lib/examples/instant_preview.lyx

   1 #LyX 2.3 created this file. For more info see http://www.lyx.org/
   2 \lyxformat 544
   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 \math_numbering_side default
  77 \quotes_style english
  78 \papercolumns 1
  79 \papersides 1
  80 \paperpagestyle default
  81 \tracking_changes false
  82 \output_changes false
  83 \html_math_output 0
  84 \html_css_as_file 0
  85 \html_be_strict true
  86 \use_minted 0
  87 \end_header
  88
  89 \begin_body
  90
  91 \begin_layout Section
  92 Introduction
  93 \end_layout
  94
  95 \begin_layout Standard
  96 In order to properly typeset the document and have instant preview working,
  97  the following packages have to be installed:
  98 \end_layout
  99
 100 \begin_layout LyX-Code
 101 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf, etex
 102 \end_layout
 103
 104 \begin_layout Standard
 105 Due to the use of postscript specials in Section
 106 \begin_inset CommandInset ref
 107 LatexCommand ref
 108 reference "sec:PSTricks"
 109
 110 \end_inset
 111
 112 , only the Postscript or PDF (ps2pdf) output formats will correctly render
 113  the included images.
 114  However, the PDF (Xe\SpecialChar TeX
 115 ) output seems to also work, while trying to typeset
 116  the document with
 117 \family typewriter
 118 pdflatex
 119 \family default
 120  or
 121 \family typewriter
 122 pdflualatex
 123 \family default
 124  will generate errors.
 125 \end_layout
 126
 127 \begin_layout Section
 128 Diagrams by XY(-pic)
 129 \end_layout
 130
 131 \begin_layout Standard
 132 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
 133  examples, see
 134 \begin_inset Flex URL
 135 status collapsed
 136
 137 \begin_layout Plain Layout
 138
 139 https://www.ctan.org/tex-archive/macros/generic/diagrams/xypic/doc/xyguide.pdf
 140 \end_layout
 141
 142 \end_inset
 143
 144 .
 145 \end_layout
 146
 147 \begin_layout Description
 148 Braid
 149 \end_layout
 150
 151 \begin_layout Standard
 152 \begin_inset Preview
 153
 154 \begin_layout Standard
 155 \begin_inset ERT
 156 status collapsed
 157
 158 \begin_layout Plain Layout
 159
 160
 161 \backslash
 162 xy
 163 \end_layout
 164
 165 \begin_layout Plain Layout
 166
 167 (5,10)*{}; (-10,-10)*{} **
 168 \backslash
 169 crv{(6,-2)&(-12,4)}
 170 \end_layout
 171
 172 \begin_layout Plain Layout
 173
 174
 175 \backslash
 176 POS?(.25)*{
 177 \backslash
 178 hole}="x"
 179 \backslash
 180 POS?(.45)*{
 181 \backslash
 182 hole}="y"
 183 \backslash
 184 POS?(.6)*{
 185 \backslash
 186 hole}="z";
 187 \end_layout
 188
 189 \begin_layout Plain Layout
 190
 191 "y"+(0,-1); (2,-10)*{} **
 192 \backslash
 193 crv{}
 194 \backslash
 195 POS?(.2)*{
 196 \backslash
 197 hole}="M";
 198 \end_layout
 199
 200 \begin_layout Plain Layout
 201
 202 (-10,10)*{}; "z" **
 203 \backslash
 204 crv{(-9,0)};
 205 \end_layout
 206
 207 \begin_layout Plain Layout
 208
 209 "z"; "M" **
 210 \backslash
 211 crv{};
 212 \end_layout
 213
 214 \begin_layout Plain Layout
 215
 216 "M"; "x" **
 217 \backslash
 218 crv{(5,0)};
 219 \end_layout
 220
 221 \begin_layout Plain Layout
 222
 223 "x"; "y" **
 224 \backslash
 225 crv{(0,7) & (-5,6)};
 226 \end_layout
 227
 228 \begin_layout Plain Layout
 229
 230
 231 \backslash
 232 endxy
 233 \end_layout
 234
 235 \end_inset
 236
 237
 238 \end_layout
 239
 240 \end_inset
 241
 242
 243 \end_layout
 244
 245 \begin_layout Description
 246 Knots
 247 \end_layout
 248
 249 \begin_layout Standard
 250 \begin_inset Preview
 251
 252 \begin_layout Standard
 253 \begin_inset ERT
 254 status collapsed
 255
 256 \begin_layout Plain Layout
 257
 258
 259 \backslash
 260 xy
 261 \end_layout
 262
 263 \begin_layout Plain Layout
 264
 265 (6,9)*{}="1";
 266 \end_layout
 267
 268 \begin_layout Plain Layout
 269
 270 (-8.5,-1)*{}="2";
 271 \end_layout
 272
 273 \begin_layout Plain Layout
 274
 275 "1";"2" **
 276 \backslash
 277 crv{~*=<.5pt>{.} (0,30)}?(.75)*
 278 \backslash
 279 dir{>}+(-2,2)*{z};
 280 \end_layout
 281
 282 \begin_layout Plain Layout
 283
 284 (-6.5,8)*{}="1";
 285 \end_layout
 286
 287 \begin_layout Plain Layout
 288
 289 (-.5,-9)*{}="2";
 290 \end_layout
 291
 292 \begin_layout Plain Layout
 293
 294 "1";"2" **
 295 \backslash
 296 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
 297 \backslash
 298 dir{>}+(-2,-2)*{u};
 299 \end_layout
 300
 301 \begin_layout Plain Layout
 302
 303 (-9.5,-3.35)*{}="1";
 304 \end_layout
 305
 306 \begin_layout Plain Layout
 307
 308 (8.5,-3)*{}="2";
 309 \end_layout
 310
 311 \begin_layout Plain Layout
 312
 313 "1";"2" **
 314 \backslash
 315 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
 316 \backslash
 317 dir{>}+(-1,-3)*{x};
 318 \end_layout
 319
 320 \begin_layout Plain Layout
 321
 322 (1,-10)*{}="1";
 323 \end_layout
 324
 325 \begin_layout Plain Layout
 326
 327 (6.5,7.13)*{}="2";
 328 \end_layout
 329
 330 \begin_layout Plain Layout
 331
 332 "1";"2" **
 333 \backslash
 334 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
 335 \backslash
 336 dir{>}+(3,-1)*{y};
 337 \end_layout
 338
 339 \begin_layout Plain Layout
 340
 341 (11,-1)*{}="1";
 342 \end_layout
 343
 344 \begin_layout Plain Layout
 345
 346 (-4,8)*{}="2";
 347 \end_layout
 348
 349 \begin_layout Plain Layout
 350
 351 "1";"2" **
 352 \backslash
 353 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
 354 \backslash
 355 dir{>}+(1,2)*{w};
 356 \end_layout
 357
 358 \begin_layout Plain Layout
 359
 360
 361 \backslash
 362 endxy
 363 \end_layout
 364
 365 \end_inset
 366
 367
 368 \end_layout
 369
 370 \end_inset
 371
 372
 373 \end_layout
 374
 375 \begin_layout Description
 376 Circles
 377 \end_layout
 378
 379 \begin_layout Standard
 380 \begin_inset Preview
 381
 382 \begin_layout Standard
 383 \begin_inset ERT
 384 status collapsed
 385
 386 \begin_layout Plain Layout
 387
 388
 389 \backslash
 390 xy
 391 \end_layout
 392
 393 \begin_layout Plain Layout
 394
 395 (0,0)*
 396 \backslash
 397 xycircle(14,8){++
 398 \backslash
 399 dir{<}};
 400 \end_layout
 401
 402 \begin_layout Plain Layout
 403
 404 (0,0)*
 405 \backslash
 406 xycircle<10pt>{{.}};
 407 \end_layout
 408
 409 \begin_layout Plain Layout
 410
 411 (0,0)*
 412 \backslash
 413 xycircle(5,2){:};
 414 \end_layout
 415
 416 \begin_layout Plain Layout
 417
 418 (0,15)*
 419 \backslash
 420 xycircle(10,4){--};
 421 \end_layout
 422
 423 \begin_layout Plain Layout
 424
 425
 426 \backslash
 427 endxy
 428 \end_layout
 429
 430 \end_inset
 431
 432
 433 \end_layout
 434
 435 \end_inset
 436
 437
 438 \end_layout
 439
 440 \begin_layout Description
 441 Cobordism
 442 \end_layout
 443
 444 \begin_layout Standard
 445 \begin_inset Preview
 446
 447 \begin_layout Standard
 448 \begin_inset ERT
 449 status collapsed
 450
 451 \begin_layout Plain Layout
 452
 453
 454 \backslash
 455 xy
 456 \end_layout
 457
 458 \begin_layout Plain Layout
 459
 460 (0,0)*
 461 \backslash
 462 ellipse(3,1){.};
 463 \end_layout
 464
 465 \begin_layout Plain Layout
 466
 467 (0,0)*
 468 \backslash
 469 ellipse(3,1)__,=:a(-180){-};
 470 \end_layout
 471
 472 \begin_layout Plain Layout
 473
 474 (-6,-8)*
 475 \backslash
 476 ellipse(3,1){.};
 477 \end_layout
 478
 479 \begin_layout Plain Layout
 480
 481 (6,-8)*
 482 \backslash
 483 ellipse(3,1){.};
 484 \end_layout
 485
 486 \begin_layout Plain Layout
 487
 488 (0,-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)__,=:a(-180){-};
 498 \end_layout
 499
 500 \begin_layout Plain Layout
 501
 502 (6,-8)*
 503 \backslash
 504 ellipse(3,1)__,=:a(-180){-};
 505 \end_layout
 506
 507 \begin_layout Plain Layout
 508
 509 (0,-8)*
 510 \backslash
 511 ellipse(3,1)__,=:a(180){-};
 512 \end_layout
 513
 514 \begin_layout Plain Layout
 515
 516 (-3,6)*
 517 \backslash
 518 ellipse(3,1){-};
 519 \end_layout
 520
 521 \begin_layout Plain Layout
 522
 523 (3,6)*
 524 \backslash
 525 ellipse(3,1){-};
 526 \end_layout
 527
 528 \begin_layout Plain Layout
 529
 530 (-3,12)*{}="1";
 531 \end_layout
 532
 533 \begin_layout Plain Layout
 534
 535 (3,12)*{}="2";
 536 \end_layout
 537
 538 \begin_layout Plain Layout
 539
 540 (-9,12)*{}="A2";
 541 \end_layout
 542
 543 \begin_layout Plain Layout
 544
 545 (9,12)*{}="B2";
 546 \end_layout
 547
 548 \begin_layout Plain Layout
 549
 550 "1";"2" **
 551 \backslash
 552 crv{(-3,7) & (3,7)};
 553 \end_layout
 554
 555 \begin_layout Plain Layout
 556
 557 (-3,0)*{}="A";
 558 \end_layout
 559
 560 \begin_layout Plain Layout
 561
 562 (3,0)*{}="B";
 563 \end_layout
 564
 565 \begin_layout Plain Layout
 566
 567 (-3,1)*{}="A1";
 568 \end_layout
 569
 570 \begin_layout Plain Layout
 571
 572 (3,1)*{}="B1";
 573 \end_layout
 574
 575 \begin_layout Plain Layout
 576
 577 "A";"A1" **
 578 \backslash
 579 dir{-};
 580 \end_layout
 581
 582 \begin_layout Plain Layout
 583
 584 "B";"B1" **
 585 \backslash
 586 dir{-};
 587 \end_layout
 588
 589 \begin_layout Plain Layout
 590
 591 "B2";"B1" **
 592 \backslash
 593 crv{(8,7) & (3,5)};
 594 \end_layout
 595
 596 \begin_layout Plain Layout
 597
 598 "A2";"A1" **
 599 \backslash
 600 crv{(-8,7) & (-3,5)};
 601 \end_layout
 602
 603 \begin_layout Plain Layout
 604
 605 %REFLECT
 606 \end_layout
 607
 608 \begin_layout Plain Layout
 609
 610 (3,-16)*{}="1";
 611 \end_layout
 612
 613 \begin_layout Plain Layout
 614
 615 (9,-16)*{}="2";
 616 \end_layout
 617
 618 \begin_layout Plain Layout
 619
 620 "1";"2" **
 621 \backslash
 622 crv{(3,-10) & (9,-10)};
 623 \end_layout
 624
 625 \begin_layout Plain Layout
 626
 627 (-3,-16)*{}="1";
 628 \end_layout
 629
 630 \begin_layout Plain Layout
 631
 632 (-9,-16)*{}="2";
 633 \end_layout
 634
 635 \begin_layout Plain Layout
 636
 637 "1";"2" **
 638 \backslash
 639 crv{(-3,-10) & (-9,-10)};
 640 \end_layout
 641
 642 \begin_layout Plain Layout
 643
 644 (-15,-16)*{}="A2";
 645 \end_layout
 646
 647 \begin_layout Plain Layout
 648
 649 (15,-16)*{}="B2";
 650 \end_layout
 651
 652 \begin_layout Plain Layout
 653
 654 (-3,0)*{}="A";
 655 \end_layout
 656
 657 \begin_layout Plain Layout
 658
 659 (3,0)*{}="B";
 660 \end_layout
 661
 662 \begin_layout Plain Layout
 663
 664 (-3,-1)*{}="A1";
 665 \end_layout
 666
 667 \begin_layout Plain Layout
 668
 669 (3,-1)*{}="B1";
 670 \end_layout
 671
 672 \begin_layout Plain Layout
 673
 674 "A";"A1" **
 675 \backslash
 676 dir{-};
 677 \end_layout
 678
 679 \begin_layout Plain Layout
 680
 681 "B";"B1" **
 682 \backslash
 683 dir{-};
 684 \end_layout
 685
 686 \begin_layout Plain Layout
 687
 688 "B2";"B1" **
 689 \backslash
 690 crv{(13,-6) & (2,-8)};
 691 \end_layout
 692
 693 \begin_layout Plain Layout
 694
 695 "A2";"A1" **
 696 \backslash
 697 crv{(-13,-6) & (-2,-8)};
 698 \end_layout
 699
 700 \begin_layout Plain Layout
 701
 702
 703 \backslash
 704 endxy
 705 \end_layout
 706
 707 \end_inset
 708
 709
 710 \end_layout
 711
 712 \end_inset
 713
 714
 715 \begin_inset Preview
 716
 717 \begin_layout Standard
 718 \begin_inset ERT
 719 status collapsed
 720
 721 \begin_layout Plain Layout
 722
 723
 724 \backslash
 725 xy 0;/r.18pc/:
 726 \end_layout
 727
 728 \begin_layout Plain Layout
 729
 730 (20,2)*{
 731 \backslash
 732 bullet}="RU"+(1,3)*{x^{
 733 \backslash
 734 ast}};
 735 \end_layout
 736
 737 \begin_layout Plain Layout
 738
 739 (16,-3)*{
 740 \backslash
 741 bullet}="RD"+(2.5,2)*{x^{
 742 \backslash
 743 ast}};
 744 \end_layout
 745
 746 \begin_layout Plain Layout
 747
 748 (-16,2)*{
 749 \backslash
 750 bullet}="LU"+(-1,2)*{x};
 751 \end_layout
 752
 753 \begin_layout Plain Layout
 754
 755 (-20,-3)*{
 756 \backslash
 757 bullet}="LD"+(-1,2)*{x};
 758 \end_layout
 759
 760 \begin_layout Plain Layout
 761
 762 "RU";"RD" **
 763 \backslash
 764 crv{(4,2) & (4,-1)}; ?(.1)*
 765 \backslash
 766 dir{<}; ?(.85)*
 767 \backslash
 768 dir{<};
 769 \end_layout
 770
 771 \begin_layout Plain Layout
 772
 773 "LD";"LU" **
 774 \backslash
 775 crv{(-4,-2) & (-4,1)};
 776 \end_layout
 777
 778 \begin_layout Plain Layout
 779
 780 ?(.08)*
 781 \backslash
 782 dir{<}; ?(.85)*
 783 \backslash
 784 dir{<};
 785 \end_layout
 786
 787 \begin_layout Plain Layout
 788
 789 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
 790 \end_layout
 791
 792 \begin_layout Plain Layout
 793
 794 "x1"; "x2" **
 795 \backslash
 796 crv{(7,-10) & (-7,-10)};
 797 \end_layout
 798
 799 \begin_layout Plain Layout
 800
 801 (16,-20)*{
 802 \backslash
 803 bullet}="RDD"+(2.5,-1)*{x^{
 804 \backslash
 805 ast}};
 806 \end_layout
 807
 808 \begin_layout Plain Layout
 809
 810 (-20,-20)*{
 811 \backslash
 812 bullet}="LDD"+(-1,-3)*{x};
 813 \end_layout
 814
 815 \begin_layout Plain Layout
 816
 817 (20,-12.5)*{
 818 \backslash
 819 bullet}="RUD"+(3.5,1)*{x^{
 820 \backslash
 821 ast}};
 822 \end_layout
 823
 824 \begin_layout Plain Layout
 825
 826 (-16,-15)*{
 827 \backslash
 828 bullet}="LUD";
 829 \end_layout
 830
 831 \begin_layout Plain Layout
 832
 833 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
 834 \end_layout
 835
 836 \begin_layout Plain Layout
 837
 838 "RD"; "RDD" **
 839 \backslash
 840 dir{-};
 841 \end_layout
 842
 843 \begin_layout Plain Layout
 844
 845 "LD"; "LDD" **
 846 \backslash
 847 dir{-};
 848 \end_layout
 849
 850 \begin_layout Plain Layout
 851
 852 "A"; "LUD" **
 853 \backslash
 854 dir{.};
 855 \end_layout
 856
 857 \begin_layout Plain Layout
 858
 859 "RDD"; "LDD" **
 860 \backslash
 861 crv{(0,-17)}; ?(.57)*
 862 \backslash
 863 dir{>};
 864 \end_layout
 865
 866 \begin_layout Plain Layout
 867
 868 "RU"; "RUD" **
 869 \backslash
 870 dir{-};
 871 \end_layout
 872
 873 \begin_layout Plain Layout
 874
 875 "LU"; "A" **
 876 \backslash
 877 dir{-};
 878 \end_layout
 879
 880 \begin_layout Plain Layout
 881
 882 "B"; "RUD" **
 883 \backslash
 884 crv{(18,-14.15)};
 885 \end_layout
 886
 887 \begin_layout Plain Layout
 888
 889 "B"; "LUD" **
 890 \backslash
 891 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
 892 \backslash
 893 dir{<};
 894 \end_layout
 895
 896 \begin_layout Plain Layout
 897
 898
 899 \backslash
 900 endxy
 901 \end_layout
 902
 903 \end_inset
 904
 905
 906 \end_layout
 907
 908 \end_inset
 909
 910
 911 \end_layout
 912
 913 \begin_layout Description
 914 Strings
 915 \end_layout
 916
 917 \begin_layout Standard
 918 \begin_inset Preview
 919
 920 \begin_layout Standard
 921 \begin_inset ERT
 922 status open
 923
 924 \begin_layout Plain Layout
 925
 926
 927 \backslash
 928 xy (-15,0)*{};(15,0)*{};
 929 \end_layout
 930
 931 \begin_layout Plain Layout
 932
 933
 934 \backslash
 935 endxy
 936 \end_layout
 937
 938 \begin_layout Plain Layout
 939
 940
 941 \backslash
 942 qquad =
 943 \backslash
 944 qquad
 945 \backslash
 946 xy
 947 \end_layout
 948
 949 \begin_layout Plain Layout
 950
 951 (-10,12)*{}; (-10,-12)*{}; **
 952 \backslash
 953 dir{-}?(.5)*
 954 \backslash
 955 dir{<}+(-4,0)*{F(x)};
 956 \end_layout
 957
 958 \begin_layout Plain Layout
 959
 960 (-2,12)*{}="1";
 961 \end_layout
 962
 963 \begin_layout Plain Layout
 964
 965 (6,-7) *{}="2";
 966 \end_layout
 967
 968 \begin_layout Plain Layout
 969
 970 (14,-7) *{}="3";
 971 \end_layout
 972
 973 \begin_layout Plain Layout
 974
 975 (14,-13)*{}="3'";
 976 \end_layout
 977
 978 \begin_layout Plain Layout
 979
 980 (18,0) *={}="";
 981 \end_layout
 982
 983 \begin_layout Plain Layout
 984
 985 "1";"2" **
 986 \backslash
 987 crv{(-4,-21)&(5,-15)};
 988 \end_layout
 989
 990 \begin_layout Plain Layout
 991
 992 ?(.15)*
 993 \backslash
 994 dir{<}+(5,10)*{
 995 \backslash
 996 overline{F(x)}};
 997 \end_layout
 998
 999 \begin_layout Plain Layout
1000
1001 "2";"3" **
1002 \backslash
1003 crv{(6,1)&(14,1)};
1004 \end_layout
1005
1006 \begin_layout Plain Layout
1007
1008 ?(0)*
1009 \backslash
1010 dir{<}+(4,8)*{
1011 \backslash
1012 widetilde{F(i_x)}} ;
1013 \end_layout
1014
1015 \begin_layout Plain Layout
1016
1017 ?(.95)*
1018 \backslash
1019 dir{<}+(5,-2)*{F(
1020 \backslash
1021 overline x)};
1022 \end_layout
1023
1024 \begin_layout Plain Layout
1025
1026 "3";"3'" **
1027 \backslash
1028 dir{-};
1029 \end_layout
1030
1031 \begin_layout Plain Layout
1032
1033 (-2,6)*{}="X1";
1034 \end_layout
1035
1036 \begin_layout Plain Layout
1037
1038 (-10,6)*{}="X2";
1039 \end_layout
1040
1041 \begin_layout Plain Layout
1042
1043 "X1";"X2" **
1044 \backslash
1045 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1046 \end_layout
1047
1048 \begin_layout Plain Layout
1049
1050 (-2,-6)*{}="XA";
1051 \end_layout
1052
1053 \begin_layout Plain Layout
1054
1055 (-10,-6)*{}="XB";
1056 \end_layout
1057
1058 \begin_layout Plain Layout
1059
1060 "XA";"XB" **
1061 \backslash
1062 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1063 \end_layout
1064
1065 \begin_layout Plain Layout
1066
1067
1068 \backslash
1069 endxy
1070 \end_layout
1071
1072 \end_inset
1073
1074
1075 \end_layout
1076
1077 \end_inset
1078
1079
1080 \end_layout
1081
1082 \begin_layout Description
1083 Categories
1084 \end_layout
1085
1086 \begin_layout Standard
1087 \begin_inset Preview
1088
1089 \begin_layout Standard
1090 \begin_inset ERT
1091 status collapsed
1092
1093 \begin_layout Plain Layout
1094
1095
1096 \backslash
1097 xymatrix{
1098 \end_layout
1099
1100 \begin_layout Plain Layout
1101
1102 (x
1103 \backslash
1104 otimes 1)
1105 \backslash
1106 otimes y
1107 \end_layout
1108
1109 \begin_layout Plain Layout
1110
1111
1112 \backslash
1113 ar[rr]^{a_{x,1,y}}
1114 \end_layout
1115
1116 \begin_layout Plain Layout
1117
1118
1119 \backslash
1120 ar[dr]_{r_x
1121 \backslash
1122 otimes 1_y}
1123 \end_layout
1124
1125 \begin_layout Plain Layout
1126
1127 && x
1128 \backslash
1129 otimes(1
1130 \backslash
1131 otimes y)
1132 \end_layout
1133
1134 \begin_layout Plain Layout
1135
1136
1137 \backslash
1138 ar[dl]^{1_x
1139 \backslash
1140 otimes
1141 \backslash
1142 ell_y }
1143 \backslash
1144
1145 \backslash
1146
1147 \end_layout
1148
1149 \begin_layout Plain Layout
1150
1151 & x
1152 \backslash
1153 otimes y }
1154 \end_layout
1155
1156 \end_inset
1157
1158
1159 \end_layout
1160
1161 \end_inset
1162
1163
1164 \begin_inset Preview
1165
1166 \begin_layout Standard
1167 \begin_inset ERT
1168 status collapsed
1169
1170 \begin_layout Plain Layout
1171
1172
1173 \backslash
1174 xy
1175 \end_layout
1176
1177 \begin_layout Plain Layout
1178
1179 (-9,0)*+{
1180 \backslash
1181 bullet}="1";
1182 \end_layout
1183
1184 \begin_layout Plain Layout
1185
1186 (0,0)*+{
1187 \backslash
1188 bullet}="2";
1189 \end_layout
1190
1191 \begin_layout Plain Layout
1192
1193 {
1194 \backslash
1195 ar@/^.9pc/ "1";"2"};
1196 \end_layout
1197
1198 \begin_layout Plain Layout
1199
1200 {
1201 \backslash
1202 ar@/_.9pc/ "1";"2"};
1203 \end_layout
1204
1205 \begin_layout Plain Layout
1206
1207 {
1208 \backslash
1209 ar@/^2pc/ "1";"2"};
1210 \end_layout
1211
1212 \begin_layout Plain Layout
1213
1214 {
1215 \backslash
1216 ar@/_2pc/ "1";"2"};
1217 \end_layout
1218
1219 \begin_layout Plain Layout
1220
1221 {
1222 \backslash
1223 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1224 \end_layout
1225
1226 \begin_layout Plain Layout
1227
1228 {
1229 \backslash
1230 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1231 \end_layout
1232
1233 \begin_layout Plain Layout
1234
1235 {
1236 \backslash
1237 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1238 \end_layout
1239
1240 \begin_layout Plain Layout
1241
1242 (0,0)*+{
1243 \backslash
1244 bullet}="1";
1245 \end_layout
1246
1247 \begin_layout Plain Layout
1248
1249 (9,0)*+{
1250 \backslash
1251 bullet}="2";
1252 \end_layout
1253
1254 \begin_layout Plain Layout
1255
1256 (18,0)*+{
1257 \backslash
1258 bullet}="3";
1259 \end_layout
1260
1261 \begin_layout Plain Layout
1262
1263 {
1264 \backslash
1265 ar "1";"2"};
1266 \end_layout
1267
1268 \begin_layout Plain Layout
1269
1270 {
1271 \backslash
1272 ar "2";"3"};
1273 \end_layout
1274
1275 \begin_layout Plain Layout
1276
1277 {
1278 \backslash
1279 ar@/^1pc/ "1";"2"};
1280 \end_layout
1281
1282 \begin_layout Plain Layout
1283
1284 {
1285 \backslash
1286 ar@/_1pc/ "1";"2"};
1287 \end_layout
1288
1289 \begin_layout Plain Layout
1290
1291 {
1292 \backslash
1293 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1294 \end_layout
1295
1296 \begin_layout Plain Layout
1297
1298 {
1299 \backslash
1300 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1301 \end_layout
1302
1303 \begin_layout Plain Layout
1304
1305
1306 \backslash
1307 endxy
1308 \end_layout
1309
1310 \end_inset
1311
1312
1313 \end_layout
1314
1315 \end_inset
1316
1317
1318 \end_layout
1319
1320 \begin_layout Description
1321 Transformations
1322 \end_layout
1323
1324 \begin_layout Standard
1325 \begin_inset Preview
1326
1327 \begin_layout Standard
1328 \begin_inset ERT
1329 status collapsed
1330
1331 \begin_layout Plain Layout
1332
1333
1334 \backslash
1335 xy %FIG.19.
1336  Natural transformation between functors.
1337 \end_layout
1338
1339 \begin_layout Plain Layout
1340
1341 (-26,-2)*+{
1342 \backslash
1343 bullet}="a";
1344 \end_layout
1345
1346 \begin_layout Plain Layout
1347
1348 (-12,3)*+{
1349 \backslash
1350 bullet}="b";
1351 \end_layout
1352
1353 \begin_layout Plain Layout
1354
1355 (-16,-5)*+{
1356 \backslash
1357 bullet}="c";
1358 \end_layout
1359
1360 \begin_layout Plain Layout
1361
1362 {
1363 \backslash
1364 ar@/^.25pc/ "a";"b"};
1365 \end_layout
1366
1367 \begin_layout Plain Layout
1368
1369 {
1370 \backslash
1371 ar@/_.25pc/"a";"c"};
1372 \end_layout
1373
1374 \begin_layout Plain Layout
1375
1376 {
1377 \backslash
1378 ar@/_.15pc/ "b";"c"};
1379 \end_layout
1380
1381 \begin_layout Plain Layout
1382
1383 %START TOP
1384 \end_layout
1385
1386 \begin_layout Plain Layout
1387
1388 (12,10)*+{
1389 \backslash
1390 bullet}="ta";
1391 \end_layout
1392
1393 \begin_layout Plain Layout
1394
1395 (26,15)*+{
1396 \backslash
1397 bullet}="tb";
1398 \end_layout
1399
1400 \begin_layout Plain Layout
1401
1402 (22,8)*+{
1403 \backslash
1404 bullet}="tc";
1405 \end_layout
1406
1407 \begin_layout Plain Layout
1408
1409 {
1410 \backslash
1411 ar@/^.25pc/ "ta";"tb"};
1412 \end_layout
1413
1414 \begin_layout Plain Layout
1415
1416 {
1417 \backslash
1418 ar@/_.25pc/ "ta";"tc"};
1419 \end_layout
1420
1421 \begin_layout Plain Layout
1422
1423 {
1424 \backslash
1425 ar@/_.15pc/ "tb";"tc"};
1426 \end_layout
1427
1428 \begin_layout Plain Layout
1429
1430 %START bottom
1431 \end_layout
1432
1433 \begin_layout Plain Layout
1434
1435 (12,-10)*+{
1436 \backslash
1437 bullet}="ba";
1438 \end_layout
1439
1440 \begin_layout Plain Layout
1441
1442 (26,-5)*+{
1443 \backslash
1444 bullet}="bb";
1445 \end_layout
1446
1447 \begin_layout Plain Layout
1448
1449 (22,-12)*+{
1450 \backslash
1451 bullet}="bc";
1452 \end_layout
1453
1454 \begin_layout Plain Layout
1455
1456 {
1457 \backslash
1458 ar@/^.25pc/@{.>} "ba";"bb"};
1459 \end_layout
1460
1461 \begin_layout Plain Layout
1462
1463 {
1464 \backslash
1465 ar@/_.25pc/ "ba";"bc"};
1466 \end_layout
1467
1468 \begin_layout Plain Layout
1469
1470 {
1471 \backslash
1472 ar@/_.15pc/ "bb";"bc"};
1473 \end_layout
1474
1475 \begin_layout Plain Layout
1476
1477 %START CONNECT
1478 \end_layout
1479
1480 \begin_layout Plain Layout
1481
1482 {
1483 \backslash
1484 ar@/_.15pc/ "ta";"ba"};
1485 \end_layout
1486
1487 \begin_layout Plain Layout
1488
1489 {
1490 \backslash
1491 ar@/_.15pc/ "tb";"bb"};
1492 \end_layout
1493
1494 \begin_layout Plain Layout
1495
1496 {
1497 \backslash
1498 ar@/_.15pc/ "tc";"bc"};
1499 \end_layout
1500
1501 \begin_layout Plain Layout
1502
1503 %START ARROWS AND LABELS
1504 \end_layout
1505
1506 \begin_layout Plain Layout
1507
1508 (-12,6)*{}="DF";
1509 \end_layout
1510
1511 \begin_layout Plain Layout
1512
1513 (6,10)*{}="CF";
1514 \end_layout
1515
1516 \begin_layout Plain Layout
1517
1518 {
1519 \backslash
1520 ar@/^.35pc/^F "DF";"CF"};
1521 \end_layout
1522
1523 \begin_layout Plain Layout
1524
1525 (-12,-6)*{}="DF";
1526 \end_layout
1527
1528 \begin_layout Plain Layout
1529
1530 (6,-10)*{}="CF";
1531 \end_layout
1532
1533 \begin_layout Plain Layout
1534
1535 {
1536 \backslash
1537 ar@/_.35pc/_G "DF";"CF"};
1538 \end_layout
1539
1540 \begin_layout Plain Layout
1541
1542 (-2,5)*{}="DF";
1543 \end_layout
1544
1545 \begin_layout Plain Layout
1546
1547 (-2,-5)*{}="CF";
1548 \end_layout
1549
1550 \begin_layout Plain Layout
1551
1552 {
1553 \backslash
1554 ar@{=>}^{
1555 \backslash
1556 alpha} "DF";"CF"};
1557 \end_layout
1558
1559 \begin_layout Plain Layout
1560
1561 (29,3)*{D};
1562 \end_layout
1563
1564 \begin_layout Plain Layout
1565
1566 (-23,3)*{C};
1567 \end_layout
1568
1569 \begin_layout Plain Layout
1570
1571
1572 \backslash
1573 endxy
1574 \end_layout
1575
1576 \end_inset
1577
1578
1579 \end_layout
1580
1581 \end_inset
1582
1583
1584 \end_layout
1585
1586 \begin_layout Section
1587 IPA
1588 \end_layout
1589
1590 \begin_layout Standard
1591 \begin_inset Preview
1592
1593 \begin_layout Standard
1594 \begin_inset ERT
1595 status collapsed
1596
1597 \begin_layout Plain Layout
1598
1599
1600 \backslash
1601 textipa{Ekspl@"neIS@n}
1602 \end_layout
1603
1604 \end_inset
1605
1606
1607 \end_layout
1608
1609 \end_inset
1610
1611
1612 \end_layout
1613
1614 \begin_layout Section
1615 QTree
1616 \end_layout
1617
1618 \begin_layout Standard
1619 \begin_inset Preview
1620
1621 \begin_layout Standard
1622 \begin_inset ERT
1623 status collapsed
1624
1625 \begin_layout Plain Layout
1626
1627
1628 \backslash
1629 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1630 \end_layout
1631
1632 \end_inset
1633
1634
1635 \end_layout
1636
1637 \end_inset
1638
1639
1640 \begin_inset Preview
1641
1642 \begin_layout Standard
1643 \begin_inset ERT
1644 status collapsed
1645
1646 \begin_layout Plain Layout
1647
1648
1649 \backslash
1650 Tree [.$
1651 \backslash
1652 sigma$ $
1653 \backslash
1654 mu$ $
1655 \backslash
1656 mu$ ]
1657 \end_layout
1658
1659 \end_inset
1660
1661
1662 \end_layout
1663
1664 \end_inset
1665
1666
1667 \end_layout
1668
1669 \begin_layout Section
1670 PSTricks
1671 \begin_inset CommandInset label
1672 LatexCommand label
1673 name "sec:PSTricks"
1674
1675 \end_inset
1676
1677
1678 \end_layout
1679
1680 \begin_layout Standard
1681 Some simple graphing examples.
1682 \end_layout
1683
1684 \begin_layout Subsection
1685 Function plotting
1686 \end_layout
1687
1688 \begin_layout Standard
1689 \begin_inset Preview
1690
1691 \begin_layout Standard
1692 \begin_inset ERT
1693 status open
1694
1695 \begin_layout Plain Layout
1696
1697
1698 \backslash
1699 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1700 \end_layout
1701
1702 \begin_layout Plain Layout
1703
1704
1705 \backslash
1706 psaxes{->}(0,0)(0,-3)(10,3)
1707 \end_layout
1708
1709 \begin_layout Plain Layout
1710
1711
1712 \backslash
1713 uput[-90](10,0){$x$}
1714 \backslash
1715 uput[0](0,3){$f(x)$}
1716 \end_layout
1717
1718 \begin_layout Plain Layout
1719
1720
1721 \backslash
1722 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1723 \end_layout
1724
1725 \begin_layout Plain Layout
1726
1727
1728 \backslash
1729 end{pspicture*}
1730 \end_layout
1731
1732 \end_inset
1733
1734
1735 \end_layout
1736
1737 \end_inset
1738
1739
1740 \end_layout
1741
1742 \begin_layout Subsection
1743 Inline data plotting
1744 \end_layout
1745
1746 \begin_layout Standard
1747 \align center
1748 \begin_inset Preview
1749
1750 \begin_layout Standard
1751 \align center
1752 \begin_inset ERT
1753 status open
1754
1755 \begin_layout Plain Layout
1756
1757
1758 \backslash
1759 begin{pspicture*}(-1.5,-1.5)(11,5)
1760 \end_layout
1761
1762 \begin_layout Plain Layout
1763
1764
1765 \backslash
1766 psaxes{->}(0,0)(0,0)(10,5)
1767 \end_layout
1768
1769 \begin_layout Plain Layout
1770
1771
1772 \backslash
1773 psset{linewidth=2.5pt}
1774 \end_layout
1775
1776 \begin_layout Plain Layout
1777
1778
1779 \backslash
1780 rput(5.0,-1.0){Speed [MPH]}
1781 \end_layout
1782
1783 \begin_layout Plain Layout
1784
1785
1786 \backslash
1787 rput(-1.0,1.0){
1788 \backslash
1789 begin{rotate}{90}Cost [Dollars]
1790 \backslash
1791 end{rotate}}
1792 \end_layout
1793
1794 \begin_layout Plain Layout
1795
1796
1797 \backslash
1798 savedata{
1799 \backslash
1800 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1801 \end_layout
1802
1803 \begin_layout Plain Layout
1804
1805
1806 \backslash
1807 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1808 \backslash
1809 mydata}
1810 \end_layout
1811
1812 \begin_layout Plain Layout
1813
1814
1815 \backslash
1816 end{pspicture*}
1817 \end_layout
1818
1819 \end_inset
1820
1821
1822 \end_layout
1823
1824 \end_inset
1825
1826
1827 \end_layout
1828
1829 \begin_layout Subsection
1830 Lissajous curves
1831 \end_layout
1832
1833 \begin_layout Standard
1834 \begin_inset Preview
1835
1836 \begin_layout Standard
1837 \begin_inset ERT
1838 status open
1839
1840 \begin_layout Plain Layout
1841
1842
1843 \backslash
1844 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1845 \end_layout
1846
1847 \begin_layout Plain Layout
1848
1849
1850 \backslash
1851 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1852  cos 100 t mul sin}
1853 \end_layout
1854
1855 \begin_layout Plain Layout
1856
1857
1858 \backslash
1859 end{pspicture*}
1860 \end_layout
1861
1862 \end_inset
1863
1864
1865 \end_layout
1866
1867 \end_inset
1868
1869
1870 \begin_inset space \hfill{}
1871 \end_inset
1872
1873
1874 \begin_inset Preview
1875
1876 \begin_layout Standard
1877 \begin_inset ERT
1878 status open
1879
1880 \begin_layout Plain Layout
1881
1882
1883 \backslash
1884 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1885 \end_layout
1886
1887 \begin_layout Plain Layout
1888
1889
1890 \backslash
1891 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1892  mul cos 100 t mul sin}
1893 \end_layout
1894
1895 \begin_layout Plain Layout
1896
1897
1898 \backslash
1899 end{pspicture*}
1900 \end_layout
1901
1902 \end_inset
1903
1904
1905 \end_layout
1906
1907 \end_inset
1908
1909
1910 \begin_inset space \hfill{}
1911 \end_inset
1912
1913
1914 \begin_inset Preview
1915
1916 \begin_layout Standard
1917 \begin_inset ERT
1918 status open
1919
1920 \begin_layout Plain Layout
1921
1922
1923 \backslash
1924 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1925 \end_layout
1926
1927 \begin_layout Plain Layout
1928
1929
1930 \backslash
1931 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1932  mul cos 200 t mul sin}
1933 \end_layout
1934
1935 \begin_layout Plain Layout
1936
1937
1938 \backslash
1939 end{pspicture*}
1940 \end_layout
1941
1942 \end_inset
1943
1944
1945 \end_layout
1946
1947 \end_inset
1948
1949
1950 \begin_inset space \hfill{}
1951 \end_inset
1952
1953
1954 \begin_inset Preview
1955
1956 \begin_layout Standard
1957 \begin_inset ERT
1958 status open
1959
1960 \begin_layout Plain Layout
1961
1962
1963 \backslash
1964 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1965 \end_layout
1966
1967 \begin_layout Plain Layout
1968
1969
1970 \backslash
1971 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1972  mul cos 200 t mul sin}
1973 \end_layout
1974
1975 \begin_layout Plain Layout
1976
1977
1978 \backslash
1979 end{pspicture*}
1980 \end_layout
1981
1982 \end_inset
1983
1984
1985 \end_layout
1986
1987 \end_inset
1988
1989
1990 \end_layout
1991
1992 \begin_layout Section
1993 TikZ
1994 \end_layout
1995
1996 \begin_layout Standard
1997 \begin_inset Flex URL
1998 status collapsed
1999
2000 \begin_layout Plain Layout
2001
2002 http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
2003 \end_layout
2004
2005 \end_inset
2006
2007
2008 \end_layout
2009
2010 \begin_layout Standard
2011 \begin_inset Preview
2012
2013 \begin_layout Standard
2014 \begin_inset ERT
2015 status collapsed
2016
2017 \begin_layout Plain Layout
2018
2019
2020 \backslash
2021 def
2022 \backslash
2023 iangle{35} % Angle of the inclined plane
2024 \end_layout
2025
2026 \begin_layout Plain Layout
2027
2028
2029 \backslash
2030 def
2031 \backslash
2032 down{-90}
2033 \end_layout
2034
2035 \begin_layout Plain Layout
2036
2037
2038 \backslash
2039 def
2040 \backslash
2041 arcr{0.5cm} % Radius of the arc used to indicate angles
2042 \end_layout
2043
2044 \begin_layout Plain Layout
2045
2046 \end_layout
2047
2048 \begin_layout Plain Layout
2049
2050
2051 \backslash
2052 begin{tikzpicture}[
2053 \end_layout
2054
2055 \begin_layout Plain Layout
2056
2057     force/.style={>=latex,draw=blue,fill=blue},
2058 \end_layout
2059
2060 \begin_layout Plain Layout
2061
2062     axis/.style={densely dashed,gray,font=
2063 \backslash
2064 small},
2065 \end_layout
2066
2067 \begin_layout Plain Layout
2068
2069     M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2070 \end_layout
2071
2072 \begin_layout Plain Layout
2073
2074     m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2075 \end_layout
2076
2077 \begin_layout Plain Layout
2078
2079     plane/.style={draw=black,fill=blue!10},
2080 \end_layout
2081
2082 \begin_layout Plain Layout
2083
2084     string/.style={draw=red, thick},
2085 \end_layout
2086
2087 \begin_layout Plain Layout
2088
2089     pulley/.style={thick},
2090 \end_layout
2091
2092 \begin_layout Plain Layout
2093
2094 ]
2095 \end_layout
2096
2097 \begin_layout Plain Layout
2098
2099 \end_layout
2100
2101 \begin_layout Plain Layout
2102
2103
2104 \backslash
2105 matrix[column sep=1cm] {
2106 \end_layout
2107
2108 \begin_layout Plain Layout
2109
2110     %% Sketch
2111 \end_layout
2112
2113 \begin_layout Plain Layout
2114
2115
2116 \backslash
2117 draw[plane] (0,-1) coordinate (base)
2118 \end_layout
2119
2120 \begin_layout Plain Layout
2121
2122                      -- coordinate[pos=0.5] (mid) ++(
2123 \backslash
2124 iangle:3) coordinate (top)
2125 \end_layout
2126
2127 \begin_layout Plain Layout
2128
2129                      |- (base) -- cycle;
2130 \end_layout
2131
2132 \begin_layout Plain Layout
2133
2134
2135 \backslash
2136 path (mid) node[M,rotate=
2137 \backslash
2138 iangle,yshift=0.25cm] (M) {};
2139 \end_layout
2140
2141 \begin_layout Plain Layout
2142
2143
2144 \backslash
2145 draw[pulley] (top) -- ++(
2146 \backslash
2147 iangle:0.25) circle (0.25cm)
2148 \end_layout
2149
2150 \begin_layout Plain Layout
2151
2152                    ++ (90-
2153 \backslash
2154 iangle:0.5) coordinate (pulley);
2155 \end_layout
2156
2157 \begin_layout Plain Layout
2158
2159
2160 \backslash
2161 draw[string] (M.east) -- ++(
2162 \backslash
2163 iangle:1.5cm) arc (90+
2164 \backslash
2165 iangle:0:0.25)
2166 \end_layout
2167
2168 \begin_layout Plain Layout
2169
2170                   -- ++(0,-1) node[m] {};
2171 \end_layout
2172
2173 \begin_layout Plain Layout
2174
2175 \end_layout
2176
2177 \begin_layout Plain Layout
2178
2179
2180 \backslash
2181 draw[->] (base)++(
2182 \backslash
2183 arcr,0) arc (0:
2184 \backslash
2185 iangle:
2186 \backslash
2187 arcr);
2188 \end_layout
2189
2190 \begin_layout Plain Layout
2191
2192
2193 \backslash
2194 path (base)++(
2195 \backslash
2196 iangle*0.5:
2197 \backslash
2198 arcr+5pt) node {$
2199 \backslash
2200 alpha$};
2201 \end_layout
2202
2203 \begin_layout Plain Layout
2204
2205     %%
2206 \end_layout
2207
2208 \begin_layout Plain Layout
2209
2210 \end_layout
2211
2212 \begin_layout Plain Layout
2213
2214 &
2215 \end_layout
2216
2217 \begin_layout Plain Layout
2218
2219     %% Free body diagram of M
2220 \end_layout
2221
2222 \begin_layout Plain Layout
2223
2224
2225 \backslash
2226 begin{scope}[rotate=
2227 \backslash
2228 iangle]
2229 \end_layout
2230
2231 \begin_layout Plain Layout
2232
2233
2234 \backslash
2235 node[M,transform shape] (M) {};
2236 \end_layout
2237
2238 \begin_layout Plain Layout
2239
2240         % Draw axes and help lines
2241 \end_layout
2242
2243 \begin_layout Plain Layout
2244
2245 \end_layout
2246
2247 \begin_layout Plain Layout
2248
2249         {[axis,->]
2250 \end_layout
2251
2252 \begin_layout Plain Layout
2253
2254
2255 \backslash
2256 draw (0,-1) -- (0,2) node[right] {$+y$};
2257 \end_layout
2258
2259 \begin_layout Plain Layout
2260
2261
2262 \backslash
2263 draw (M) -- ++(2,0) node[right] {$+x$};
2264 \end_layout
2265
2266 \begin_layout Plain Layout
2267
2268             % Indicate angle.
2269  The code is a bit awkward.
2270 \end_layout
2271
2272 \begin_layout Plain Layout
2273
2274 \end_layout
2275
2276 \begin_layout Plain Layout
2277
2278
2279 \backslash
2280 draw[solid,shorten >=0.5pt] (
2281 \backslash
2282 down-
2283 \backslash
2284 iangle:
2285 \backslash
2286 arcr)
2287 \end_layout
2288
2289 \begin_layout Plain Layout
2290
2291                 arc(
2292 \backslash
2293 down-
2294 \backslash
2295 iangle:
2296 \backslash
2297 down:
2298 \backslash
2299 arcr);
2300 \end_layout
2301
2302 \begin_layout Plain Layout
2303
2304
2305 \backslash
2306 node at (
2307 \backslash
2308 down-0.5*
2309 \backslash
2310 iangle:1.3*
2311 \backslash
2312 arcr) {$
2313 \backslash
2314 alpha$};
2315 \end_layout
2316
2317 \begin_layout Plain Layout
2318
2319         }
2320 \end_layout
2321
2322 \begin_layout Plain Layout
2323
2324 \end_layout
2325
2326 \begin_layout Plain Layout
2327
2328         % Forces
2329 \end_layout
2330
2331 \begin_layout Plain Layout
2332
2333         {[force,->]
2334 \end_layout
2335
2336 \begin_layout Plain Layout
2337
2338             % Assuming that Mg = 1.
2339  The normal force will therefore be cos(alpha)
2340 \end_layout
2341
2342 \begin_layout Plain Layout
2343
2344
2345 \backslash
2346 draw (M.center) -- ++(0,{cos(
2347 \backslash
2348 iangle)}) node[above right] {$N$};
2349 \end_layout
2350
2351 \begin_layout Plain Layout
2352
2353
2354 \backslash
2355 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2356 \end_layout
2357
2358 \begin_layout Plain Layout
2359
2360
2361 \backslash
2362 draw (M.east) -- ++(1,0) node[above] {$T$};
2363 \end_layout
2364
2365 \begin_layout Plain Layout
2366
2367         }
2368 \end_layout
2369
2370 \begin_layout Plain Layout
2371
2372 \end_layout
2373
2374 \begin_layout Plain Layout
2375
2376
2377 \backslash
2378 end{scope}
2379 \end_layout
2380
2381 \begin_layout Plain Layout
2382
2383     % Draw gravity force.
2384  The code is put outside the rotated
2385 \end_layout
2386
2387 \begin_layout Plain Layout
2388
2389     % scope for simplicity.
2390  No need to do any angle calculations.
2391
2392 \end_layout
2393
2394 \begin_layout Plain Layout
2395
2396
2397 \backslash
2398 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2399 \end_layout
2400
2401 \begin_layout Plain Layout
2402
2403     %%
2404 \end_layout
2405
2406 \begin_layout Plain Layout
2407
2408 \end_layout
2409
2410 \begin_layout Plain Layout
2411
2412 &
2413 \end_layout
2414
2415 \begin_layout Plain Layout
2416
2417     %%%
2418 \end_layout
2419
2420 \begin_layout Plain Layout
2421
2422     % Free body diagram of m
2423 \end_layout
2424
2425 \begin_layout Plain Layout
2426
2427
2428 \backslash
2429 node[m] (m) {};
2430 \end_layout
2431
2432 \begin_layout Plain Layout
2433
2434
2435 \backslash
2436 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2437 \end_layout
2438
2439 \begin_layout Plain Layout
2440
2441     {[force,->]
2442 \end_layout
2443
2444 \begin_layout Plain Layout
2445
2446
2447 \backslash
2448 draw (m.north) -- ++(0,1) node[above] {$T'$};
2449 \end_layout
2450
2451 \begin_layout Plain Layout
2452
2453
2454 \backslash
2455 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2456 \end_layout
2457
2458 \begin_layout Plain Layout
2459
2460     }
2461 \end_layout
2462
2463 \begin_layout Plain Layout
2464
2465 \end_layout
2466
2467 \begin_layout Plain Layout
2468
2469
2470 \backslash
2471
2472 \backslash
2473
2474 \end_layout
2475
2476 \begin_layout Plain Layout
2477
2478 };
2479 \end_layout
2480
2481 \begin_layout Plain Layout
2482
2483
2484 \backslash
2485 end{tikzpicture}
2486 \end_layout
2487
2488 \begin_layout Plain Layout
2489
2490 \end_layout
2491
2492 \end_inset
2493
2494
2495 \end_layout
2496
2497 \end_inset
2498
2499
2500 \end_layout
2501
2502 \end_body
2503 \end_document