{u};
 313 \end_layout
 314
 315 \begin_layout Plain Layout
 316
 317 (-9.5,-3.35)*{}="1";
 318 \end_layout
 319
 320 \begin_layout Plain Layout
 321
 322 (8.5,-3)*{}="2";
 323 \end_layout
 324
 325 \begin_layout Plain Layout
 326
 327 "1";"2" **
 328 \backslash
 329 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
 330 \backslash
 331 dir{>}+(-1,-3)*{x};
 332 \end_layout
 333
 334 \begin_layout Plain Layout
 335
 336 (1,-10)*{}="1";
 337 \end_layout
 338
 339 \begin_layout Plain Layout
 340
 341 (6.5,7.13)*{}="2";
 342 \end_layout
 343
 344 \begin_layout Plain Layout
 345
 346 "1";"2" **
 347 \backslash
 348 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
 349 \backslash
 350 dir{>}+(3,-1)*{y};
 351 \end_layout
 352
 353 \begin_layout Plain Layout
 354
 355 (11,-1)*{}="1";
 356 \end_layout
 357
 358 \begin_layout Plain Layout
 359
 360 (-4,8)*{}="2";
 361 \end_layout
 362
 363 \begin_layout Plain Layout
 364
 365 "1";"2" **
 366 \backslash
 367 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
 368 \backslash
 369 dir{>}+(1,2)*{w};
 370 \end_layout
 371
 372 \begin_layout Plain Layout
 373
 374
 375 \backslash
 376 endxy
 377 \end_layout
 378
 379 \end_inset
 380
 381
 382 \end_layout
 383
 384 \end_inset
 385
 386
 387 \end_layout
 388
 389 \begin_layout Description
 390 Circles
 391 \end_layout
 392
 393 \begin_layout Standard
 394 \begin_inset Preview
 395
 396 \begin_layout Standard
 397 \begin_inset ERT
 398 status collapsed
 399
 400 \begin_layout Plain Layout
 401
 402
 403 \backslash
 404 xy
 405 \end_layout
 406
 407 \begin_layout Plain Layout
 408
 409 (0,0)*
 410 \backslash
 411 xycircle(14,8){++
 412 \backslash
 413 dir{<}};
 414 \end_layout
 415
 416 \begin_layout Plain Layout
 417
 418 (0,0)*
 419 \backslash
 420 xycircle<10pt>{{.}};
 421 \end_layout
 422
 423 \begin_layout Plain Layout
 424
 425 (0,0)*
 426 \backslash
 427 xycircle(5,2){:};
 428 \end_layout
 429
 430 \begin_layout Plain Layout
 431
 432 (0,15)*
 433 \backslash
 434 xycircle(10,4){--};
 435 \end_layout
 436
 437 \begin_layout Plain Layout
 438
 439
 440 \backslash
 441 endxy
 442 \end_layout
 443
 444 \end_inset
 445
 446
 447 \end_layout
 448
 449 \end_inset
 450
 451
 452 \end_layout
 453
 454 \begin_layout Description
 455 Cobordism
 456 \end_layout
 457
 458 \begin_layout Standard
 459 \begin_inset Preview
 460
 461 \begin_layout Standard
 462 \begin_inset ERT
 463 status collapsed
 464
 465 \begin_layout Plain Layout
 466
 467
 468 \backslash
 469 xy
 470 \end_layout
 471
 472 \begin_layout Plain Layout
 473
 474 (0,0)*
 475 \backslash
 476 ellipse(3,1){.};
 477 \end_layout
 478
 479 \begin_layout Plain Layout
 480
 481 (0,0)*
 482 \backslash
 483 ellipse(3,1)__,=:a(-180){-};
 484 \end_layout
 485
 486 \begin_layout Plain Layout
 487
 488 (-6,-8)*
 489 \backslash
 490 ellipse(3,1){.};
 491 \end_layout
 492
 493 \begin_layout Plain Layout
 494
 495 (6,-8)*
 496 \backslash
 497 ellipse(3,1){.};
 498 \end_layout
 499
 500 \begin_layout Plain Layout
 501
 502 (0,-8)*
 503 \backslash
 504 ellipse(3,1){.};
 505 \end_layout
 506
 507 \begin_layout Plain Layout
 508
 509 (-6,-8)*
 510 \backslash
 511 ellipse(3,1)__,=:a(-180){-};
 512 \end_layout
 513
 514 \begin_layout Plain Layout
 515
 516 (6,-8)*
 517 \backslash
 518 ellipse(3,1)__,=:a(-180){-};
 519 \end_layout
 520
 521 \begin_layout Plain Layout
 522
 523 (0,-8)*
 524 \backslash
 525 ellipse(3,1)__,=:a(180){-};
 526 \end_layout
 527
 528 \begin_layout Plain Layout
 529
 530 (-3,6)*
 531 \backslash
 532 ellipse(3,1){-};
 533 \end_layout
 534
 535 \begin_layout Plain Layout
 536
 537 (3,6)*
 538 \backslash
 539 ellipse(3,1){-};
 540 \end_layout
 541
 542 \begin_layout Plain Layout
 543
 544 (-3,12)*{}="1";
 545 \end_layout
 546
 547 \begin_layout Plain Layout
 548
 549 (3,12)*{}="2";
 550 \end_layout
 551
 552 \begin_layout Plain Layout
 553
 554 (-9,12)*{}="A2";
 555 \end_layout
 556
 557 \begin_layout Plain Layout
 558
 559 (9,12)*{}="B2";
 560 \end_layout
 561
 562 \begin_layout Plain Layout
 563
 564 "1";"2" **
 565 \backslash
 566 crv{(-3,7) & (3,7)};
 567 \end_layout
 568
 569 \begin_layout Plain Layout
 570
 571 (-3,0)*{}="A";
 572 \end_layout
 573
 574 \begin_layout Plain Layout
 575
 576 (3,0)*{}="B";
 577 \end_layout
 578
 579 \begin_layout Plain Layout
 580
 581 (-3,1)*{}="A1";
 582 \end_layout
 583
 584 \begin_layout Plain Layout
 585
 586 (3,1)*{}="B1";
 587 \end_layout
 588
 589 \begin_layout Plain Layout
 590
 591 "A";"A1" **
 592 \backslash
 593 dir{-};
 594 \end_layout
 595
 596 \begin_layout Plain Layout
 597
 598 "B";"B1" **
 599 \backslash
 600 dir{-};
 601 \end_layout
 602
 603 \begin_layout Plain Layout
 604
 605 "B2";"B1" **
 606 \backslash
 607 crv{(8,7) & (3,5)};
 608 \end_layout
 609
 610 \begin_layout Plain Layout
 611
 612 "A2";"A1" **
 613 \backslash
 614 crv{(-8,7) & (-3,5)};
 615 \end_layout
 616
 617 \begin_layout Plain Layout
 618
 619 %REFLECT
 620 \end_layout
 621
 622 \begin_layout Plain Layout
 623
 624 (3,-16)*{}="1";
 625 \end_layout
 626
 627 \begin_layout Plain Layout
 628
 629 (9,-16)*{}="2";
 630 \end_layout
 631
 632 \begin_layout Plain Layout
 633
 634 "1";"2" **
 635 \backslash
 636 crv{(3,-10) & (9,-10)};
 637 \end_layout
 638
 639 \begin_layout Plain Layout
 640
 641 (-3,-16)*{}="1";
 642 \end_layout
 643
 644 \begin_layout Plain Layout
 645
 646 (-9,-16)*{}="2";
 647 \end_layout
 648
 649 \begin_layout Plain Layout
 650
 651 "1";"2" **
 652 \backslash
 653 crv{(-3,-10) & (-9,-10)};
 654 \end_layout
 655
 656 \begin_layout Plain Layout
 657
 658 (-15,-16)*{}="A2";
 659 \end_layout
 660
 661 \begin_layout Plain Layout
 662
 663 (15,-16)*{}="B2";
 664 \end_layout
 665
 666 \begin_layout Plain Layout
 667
 668 (-3,0)*{}="A";
 669 \end_layout
 670
 671 \begin_layout Plain Layout
 672
 673 (3,0)*{}="B";
 674 \end_layout
 675
 676 \begin_layout Plain Layout
 677
 678 (-3,-1)*{}="A1";
 679 \end_layout
 680
 681 \begin_layout Plain Layout
 682
 683 (3,-1)*{}="B1";
 684 \end_layout
 685
 686 \begin_layout Plain Layout
 687
 688 "A";"A1" **
 689 \backslash
 690 dir{-};
 691 \end_layout
 692
 693 \begin_layout Plain Layout
 694
 695 "B";"B1" **
 696 \backslash
 697 dir{-};
 698 \end_layout
 699
 700 \begin_layout Plain Layout
 701
 702 "B2";"B1" **
 703 \backslash
 704 crv{(13,-6) & (2,-8)};
 705 \end_layout
 706
 707 \begin_layout Plain Layout
 708
 709 "A2";"A1" **
 710 \backslash
 711 crv{(-13,-6) & (-2,-8)};
 712 \end_layout
 713
 714 \begin_layout Plain Layout
 715
 716
 717 \backslash
 718 endxy
 719 \end_layout
 720
 721 \end_inset
 722
 723
 724 \end_layout
 725
 726 \end_inset
 727
 728
 729 \begin_inset Preview
 730
 731 \begin_layout Standard
 732 \begin_inset ERT
 733 status collapsed
 734
 735 \begin_layout Plain Layout
 736
 737
 738 \backslash
 739 xy 0;/r.18pc/:
 740 \end_layout
 741
 742 \begin_layout Plain Layout
 743
 744 (20,2)*{
 745 \backslash
 746 bullet}="RU"+(1,3)*{x^{
 747 \backslash
 748 ast}};
 749 \end_layout
 750
 751 \begin_layout Plain Layout
 752
 753 (16,-3)*{
 754 \backslash
 755 bullet}="RD"+(2.5,2)*{x^{
 756 \backslash
 757 ast}};
 758 \end_layout
 759
 760 \begin_layout Plain Layout
 761
 762 (-16,2)*{
 763 \backslash
 764 bullet}="LU"+(-1,2)*{x};
 765 \end_layout
 766
 767 \begin_layout Plain Layout
 768
 769 (-20,-3)*{
 770 \backslash
 771 bullet}="LD"+(-1,2)*{x};
 772 \end_layout
 773
 774 \begin_layout Plain Layout
 775
 776 "RU";"RD" **
 777 \backslash
 778 crv{(4,2) & (4,-1)}; ?(.1)*
 779 \backslash
 780 dir{<}; ?(.85)*
 781 \backslash
 782 dir{<};
 783 \end_layout
 784
 785 \begin_layout Plain Layout
 786
 787 "LD";"LU" **
 788 \backslash
 789 crv{(-4,-2) & (-4,1)};
 790 \end_layout
 791
 792 \begin_layout Plain Layout
 793
 794 ?(.08)*
 795 \backslash
 796 dir{<}; ?(.85)*
 797 \backslash
 798 dir{<};
 799 \end_layout
 800
 801 \begin_layout Plain Layout
 802
 803 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
 804 \end_layout
 805
 806 \begin_layout Plain Layout
 807
 808 "x1"; "x2" **
 809 \backslash
 810 crv{(7,-10) & (-7,-10)};
 811 \end_layout
 812
 813 \begin_layout Plain Layout
 814
 815 (16,-20)*{
 816 \backslash
 817 bullet}="RDD"+(2.5,-1)*{x^{
 818 \backslash
 819 ast}};
 820 \end_layout
 821
 822 \begin_layout Plain Layout
 823
 824 (-20,-20)*{
 825 \backslash
 826 bullet}="LDD"+(-1,-3)*{x};
 827 \end_layout
 828
 829 \begin_layout Plain Layout
 830
 831 (20,-12.5)*{
 832 \backslash
 833 bullet}="RUD"+(3.5,1)*{x^{
 834 \backslash
 835 ast}};
 836 \end_layout
 837
 838 \begin_layout Plain Layout
 839
 840 (-16,-15)*{
 841 \backslash
 842 bullet}="LUD";
 843 \end_layout
 844
 845 \begin_layout Plain Layout
 846
 847 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
 848 \end_layout
 849
 850 \begin_layout Plain Layout
 851
 852 "RD"; "RDD" **
 853 \backslash
 854 dir{-};
 855 \end_layout
 856
 857 \begin_layout Plain Layout
 858
 859 "LD"; "LDD" **
 860 \backslash
 861 dir{-};
 862 \end_layout
 863
 864 \begin_layout Plain Layout
 865
 866 "A"; "LUD" **
 867 \backslash
 868 dir{.};
 869 \end_layout
 870
 871 \begin_layout Plain Layout
 872
 873 "RDD"; "LDD" **
 874 \backslash
 875 crv{(0,-17)}; ?(.57)*
 876 \backslash
 877 dir{>};
 878 \end_layout
 879
 880 \begin_layout Plain Layout
 881
 882 "RU"; "RUD" **
 883 \backslash
 884 dir{-};
 885 \end_layout
 886
 887 \begin_layout Plain Layout
 888
 889 "LU"; "A" **
 890 \backslash
 891 dir{-};
 892 \end_layout
 893
 894 \begin_layout Plain Layout
 895
 896 "B"; "RUD" **
 897 \backslash
 898 crv{(18,-14.15)};
 899 \end_layout
 900
 901 \begin_layout Plain Layout
 902
 903 "B"; "LUD" **
 904 \backslash
 905 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
 906 \backslash
 907 dir{<};
 908 \end_layout
 909
 910 \begin_layout Plain Layout
 911
 912
 913 \backslash
 914 endxy
 915 \end_layout
 916
 917 \end_inset
 918
 919
 920 \end_layout
 921
 922 \end_inset
 923
 924
 925 \end_layout
 926
 927 \begin_layout Description
 928 Strings
 929 \end_layout
 930
 931 \begin_layout Standard
 932 \begin_inset Preview
 933
 934 \begin_layout Standard
 935 \begin_inset ERT
 936 status open
 937
 938 \begin_layout Plain Layout
 939
 940
 941 \backslash
 942 xy (-15,0)*{};(15,0)*{};
 943 \end_layout
 944
 945 \begin_layout Plain Layout
 946
 947
 948 \backslash
 949 endxy
 950 \end_layout
 951
 952 \begin_layout Plain Layout
 953
 954
 955 \backslash
 956 qquad =
 957 \backslash
 958 qquad
 959 \backslash
 960 xy
 961 \end_layout
 962
 963 \begin_layout Plain Layout
 964
 965 (-10,12)*{}; (-10,-12)*{}; **
 966 \backslash
 967 dir{-}?(.5)*
 968 \backslash
 969 dir{<}+(-4,0)*{F(x)};
 970 \end_layout
 971
 972 \begin_layout Plain Layout
 973
 974 (-2,12)*{}="1";
 975 \end_layout
 976
 977 \begin_layout Plain Layout
 978
 979 (6,-7) *{}="2";
 980 \end_layout
 981
 982 \begin_layout Plain Layout
 983
 984 (14,-7) *{}="3";
 985 \end_layout
 986
 987 \begin_layout Plain Layout
 988
 989 (14,-13)*{}="3'";
 990 \end_layout
 991
 992 \begin_layout Plain Layout
 993
 994 (18,0) *={}="";
 995 \end_layout
 996
 997 \begin_layout Plain Layout
 998
 999 "1";"2" **
1000 \backslash
1001 crv{(-4,-21)&(5,-15)};
1002 \end_layout
1003
1004 \begin_layout Plain Layout
1005
1006 ?(.15)*
1007 \backslash
1008 dir{<}+(5,10)*{
1009 \backslash
1010 overline{F(x)}};
1011 \end_layout
1012
1013 \begin_layout Plain Layout
1014
1015 "2";"3" **
1016 \backslash
1017 crv{(6,1)&(14,1)};
1018 \end_layout
1019
1020 \begin_layout Plain Layout
1021
1022 ?(0)*
1023 \backslash
1024 dir{<}+(4,8)*{
1025 \backslash
1026 widetilde{F(i_x)}} ;
1027 \end_layout
1028
1029 \begin_layout Plain Layout
1030
1031 ?(.95)*
1032 \backslash
1033 dir{<}+(5,-2)*{F(
1034 \backslash
1035 overline x)};
1036 \end_layout
1037
1038 \begin_layout Plain Layout
1039
1040 "3";"3'" **
1041 \backslash
1042 dir{-};
1043 \end_layout
1044
1045 \begin_layout Plain Layout
1046
1047 (-2,6)*{}="X1";
1048 \end_layout
1049
1050 \begin_layout Plain Layout
1051
1052 (-10,6)*{}="X2";
1053 \end_layout
1054
1055 \begin_layout Plain Layout
1056
1057 "X1";"X2" **
1058 \backslash
1059 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1060 \end_layout
1061
1062 \begin_layout Plain Layout
1063
1064 (-2,-6)*{}="XA";
1065 \end_layout
1066
1067 \begin_layout Plain Layout
1068
1069 (-10,-6)*{}="XB";
1070 \end_layout
1071
1072 \begin_layout Plain Layout
1073
1074 "XA";"XB" **
1075 \backslash
1076 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1077 \end_layout
1078
1079 \begin_layout Plain Layout
1080
1081
1082 \backslash
1083 endxy
1084 \end_layout
1085
1086 \end_inset
1087
1088
1089 \end_layout
1090
1091 \end_inset
1092
1093
1094 \end_layout
1095
1096 \begin_layout Description
1097 Categories
1098 \end_layout
1099
1100 \begin_layout Standard
1101 \begin_inset Preview
1102
1103 \begin_layout Standard
1104 \begin_inset ERT
1105 status collapsed
1106
1107 \begin_layout Plain Layout
1108
1109
1110 \backslash
1111 xymatrix{
1112 \end_layout
1113
1114 \begin_layout Plain Layout
1115
1116 (x
1117 \backslash
1118 otimes 1)
1119 \backslash
1120 otimes y
1121 \end_layout
1122
1123 \begin_layout Plain Layout
1124
1125
1126 \backslash
1127 ar[rr]^{a_{x,1,y}}
1128 \end_layout
1129
1130 \begin_layout Plain Layout
1131
1132
1133 \backslash
1134 ar[dr]_{r_x
1135 \backslash
1136 otimes 1_y}
1137 \end_layout
1138
1139 \begin_layout Plain Layout
1140
1141 && x
1142 \backslash
1143 otimes(1
1144 \backslash
1145 otimes y)
1146 \end_layout
1147
1148 \begin_layout Plain Layout
1149
1150
1151 \backslash
1152 ar[dl]^{1_x
1153 \backslash
1154 otimes
1155 \backslash
1156 ell_y }
1157 \backslash
1158
1159 \backslash
1160
1161 \end_layout
1162
1163 \begin_layout Plain Layout
1164
1165 & x
1166 \backslash
1167 otimes y }
1168 \end_layout
1169
1170 \end_inset
1171
1172
1173 \end_layout
1174
1175 \end_inset
1176
1177
1178 \begin_inset Preview
1179
1180 \begin_layout Standard
1181 \begin_inset ERT
1182 status collapsed
1183
1184 \begin_layout Plain Layout
1185
1186
1187 \backslash
1188 xy
1189 \end_layout
1190
1191 \begin_layout Plain Layout
1192
1193 (-9,0)*+{
1194 \backslash
1195 bullet}="1";
1196 \end_layout
1197
1198 \begin_layout Plain Layout
1199
1200 (0,0)*+{
1201 \backslash
1202 bullet}="2";
1203 \end_layout
1204
1205 \begin_layout Plain Layout
1206
1207 {
1208 \backslash
1209 ar@/^.9pc/ "1";"2"};
1210 \end_layout
1211
1212 \begin_layout Plain Layout
1213
1214 {
1215 \backslash
1216 ar@/_.9pc/ "1";"2"};
1217 \end_layout
1218
1219 \begin_layout Plain Layout
1220
1221 {
1222 \backslash
1223 ar@/^2pc/ "1";"2"};
1224 \end_layout
1225
1226 \begin_layout Plain Layout
1227
1228 {
1229 \backslash
1230 ar@/_2pc/ "1";"2"};
1231 \end_layout
1232
1233 \begin_layout Plain Layout
1234
1235 {
1236 \backslash
1237 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1238 \end_layout
1239
1240 \begin_layout Plain Layout
1241
1242 {
1243 \backslash
1244 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1245 \end_layout
1246
1247 \begin_layout Plain Layout
1248
1249 {
1250 \backslash
1251 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1252 \end_layout
1253
1254 \begin_layout Plain Layout
1255
1256 (0,0)*+{
1257 \backslash
1258 bullet}="1";
1259 \end_layout
1260
1261 \begin_layout Plain Layout
1262
1263 (9,0)*+{
1264 \backslash
1265 bullet}="2";
1266 \end_layout
1267
1268 \begin_layout Plain Layout
1269
1270 (18,0)*+{
1271 \backslash
1272 bullet}="3";
1273 \end_layout
1274
1275 \begin_layout Plain Layout
1276
1277 {
1278 \backslash
1279 ar "1";"2"};
1280 \end_layout
1281
1282 \begin_layout Plain Layout
1283
1284 {
1285 \backslash
1286 ar "2";"3"};
1287 \end_layout
1288
1289 \begin_layout Plain Layout
1290
1291 {
1292 \backslash
1293 ar@/^1pc/ "1";"2"};
1294 \end_layout
1295
1296 \begin_layout Plain Layout
1297
1298 {
1299 \backslash
1300 ar@/_1pc/ "1";"2"};
1301 \end_layout
1302
1303 \begin_layout Plain Layout
1304
1305 {
1306 \backslash
1307 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1308 \end_layout
1309
1310 \begin_layout Plain Layout
1311
1312 {
1313 \backslash
1314 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1315 \end_layout
1316
1317 \begin_layout Plain Layout
1318
1319
1320 \backslash
1321 endxy
1322 \end_layout
1323
1324 \end_inset
1325
1326
1327 \end_layout
1328
1329 \end_inset
1330
1331
1332 \end_layout
1333
1334 \begin_layout Description
1335 Transformations
1336 \end_layout
1337
1338 \begin_layout Standard
1339 \begin_inset Preview
1340
1341 \begin_layout Standard
1342 \begin_inset ERT
1343 status collapsed
1344
1345 \begin_layout Plain Layout
1346
1347
1348 \backslash
1349 xy %FIG.19.
1350  Natural transformation between functors.
1351 \end_layout
1352
1353 \begin_layout Plain Layout
1354
1355 (-26,-2)*+{
1356 \backslash
1357 bullet}="a";
1358 \end_layout
1359
1360 \begin_layout Plain Layout
1361
1362 (-12,3)*+{
1363 \backslash
1364 bullet}="b";
1365 \end_layout
1366
1367 \begin_layout Plain Layout
1368
1369 (-16,-5)*+{
1370 \backslash
1371 bullet}="c";
1372 \end_layout
1373
1374 \begin_layout Plain Layout
1375
1376 {
1377 \backslash
1378 ar@/^.25pc/ "a";"b"};
1379 \end_layout
1380
1381 \begin_layout Plain Layout
1382
1383 {
1384 \backslash
1385 ar@/_.25pc/"a";"c"};
1386 \end_layout
1387
1388 \begin_layout Plain Layout
1389
1390 {
1391 \backslash
1392 ar@/_.15pc/ "b";"c"};
1393 \end_layout
1394
1395 \begin_layout Plain Layout
1396
1397 %START TOP
1398 \end_layout
1399
1400 \begin_layout Plain Layout
1401
1402 (12,10)*+{
1403 \backslash
1404 bullet}="ta";
1405 \end_layout
1406
1407 \begin_layout Plain Layout
1408
1409 (26,15)*+{
1410 \backslash
1411 bullet}="tb";
1412 \end_layout
1413
1414 \begin_layout Plain Layout
1415
1416 (22,8)*+{
1417 \backslash
1418 bullet}="tc";
1419 \end_layout
1420
1421 \begin_layout Plain Layout
1422
1423 {
1424 \backslash
1425 ar@/^.25pc/ "ta";"tb"};
1426 \end_layout
1427
1428 \begin_layout Plain Layout
1429
1430 {
1431 \backslash
1432 ar@/_.25pc/ "ta";"tc"};
1433 \end_layout
1434
1435 \begin_layout Plain Layout
1436
1437 {
1438 \backslash
1439 ar@/_.15pc/ "tb";"tc"};
1440 \end_layout
1441
1442 \begin_layout Plain Layout
1443
1444 %START bottom
1445 \end_layout
1446
1447 \begin_layout Plain Layout
1448
1449 (12,-10)*+{
1450 \backslash
1451 bullet}="ba";
1452 \end_layout
1453
1454 \begin_layout Plain Layout
1455
1456 (26,-5)*+{
1457 \backslash
1458 bullet}="bb";
1459 \end_layout
1460
1461 \begin_layout Plain Layout
1462
1463 (22,-12)*+{
1464 \backslash
1465 bullet}="bc";
1466 \end_layout
1467
1468 \begin_layout Plain Layout
1469
1470 {
1471 \backslash
1472 ar@/^.25pc/@{.>} "ba";"bb"};
1473 \end_layout
1474
1475 \begin_layout Plain Layout
1476
1477 {
1478 \backslash
1479 ar@/_.25pc/ "ba";"bc"};
1480 \end_layout
1481
1482 \begin_layout Plain Layout
1483
1484 {
1485 \backslash
1486 ar@/_.15pc/ "bb";"bc"};
1487 \end_layout
1488
1489 \begin_layout Plain Layout
1490
1491 %START CONNECT
1492 \end_layout
1493
1494 \begin_layout Plain Layout
1495
1496 {
1497 \backslash
1498 ar@/_.15pc/ "ta";"ba"};
1499 \end_layout
1500
1501 \begin_layout Plain Layout
1502
1503 {
1504 \backslash
1505 ar@/_.15pc/ "tb";"bb"};
1506 \end_layout
1507
1508 \begin_layout Plain Layout
1509
1510 {
1511 \backslash
1512 ar@/_.15pc/ "tc";"bc"};
1513 \end_layout
1514
1515 \begin_layout Plain Layout
1516
1517 %START ARROWS AND LABELS
1518 \end_layout
1519
1520 \begin_layout Plain Layout
1521
1522 (-12,6)*{}="DF";
1523 \end_layout
1524
1525 \begin_layout Plain Layout
1526
1527 (6,10)*{}="CF";
1528 \end_layout
1529
1530 \begin_layout Plain Layout
1531
1532 {
1533 \backslash
1534 ar@/^.35pc/^F "DF";"CF"};
1535 \end_layout
1536
1537 \begin_layout Plain Layout
1538
1539 (-12,-6)*{}="DF";
1540 \end_layout
1541
1542 \begin_layout Plain Layout
1543
1544 (6,-10)*{}="CF";
1545 \end_layout
1546
1547 \begin_layout Plain Layout
1548
1549 {
1550 \backslash
1551 ar@/_.35pc/_G "DF";"CF"};
1552 \end_layout
1553
1554 \begin_layout Plain Layout
1555
1556 (-2,5)*{}="DF";
1557 \end_layout
1558
1559 \begin_layout Plain Layout
1560
1561 (-2,-5)*{}="CF";
1562 \end_layout
1563
1564 \begin_layout Plain Layout
1565
1566 {
1567 \backslash
1568 ar@{=>}^{
1569 \backslash
1570 alpha} "DF";"CF"};
1571 \end_layout
1572
1573 \begin_layout Plain Layout
1574
1575 (29,3)*{D};
1576 \end_layout
1577
1578 \begin_layout Plain Layout
1579
1580 (-23,3)*{C};
1581 \end_layout
1582
1583 \begin_layout Plain Layout
1584
1585
1586 \backslash
1587 endxy
1588 \end_layout
1589
1590 \end_inset
1591
1592
1593 \end_layout
1594
1595 \end_inset
1596
1597
1598 \end_layout
1599
1600 \begin_layout Section
1601 IPA
1602 \end_layout
1603
1604 \begin_layout Standard
1605 \begin_inset Preview
1606
1607 \begin_layout Standard
1608 \begin_inset ERT
1609 status collapsed
1610
1611 \begin_layout Plain Layout
1612
1613
1614 \backslash
1615 textipa{Ekspl@"neIS@n}
1616 \end_layout
1617
1618 \end_inset
1619
1620
1621 \end_layout
1622
1623 \end_inset
1624
1625
1626 \end_layout
1627
1628 \begin_layout Section
1629 QTree
1630 \end_layout
1631
1632 \begin_layout Standard
1633 \begin_inset Preview
1634
1635 \begin_layout Standard
1636 \begin_inset ERT
1637 status collapsed
1638
1639 \begin_layout Plain Layout
1640
1641
1642 \backslash
1643 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1644 \end_layout
1645
1646 \end_inset
1647
1648
1649 \end_layout
1650
1651 \end_inset
1652
1653
1654 \begin_inset Preview
1655
1656 \begin_layout Standard
1657 \begin_inset ERT
1658 status collapsed
1659
1660 \begin_layout Plain Layout
1661
1662
1663 \backslash
1664 Tree [.$
1665 \backslash
1666 sigma$ $
1667 \backslash
1668 mu$ $
1669 \backslash
1670 mu$ ]
1671 \end_layout
1672
1673 \end_inset
1674
1675
1676 \end_layout
1677
1678 \end_inset
1679
1680
1681 \end_layout
1682
1683 \begin_layout Section
1684 PSTricks
1685 \begin_inset CommandInset label
1686 LatexCommand label
1687 name "sec:PSTricks"
1688
1689 \end_inset
1690
1691
1692 \end_layout
1693
1694 \begin_layout Standard
1695 Some simple graphing examples.
1696 \end_layout
1697
1698 \begin_layout Subsection
1699 Function plotting
1700 \end_layout
1701
1702 \begin_layout Standard
1703 \begin_inset Preview
1704
1705 \begin_layout Standard
1706 \begin_inset ERT
1707 status open
1708
1709 \begin_layout Plain Layout
1710
1711
1712 \backslash
1713 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1714 \end_layout
1715
1716 \begin_layout Plain Layout
1717
1718
1719 \backslash
1720 psaxes{->}(0,0)(0,-3)(10,3)
1721 \end_layout
1722
1723 \begin_layout Plain Layout
1724
1725
1726 \backslash
1727 uput[-90](10,0){$x$}
1728 \backslash
1729 uput[0](0,3){$f(x)$}
1730 \end_layout
1731
1732 \begin_layout Plain Layout
1733
1734
1735 \backslash
1736 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1737 \end_layout
1738
1739 \begin_layout Plain Layout
1740
1741
1742 \backslash
1743 end{pspicture*}
1744 \end_layout
1745
1746 \end_inset
1747
1748
1749 \end_layout
1750
1751 \end_inset
1752
1753
1754 \end_layout
1755
1756 \begin_layout Subsection
1757 Inline data plotting
1758 \end_layout
1759
1760 \begin_layout Standard
1761 \align center
1762 \begin_inset Preview
1763
1764 \begin_layout Standard
1765 \align center
1766 \begin_inset ERT
1767 status open
1768
1769 \begin_layout Plain Layout
1770
1771
1772 \backslash
1773 begin{pspicture*}(-1.5,-1.5)(11,5)
1774 \end_layout
1775
1776 \begin_layout Plain Layout
1777
1778
1779 \backslash
1780 psaxes{->}(0,0)(0,0)(10,5)
1781 \end_layout
1782
1783 \begin_layout Plain Layout
1784
1785
1786 \backslash
1787 psset{linewidth=2.5pt}
1788 \end_layout
1789
1790 \begin_layout Plain Layout
1791
1792
1793 \backslash
1794 rput(5.0,-1.0){Speed [MPH]}
1795 \end_layout
1796
1797 \begin_layout Plain Layout
1798
1799
1800 \backslash
1801 rput(-1.0,1.0){
1802 \backslash
1803 begin{rotate}{90}Cost [Dollars]
1804 \backslash
1805 end{rotate}}
1806 \end_layout
1807
1808 \begin_layout Plain Layout
1809
1810
1811 \backslash
1812 savedata{
1813 \backslash
1814 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1815 \end_layout
1816
1817 \begin_layout Plain Layout
1818
1819
1820 \backslash
1821 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1822 \backslash
1823 mydata}
1824 \end_layout
1825
1826 \begin_layout Plain Layout
1827
1828
1829 \backslash
1830 end{pspicture*}
1831 \end_layout
1832
1833 \end_inset
1834
1835
1836 \end_layout
1837
1838 \end_inset
1839
1840
1841 \end_layout
1842
1843 \begin_layout Subsection
1844 Lissajous curves
1845 \end_layout
1846
1847 \begin_layout Standard
1848 \begin_inset Preview
1849
1850 \begin_layout Standard
1851 \begin_inset ERT
1852 status open
1853
1854 \begin_layout Plain Layout
1855
1856
1857 \backslash
1858 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1859 \end_layout
1860
1861 \begin_layout Plain Layout
1862
1863
1864 \backslash
1865 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1866  cos 100 t mul sin}
1867 \end_layout
1868
1869 \begin_layout Plain Layout
1870
1871
1872 \backslash
1873 end{pspicture*}
1874 \end_layout
1875
1876 \end_inset
1877
1878
1879 \end_layout
1880
1881 \end_inset
1882
1883
1884 \begin_inset space \hfill{}
1885 \end_inset
1886
1887
1888 \begin_inset Preview
1889
1890 \begin_layout Standard
1891 \begin_inset ERT
1892 status open
1893
1894 \begin_layout Plain Layout
1895
1896
1897 \backslash
1898 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1899 \end_layout
1900
1901 \begin_layout Plain Layout
1902
1903
1904 \backslash
1905 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1906  mul cos 100 t mul sin}
1907 \end_layout
1908
1909 \begin_layout Plain Layout
1910
1911
1912 \backslash
1913 end{pspicture*}
1914 \end_layout
1915
1916 \end_inset
1917
1918
1919 \end_layout
1920
1921 \end_inset
1922
1923
1924 \begin_inset space \hfill{}
1925 \end_inset
1926
1927
1928 \begin_inset Preview
1929
1930 \begin_layout Standard
1931 \begin_inset ERT
1932 status open
1933
1934 \begin_layout Plain Layout
1935
1936
1937 \backslash
1938 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1939 \end_layout
1940
1941 \begin_layout Plain Layout
1942
1943
1944 \backslash
1945 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1946  mul cos 200 t mul sin}
1947 \end_layout
1948
1949 \begin_layout Plain Layout
1950
1951
1952 \backslash
1953 end{pspicture*}
1954 \end_layout
1955
1956 \end_inset
1957
1958
1959 \end_layout
1960
1961 \end_inset
1962
1963
1964 \begin_inset space \hfill{}
1965 \end_inset
1966
1967
1968 \begin_inset Preview
1969
1970 \begin_layout Standard
1971 \begin_inset ERT
1972 status open
1973
1974 \begin_layout Plain Layout
1975
1976
1977 \backslash
1978 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1979 \end_layout
1980
1981 \begin_layout Plain Layout
1982
1983
1984 \backslash
1985 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1986  mul cos 200 t mul sin}
1987 \end_layout
1988
1989 \begin_layout Plain Layout
1990
1991
1992 \backslash
1993 end{pspicture*}
1994 \end_layout
1995
1996 \end_inset
1997
1998
1999 \end_layout
2000
2001 \end_inset
2002
2003
2004 \end_layout
2005
2006 \begin_layout Section
2007 TikZ
2008 \end_layout
2009
2010 \begin_layout Standard
2011 \begin_inset Flex URL
2012 status collapsed
2013
2014 \begin_layout Plain Layout
2015
2016 http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
2017 \end_layout
2018
2019 \end_inset
2020
2021
2022 \end_layout
2023
2024 \begin_layout Standard
2025 \begin_inset Preview
2026
2027 \begin_layout Standard
2028 \begin_inset ERT
2029 status collapsed
2030
2031 \begin_layout Plain Layout
2032
2033
2034 \backslash
2035 def
2036 \backslash
2037 iangle{35} % Angle of the inclined plane
2038 \end_layout
2039
2040 \begin_layout Plain Layout
2041
2042
2043 \backslash
2044 def
2045 \backslash
2046 down{-90}
2047 \end_layout
2048
2049 \begin_layout Plain Layout
2050
2051
2052 \backslash
2053 def
2054 \backslash
2055 arcr{0.5cm} % Radius of the arc used to indicate angles
2056 \end_layout
2057
2058 \begin_layout Plain Layout
2059
2060 \end_layout
2061
2062 \begin_layout Plain Layout
2063
2064
2065 \backslash
2066 begin{tikzpicture}[
2067 \end_layout
2068
2069 \begin_layout Plain Layout
2070
2071     force/.style={>=latex,draw=blue,fill=blue},
2072 \end_layout
2073
2074 \begin_layout Plain Layout
2075
2076     axis/.style={densely dashed,gray,font=
2077 \backslash
2078 small},
2079 \end_layout
2080
2081 \begin_layout Plain Layout
2082
2083     M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2084 \end_layout
2085
2086 \begin_layout Plain Layout
2087
2088     m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2089 \end_layout
2090
2091 \begin_layout Plain Layout
2092
2093     plane/.style={draw=black,fill=blue!10},
2094 \end_layout
2095
2096 \begin_layout Plain Layout
2097
2098     string/.style={draw=red, thick},
2099 \end_layout
2100
2101 \begin_layout Plain Layout
2102
2103     pulley/.style={thick},
2104 \end_layout
2105
2106 \begin_layout Plain Layout
2107
2108 ]
2109 \end_layout
2110
2111 \begin_layout Plain Layout
2112
2113 \end_layout
2114
2115 \begin_layout Plain Layout
2116
2117
2118 \backslash
2119 matrix[column sep=1cm] {
2120 \end_layout
2121
2122 \begin_layout Plain Layout
2123
2124     %% Sketch
2125 \end_layout
2126
2127 \begin_layout Plain Layout
2128
2129
2130 \backslash
2131 draw[plane] (0,-1) coordinate (base)
2132 \end_layout
2133
2134 \begin_layout Plain Layout
2135
2136                      -- coordinate[pos=0.5] (mid) ++(
2137 \backslash
2138 iangle:3) coordinate (top)
2139 \end_layout
2140
2141 \begin_layout Plain Layout
2142
2143                      |- (base) -- cycle;
2144 \end_layout
2145
2146 \begin_layout Plain Layout
2147
2148
2149 \backslash
2150 path (mid) node[M,rotate=
2151 \backslash
2152 iangle,yshift=0.25cm] (M) {};
2153 \end_layout
2154
2155 \begin_layout Plain Layout
2156
2157
2158 \backslash
2159 draw[pulley] (top) -- ++(
2160 \backslash
2161 iangle:0.25) circle (0.25cm)
2162 \end_layout
2163
2164 \begin_layout Plain Layout
2165
2166                    ++ (90-
2167 \backslash
2168 iangle:0.5) coordinate (pulley);
2169 \end_layout
2170
2171 \begin_layout Plain Layout
2172
2173
2174 \backslash
2175 draw[string] (M.east) -- ++(
2176 \backslash
2177 iangle:1.5cm) arc (90+
2178 \backslash
2179 iangle:0:0.25)
2180 \end_layout
2181
2182 \begin_layout Plain Layout
2183
2184                   -- ++(0,-1) node[m] {};
2185 \end_layout
2186
2187 \begin_layout Plain Layout
2188
2189 \end_layout
2190
2191 \begin_layout Plain Layout
2192
2193
2194 \backslash
2195 draw[->] (base)++(
2196 \backslash
2197 arcr,0) arc (0:
2198 \backslash
2199 iangle:
2200 \backslash
2201 arcr);
2202 \end_layout
2203
2204 \begin_layout Plain Layout
2205
2206
2207 \backslash
2208 path (base)++(
2209 \backslash
2210 iangle*0.5:
2211 \backslash
2212 arcr+5pt) node {$
2213 \backslash
2214 alpha$};
2215 \end_layout
2216
2217 \begin_layout Plain Layout
2218
2219     %%
2220 \end_layout
2221
2222 \begin_layout Plain Layout
2223
2224 \end_layout
2225
2226 \begin_layout Plain Layout
2227
2228 &
2229 \end_layout
2230
2231 \begin_layout Plain Layout
2232
2233     %% Free body diagram of M
2234 \end_layout
2235
2236 \begin_layout Plain Layout
2237
2238
2239 \backslash
2240 begin{scope}[rotate=
2241 \backslash
2242 iangle]
2243 \end_layout
2244
2245 \begin_layout Plain Layout
2246
2247
2248 \backslash
2249 node[M,transform shape] (M) {};
2250 \end_layout
2251
2252 \begin_layout Plain Layout
2253
2254         % Draw axes and help lines
2255 \end_layout
2256
2257 \begin_layout Plain Layout
2258
2259 \end_layout
2260
2261 \begin_layout Plain Layout
2262
2263         {[axis,->]
2264 \end_layout
2265
2266 \begin_layout Plain Layout
2267
2268
2269 \backslash
2270 draw (0,-1) -- (0,2) node[right] {$+y$};
2271 \end_layout
2272
2273 \begin_layout Plain Layout
2274
2275
2276 \backslash
2277 draw (M) -- ++(2,0) node[right] {$+x$};
2278 \end_layout
2279
2280 \begin_layout Plain Layout
2281
2282             % Indicate angle.
2283  The code is a bit awkward.
2284 \end_layout
2285
2286 \begin_layout Plain Layout
2287
2288 \end_layout
2289
2290 \begin_layout Plain Layout
2291
2292
2293 \backslash
2294 draw[solid,shorten >=0.5pt] (
2295 \backslash
2296 down-
2297 \backslash
2298 iangle:
2299 \backslash
2300 arcr)
2301 \end_layout
2302
2303 \begin_layout Plain Layout
2304
2305                 arc(
2306 \backslash
2307 down-
2308 \backslash
2309 iangle:
2310 \backslash
2311 down:
2312 \backslash
2313 arcr);
2314 \end_layout
2315
2316 \begin_layout Plain Layout
2317
2318
2319 \backslash
2320 node at (
2321 \backslash
2322 down-0.5*
2323 \backslash
2324 iangle:1.3*
2325 \backslash
2326 arcr) {$
2327 \backslash
2328 alpha$};
2329 \end_layout
2330
2331 \begin_layout Plain Layout
2332
2333         }
2334 \end_layout
2335
2336 \begin_layout Plain Layout
2337
2338 \end_layout
2339
2340 \begin_layout Plain Layout
2341
2342         % Forces
2343 \end_layout
2344
2345 \begin_layout Plain Layout
2346
2347         {[force,->]
2348 \end_layout
2349
2350 \begin_layout Plain Layout
2351
2352             % Assuming that Mg = 1.
2353  The normal force will therefore be cos(alpha)
2354 \end_layout
2355
2356 \begin_layout Plain Layout
2357
2358
2359 \backslash
2360 draw (M.center) -- ++(0,{cos(
2361 \backslash
2362 iangle)}) node[above right] {$N$};
2363 \end_layout
2364
2365 \begin_layout Plain Layout
2366
2367
2368 \backslash
2369 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2370 \end_layout
2371
2372 \begin_layout Plain Layout
2373
2374
2375 \backslash
2376 draw (M.east) -- ++(1,0) node[above] {$T$};
2377 \end_layout
2378
2379 \begin_layout Plain Layout
2380
2381         }
2382 \end_layout
2383
2384 \begin_layout Plain Layout
2385
2386 \end_layout
2387
2388 \begin_layout Plain Layout
2389
2390
2391 \backslash
2392 end{scope}
2393 \end_layout
2394
2395 \begin_layout Plain Layout
2396
2397     % Draw gravity force.
2398  The code is put outside the rotated
2399 \end_layout
2400
2401 \begin_layout Plain Layout
2402
2403     % scope for simplicity.
2404  No need to do any angle calculations.
2405
2406 \end_layout
2407
2408 \begin_layout Plain Layout
2409
2410
2411 \backslash
2412 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2413 \end_layout
2414
2415 \begin_layout Plain Layout
2416
2417     %%
2418 \end_layout
2419
2420 \begin_layout Plain Layout
2421
2422 \end_layout
2423
2424 \begin_layout Plain Layout
2425
2426 &
2427 \end_layout
2428
2429 \begin_layout Plain Layout
2430
2431     %%%
2432 \end_layout
2433
2434 \begin_layout Plain Layout
2435
2436     % Free body diagram of m
2437 \end_layout
2438
2439 \begin_layout Plain Layout
2440
2441
2442 \backslash
2443 node[m] (m) {};
2444 \end_layout
2445
2446 \begin_layout Plain Layout
2447
2448
2449 \backslash
2450 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2451 \end_layout
2452
2453 \begin_layout Plain Layout
2454
2455     {[force,->]
2456 \end_layout
2457
2458 \begin_layout Plain Layout
2459
2460
2461 \backslash
2462 draw (m.north) -- ++(0,1) node[above] {$T'$};
2463 \end_layout
2464
2465 \begin_layout Plain Layout
2466
2467
2468 \backslash
2469 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2470 \end_layout
2471
2472 \begin_layout Plain Layout
2473
2474     }
2475 \end_layout
2476
2477 \begin_layout Plain Layout
2478
2479 \end_layout
2480
2481 \begin_layout Plain Layout
2482
2483
2484 \backslash
2485
2486 \backslash
2487
2488 \end_layout
2489
2490 \begin_layout Plain Layout
2491
2492 };
2493 \end_layout
2494
2495 \begin_layout Plain Layout
2496
2497
2498 \backslash
2499 end{tikzpicture}
2500 \end_layout
2501
2502 \begin_layout Plain Layout
2503
2504 \end_layout
2505
2506 \end_inset
2507
2508
2509 \end_layout
2510
2511 \end_inset
2512
2513
2514 \end_layout
2515
2516 \end_body
2517 \end_document