lib/examples/instant_preview.lyx

   1 #LyX 2.2 created this file. For more info see http://www.lyx.org/
   2 \lyxformat 508
   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 \graphics default
  37 \default_output_format pdf
  38 \output_sync 0
  39 \bibtex_command default
  40 \index_command default
  41 \paperfontsize default
  42 \spacing single
  43 \use_hyperref false
  44 \papersize default
  45 \use_geometry false
  46 \use_package amsmath 1
  47 \use_package amssymb 1
  48 \use_package cancel 0
  49 \use_package esint 1
  50 \use_package mathdots 1
  51 \use_package mathtools 0
  52 \use_package mhchem 1
  53 \use_package stackrel 0
  54 \use_package stmaryrd 0
  55 \use_package undertilde 0
  56 \cite_engine basic
  57 \cite_engine_type default
  58 \biblio_style plain
  59 \use_bibtopic false
  60 \use_indices false
  61 \paperorientation portrait
  62 \suppress_date false
  63 \justification true
  64 \use_refstyle 0
  65 \index Index
  66 \shortcut idx
  67 \color #008000
  68 \end_index
  69 \secnumdepth 3
  70 \tocdepth 3
  71 \paragraph_separation indent
  72 \paragraph_indentation default
  73 \quotes_language english
  74 \papercolumns 1
  75 \papersides 1
  76 \paperpagestyle default
  77 \tracking_changes false
  78 \output_changes false
  79 \html_math_output 0
  80 \html_css_as_file 0
  81 \html_be_strict true
  82 \end_header
  83
  84 \begin_body
  85
  86 \begin_layout Section
  87 Introduction
  88 \end_layout
  89
  90 \begin_layout Standard
  91 In order to properly typeset the document and have instant preview working,
  92  the following packages have to be installed:
  93 \end_layout
  94
  95 \begin_layout LyX-Code
  96 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf, etex
  97 \end_layout
  98
  99 \begin_layout Standard
 100 Due to the use of postscript specials in Section
 101 \begin_inset CommandInset ref
 102 LatexCommand ref
 103 reference "sec:PSTricks"
 104
 105 \end_inset
 106
 107 , only the Postscript or PDF (ps2pdf) output formats will correctly render
 108  the included images.
 109  However, the PDF (Xe\SpecialChar TeX
 110 ) output seems to also work, while trying to typeset
 111  the document with
 112 \family typewriter
 113 pdflatex
 114 \family default
 115  or
 116 \family typewriter
 117 pdflualatex
 118 \family default
 119  will generate errors.
 120 \end_layout
 121
 122 \begin_layout Section
 123 Diagrams by XY(-pic)
 124 \end_layout
 125
 126 \begin_layout Standard
 127 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
 128  examples, see
 129 \begin_inset Flex URL
 130 status collapsed
 131
 132 \begin_layout Plain Layout
 133
 134 https://www.ctan.org/tex-archive/macros/generic/diagrams/xypic/doc/xyguide.pdf
 135 \end_layout
 136
 137 \end_inset
 138
 139 .
 140 \end_layout
 141
 142 \begin_layout Description
 143 Braid
 144 \end_layout
 145
 146 \begin_layout Standard
 147 \begin_inset Preview
 148
 149 \begin_layout Standard
 150 \begin_inset ERT
 151 status collapsed
 152
 153 \begin_layout Plain Layout
 154
 155
 156 \backslash
 157 xy
 158 \end_layout
 159
 160 \begin_layout Plain Layout
 161
 162 (5,10)*{}; (-10,-10)*{} **
 163 \backslash
 164 crv{(6,-2)&(-12,4)}
 165 \end_layout
 166
 167 \begin_layout Plain Layout
 168
 169
 170 \backslash
 171 POS?(.25)*{
 172 \backslash
 173 hole}="x"
 174 \backslash
 175 POS?(.45)*{
 176 \backslash
 177 hole}="y"
 178 \backslash
 179 POS?(.6)*{
 180 \backslash
 181 hole}="z";
 182 \end_layout
 183
 184 \begin_layout Plain Layout
 185
 186 "y"+(0,-1); (2,-10)*{} **
 187 \backslash
 188 crv{}
 189 \backslash
 190 POS?(.2)*{
 191 \backslash
 192 hole}="M";
 193 \end_layout
 194
 195 \begin_layout Plain Layout
 196
 197 (-10,10)*{}; "z" **
 198 \backslash
 199 crv{(-9,0)};
 200 \end_layout
 201
 202 \begin_layout Plain Layout
 203
 204 "z"; "M" **
 205 \backslash
 206 crv{};
 207 \end_layout
 208
 209 \begin_layout Plain Layout
 210
 211 "M"; "x" **
 212 \backslash
 213 crv{(5,0)};
 214 \end_layout
 215
 216 \begin_layout Plain Layout
 217
 218 "x"; "y" **
 219 \backslash
 220 crv{(0,7) & (-5,6)};
 221 \end_layout
 222
 223 \begin_layout Plain Layout
 224
 225
 226 \backslash
 227 endxy
 228 \end_layout
 229
 230 \end_inset
 231
 232
 233 \end_layout
 234
 235 \end_inset
 236
 237
 238 \end_layout
 239
 240 \begin_layout Description
 241 Knots
 242 \end_layout
 243
 244 \begin_layout Standard
 245 \begin_inset Preview
 246
 247 \begin_layout Standard
 248 \begin_inset ERT
 249 status collapsed
 250
 251 \begin_layout Plain Layout
 252
 253
 254 \backslash
 255 xy
 256 \end_layout
 257
 258 \begin_layout Plain Layout
 259
 260 (6,9)*{}="1";
 261 \end_layout
 262
 263 \begin_layout Plain Layout
 264
 265 (-8.5,-1)*{}="2";
 266 \end_layout
 267
 268 \begin_layout Plain Layout
 269
 270 "1";"2" **
 271 \backslash
 272 crv{~*=<.5pt>{.} (0,30)}?(.75)*
 273 \backslash
 274 dir{>}+(-2,2)*{z};
 275 \end_layout
 276
 277 \begin_layout Plain Layout
 278
 279 (-6.5,8)*{}="1";
 280 \end_layout
 281
 282 \begin_layout Plain Layout
 283
 284 (-.5,-9)*{}="2";
 285 \end_layout
 286
 287 \begin_layout Plain Layout
 288
 289 "1";"2" **
 290 \backslash
 291 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
 292 \backslash
 293 dir{>}+(-2,-2)*{u};
 294 \end_layout
 295
 296 \begin_layout Plain Layout
 297
 298 (-9.5,-3.35)*{}="1";
 299 \end_layout
 300
 301 \begin_layout Plain Layout
 302
 303 (8.5,-3)*{}="2";
 304 \end_layout
 305
 306 \begin_layout Plain Layout
 307
 308 "1";"2" **
 309 \backslash
 310 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
 311 \backslash
 312 dir{>}+(-1,-3)*{x};
 313 \end_layout
 314
 315 \begin_layout Plain Layout
 316
 317 (1,-10)*{}="1";
 318 \end_layout
 319
 320 \begin_layout Plain Layout
 321
 322 (6.5,7.13)*{}="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{>}+(3,-1)*{y};
 332 \end_layout
 333
 334 \begin_layout Plain Layout
 335
 336 (11,-1)*{}="1";
 337 \end_layout
 338
 339 \begin_layout Plain Layout
 340
 341 (-4,8)*{}="2";
 342 \end_layout
 343
 344 \begin_layout Plain Layout
 345
 346 "1";"2" **
 347 \backslash
 348 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
 349 \backslash
 350 dir{>}+(1,2)*{w};
 351 \end_layout
 352
 353 \begin_layout Plain Layout
 354
 355
 356 \backslash
 357 endxy
 358 \end_layout
 359
 360 \end_inset
 361
 362
 363 \end_layout
 364
 365 \end_inset
 366
 367
 368 \end_layout
 369
 370 \begin_layout Description
 371 Circles
 372 \end_layout
 373
 374 \begin_layout Standard
 375 \begin_inset Preview
 376
 377 \begin_layout Standard
 378 \begin_inset ERT
 379 status collapsed
 380
 381 \begin_layout Plain Layout
 382
 383
 384 \backslash
 385 xy
 386 \end_layout
 387
 388 \begin_layout Plain Layout
 389
 390 (0,0)*
 391 \backslash
 392 xycircle(14,8){++
 393 \backslash
 394 dir{<}};
 395 \end_layout
 396
 397 \begin_layout Plain Layout
 398
 399 (0,0)*
 400 \backslash
 401 xycircle<10pt>{{.}};
 402 \end_layout
 403
 404 \begin_layout Plain Layout
 405
 406 (0,0)*
 407 \backslash
 408 xycircle(5,2){:};
 409 \end_layout
 410
 411 \begin_layout Plain Layout
 412
 413 (0,15)*
 414 \backslash
 415 xycircle(10,4){--};
 416 \end_layout
 417
 418 \begin_layout Plain Layout
 419
 420
 421 \backslash
 422 endxy
 423 \end_layout
 424
 425 \end_inset
 426
 427
 428 \end_layout
 429
 430 \end_inset
 431
 432
 433 \end_layout
 434
 435 \begin_layout Description
 436 Cobordism
 437 \end_layout
 438
 439 \begin_layout Standard
 440 \begin_inset Preview
 441
 442 \begin_layout Standard
 443 \begin_inset ERT
 444 status collapsed
 445
 446 \begin_layout Plain Layout
 447
 448
 449 \backslash
 450 xy
 451 \end_layout
 452
 453 \begin_layout Plain Layout
 454
 455 (0,0)*
 456 \backslash
 457 ellipse(3,1){.};
 458 \end_layout
 459
 460 \begin_layout Plain Layout
 461
 462 (0,0)*
 463 \backslash
 464 ellipse(3,1)__,=:a(-180){-};
 465 \end_layout
 466
 467 \begin_layout Plain Layout
 468
 469 (-6,-8)*
 470 \backslash
 471 ellipse(3,1){.};
 472 \end_layout
 473
 474 \begin_layout Plain Layout
 475
 476 (6,-8)*
 477 \backslash
 478 ellipse(3,1){.};
 479 \end_layout
 480
 481 \begin_layout Plain Layout
 482
 483 (0,-8)*
 484 \backslash
 485 ellipse(3,1){.};
 486 \end_layout
 487
 488 \begin_layout Plain Layout
 489
 490 (-6,-8)*
 491 \backslash
 492 ellipse(3,1)__,=:a(-180){-};
 493 \end_layout
 494
 495 \begin_layout Plain Layout
 496
 497 (6,-8)*
 498 \backslash
 499 ellipse(3,1)__,=:a(-180){-};
 500 \end_layout
 501
 502 \begin_layout Plain Layout
 503
 504 (0,-8)*
 505 \backslash
 506 ellipse(3,1)__,=:a(180){-};
 507 \end_layout
 508
 509 \begin_layout Plain Layout
 510
 511 (-3,6)*
 512 \backslash
 513 ellipse(3,1){-};
 514 \end_layout
 515
 516 \begin_layout Plain Layout
 517
 518 (3,6)*
 519 \backslash
 520 ellipse(3,1){-};
 521 \end_layout
 522
 523 \begin_layout Plain Layout
 524
 525 (-3,12)*{}="1";
 526 \end_layout
 527
 528 \begin_layout Plain Layout
 529
 530 (3,12)*{}="2";
 531 \end_layout
 532
 533 \begin_layout Plain Layout
 534
 535 (-9,12)*{}="A2";
 536 \end_layout
 537
 538 \begin_layout Plain Layout
 539
 540 (9,12)*{}="B2";
 541 \end_layout
 542
 543 \begin_layout Plain Layout
 544
 545 "1";"2" **
 546 \backslash
 547 crv{(-3,7) & (3,7)};
 548 \end_layout
 549
 550 \begin_layout Plain Layout
 551
 552 (-3,0)*{}="A";
 553 \end_layout
 554
 555 \begin_layout Plain Layout
 556
 557 (3,0)*{}="B";
 558 \end_layout
 559
 560 \begin_layout Plain Layout
 561
 562 (-3,1)*{}="A1";
 563 \end_layout
 564
 565 \begin_layout Plain Layout
 566
 567 (3,1)*{}="B1";
 568 \end_layout
 569
 570 \begin_layout Plain Layout
 571
 572 "A";"A1" **
 573 \backslash
 574 dir{-};
 575 \end_layout
 576
 577 \begin_layout Plain Layout
 578
 579 "B";"B1" **
 580 \backslash
 581 dir{-};
 582 \end_layout
 583
 584 \begin_layout Plain Layout
 585
 586 "B2";"B1" **
 587 \backslash
 588 crv{(8,7) & (3,5)};
 589 \end_layout
 590
 591 \begin_layout Plain Layout
 592
 593 "A2";"A1" **
 594 \backslash
 595 crv{(-8,7) & (-3,5)};
 596 \end_layout
 597
 598 \begin_layout Plain Layout
 599
 600 %REFLECT
 601 \end_layout
 602
 603 \begin_layout Plain Layout
 604
 605 (3,-16)*{}="1";
 606 \end_layout
 607
 608 \begin_layout Plain Layout
 609
 610 (9,-16)*{}="2";
 611 \end_layout
 612
 613 \begin_layout Plain Layout
 614
 615 "1";"2" **
 616 \backslash
 617 crv{(3,-10) & (9,-10)};
 618 \end_layout
 619
 620 \begin_layout Plain Layout
 621
 622 (-3,-16)*{}="1";
 623 \end_layout
 624
 625 \begin_layout Plain Layout
 626
 627 (-9,-16)*{}="2";
 628 \end_layout
 629
 630 \begin_layout Plain Layout
 631
 632 "1";"2" **
 633 \backslash
 634 crv{(-3,-10) & (-9,-10)};
 635 \end_layout
 636
 637 \begin_layout Plain Layout
 638
 639 (-15,-16)*{}="A2";
 640 \end_layout
 641
 642 \begin_layout Plain Layout
 643
 644 (15,-16)*{}="B2";
 645 \end_layout
 646
 647 \begin_layout Plain Layout
 648
 649 (-3,0)*{}="A";
 650 \end_layout
 651
 652 \begin_layout Plain Layout
 653
 654 (3,0)*{}="B";
 655 \end_layout
 656
 657 \begin_layout Plain Layout
 658
 659 (-3,-1)*{}="A1";
 660 \end_layout
 661
 662 \begin_layout Plain Layout
 663
 664 (3,-1)*{}="B1";
 665 \end_layout
 666
 667 \begin_layout Plain Layout
 668
 669 "A";"A1" **
 670 \backslash
 671 dir{-};
 672 \end_layout
 673
 674 \begin_layout Plain Layout
 675
 676 "B";"B1" **
 677 \backslash
 678 dir{-};
 679 \end_layout
 680
 681 \begin_layout Plain Layout
 682
 683 "B2";"B1" **
 684 \backslash
 685 crv{(13,-6) & (2,-8)};
 686 \end_layout
 687
 688 \begin_layout Plain Layout
 689
 690 "A2";"A1" **
 691 \backslash
 692 crv{(-13,-6) & (-2,-8)};
 693 \end_layout
 694
 695 \begin_layout Plain Layout
 696
 697
 698 \backslash
 699 endxy
 700 \end_layout
 701
 702 \end_inset
 703
 704
 705 \end_layout
 706
 707 \end_inset
 708
 709
 710 \begin_inset Preview
 711
 712 \begin_layout Standard
 713 \begin_inset ERT
 714 status collapsed
 715
 716 \begin_layout Plain Layout
 717
 718
 719 \backslash
 720 xy 0;/r.18pc/:
 721 \end_layout
 722
 723 \begin_layout Plain Layout
 724
 725 (20,2)*{
 726 \backslash
 727 bullet}="RU"+(1,3)*{x^{
 728 \backslash
 729 ast}};
 730 \end_layout
 731
 732 \begin_layout Plain Layout
 733
 734 (16,-3)*{
 735 \backslash
 736 bullet}="RD"+(2.5,2)*{x^{
 737 \backslash
 738 ast}};
 739 \end_layout
 740
 741 \begin_layout Plain Layout
 742
 743 (-16,2)*{
 744 \backslash
 745 bullet}="LU"+(-1,2)*{x};
 746 \end_layout
 747
 748 \begin_layout Plain Layout
 749
 750 (-20,-3)*{
 751 \backslash
 752 bullet}="LD"+(-1,2)*{x};
 753 \end_layout
 754
 755 \begin_layout Plain Layout
 756
 757 "RU";"RD" **
 758 \backslash
 759 crv{(4,2) & (4,-1)}; ?(.1)*
 760 \backslash
 761 dir{<}; ?(.85)*
 762 \backslash
 763 dir{<};
 764 \end_layout
 765
 766 \begin_layout Plain Layout
 767
 768 "LD";"LU" **
 769 \backslash
 770 crv{(-4,-2) & (-4,1)};
 771 \end_layout
 772
 773 \begin_layout Plain Layout
 774
 775 ?(.08)*
 776 \backslash
 777 dir{<}; ?(.85)*
 778 \backslash
 779 dir{<};
 780 \end_layout
 781
 782 \begin_layout Plain Layout
 783
 784 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
 785 \end_layout
 786
 787 \begin_layout Plain Layout
 788
 789 "x1"; "x2" **
 790 \backslash
 791 crv{(7,-10) & (-7,-10)};
 792 \end_layout
 793
 794 \begin_layout Plain Layout
 795
 796 (16,-20)*{
 797 \backslash
 798 bullet}="RDD"+(2.5,-1)*{x^{
 799 \backslash
 800 ast}};
 801 \end_layout
 802
 803 \begin_layout Plain Layout
 804
 805 (-20,-20)*{
 806 \backslash
 807 bullet}="LDD"+(-1,-3)*{x};
 808 \end_layout
 809
 810 \begin_layout Plain Layout
 811
 812 (20,-12.5)*{
 813 \backslash
 814 bullet}="RUD"+(3.5,1)*{x^{
 815 \backslash
 816 ast}};
 817 \end_layout
 818
 819 \begin_layout Plain Layout
 820
 821 (-16,-15)*{
 822 \backslash
 823 bullet}="LUD";
 824 \end_layout
 825
 826 \begin_layout Plain Layout
 827
 828 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
 829 \end_layout
 830
 831 \begin_layout Plain Layout
 832
 833 "RD"; "RDD" **
 834 \backslash
 835 dir{-};
 836 \end_layout
 837
 838 \begin_layout Plain Layout
 839
 840 "LD"; "LDD" **
 841 \backslash
 842 dir{-};
 843 \end_layout
 844
 845 \begin_layout Plain Layout
 846
 847 "A"; "LUD" **
 848 \backslash
 849 dir{.};
 850 \end_layout
 851
 852 \begin_layout Plain Layout
 853
 854 "RDD"; "LDD" **
 855 \backslash
 856 crv{(0,-17)}; ?(.57)*
 857 \backslash
 858 dir{>};
 859 \end_layout
 860
 861 \begin_layout Plain Layout
 862
 863 "RU"; "RUD" **
 864 \backslash
 865 dir{-};
 866 \end_layout
 867
 868 \begin_layout Plain Layout
 869
 870 "LU"; "A" **
 871 \backslash
 872 dir{-};
 873 \end_layout
 874
 875 \begin_layout Plain Layout
 876
 877 "B"; "RUD" **
 878 \backslash
 879 crv{(18,-14.15)};
 880 \end_layout
 881
 882 \begin_layout Plain Layout
 883
 884 "B"; "LUD" **
 885 \backslash
 886 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
 887 \backslash
 888 dir{<};
 889 \end_layout
 890
 891 \begin_layout Plain Layout
 892
 893
 894 \backslash
 895 endxy
 896 \end_layout
 897
 898 \end_inset
 899
 900
 901 \end_layout
 902
 903 \end_inset
 904
 905
 906 \end_layout
 907
 908 \begin_layout Description
 909 Strings
 910 \end_layout
 911
 912 \begin_layout Standard
 913 \begin_inset Preview
 914
 915 \begin_layout Standard
 916 \begin_inset ERT
 917 status open
 918
 919 \begin_layout Plain Layout
 920
 921
 922 \backslash
 923 xy (-15,0)*{};(15,0)*{};
 924 \end_layout
 925
 926 \begin_layout Plain Layout
 927
 928
 929 \backslash
 930 endxy
 931 \end_layout
 932
 933 \begin_layout Plain Layout
 934
 935
 936 \backslash
 937 qquad =
 938 \backslash
 939 qquad
 940 \backslash
 941 xy
 942 \end_layout
 943
 944 \begin_layout Plain Layout
 945
 946 (-10,12)*{}; (-10,-12)*{}; **
 947 \backslash
 948 dir{-}?(.5)*
 949 \backslash
 950 dir{<}+(-4,0)*{F(x)};
 951 \end_layout
 952
 953 \begin_layout Plain Layout
 954
 955 (-2,12)*{}="1";
 956 \end_layout
 957
 958 \begin_layout Plain Layout
 959
 960 (6,-7) *{}="2";
 961 \end_layout
 962
 963 \begin_layout Plain Layout
 964
 965 (14,-7) *{}="3";
 966 \end_layout
 967
 968 \begin_layout Plain Layout
 969
 970 (14,-13)*{}="3'";
 971 \end_layout
 972
 973 \begin_layout Plain Layout
 974
 975 (18,0) *={}="";
 976 \end_layout
 977
 978 \begin_layout Plain Layout
 979
 980 "1";"2" **
 981 \backslash
 982 crv{(-4,-21)&(5,-15)};
 983 \end_layout
 984
 985 \begin_layout Plain Layout
 986
 987 ?(.15)*
 988 \backslash
 989 dir{<}+(5,10)*{
 990 \backslash
 991 overline{F(x)}};
 992 \end_layout
 993
 994 \begin_layout Plain Layout
 995
 996 "2";"3" **
 997 \backslash
 998 crv{(6,1)&(14,1)};
 999 \end_layout
1000
1001 \begin_layout Plain Layout
1002
1003 ?(0)*
1004 \backslash
1005 dir{<}+(4,8)*{
1006 \backslash
1007 widetilde{F(i_x)}} ;
1008 \end_layout
1009
1010 \begin_layout Plain Layout
1011
1012 ?(.95)*
1013 \backslash
1014 dir{<}+(5,-2)*{F(
1015 \backslash
1016 overline x)};
1017 \end_layout
1018
1019 \begin_layout Plain Layout
1020
1021 "3";"3'" **
1022 \backslash
1023 dir{-};
1024 \end_layout
1025
1026 \begin_layout Plain Layout
1027
1028 (-2,6)*{}="X1";
1029 \end_layout
1030
1031 \begin_layout Plain Layout
1032
1033 (-10,6)*{}="X2";
1034 \end_layout
1035
1036 \begin_layout Plain Layout
1037
1038 "X1";"X2" **
1039 \backslash
1040 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1041 \end_layout
1042
1043 \begin_layout Plain Layout
1044
1045 (-2,-6)*{}="XA";
1046 \end_layout
1047
1048 \begin_layout Plain Layout
1049
1050 (-10,-6)*{}="XB";
1051 \end_layout
1052
1053 \begin_layout Plain Layout
1054
1055 "XA";"XB" **
1056 \backslash
1057 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1058 \end_layout
1059
1060 \begin_layout Plain Layout
1061
1062
1063 \backslash
1064 endxy
1065 \end_layout
1066
1067 \end_inset
1068
1069
1070 \end_layout
1071
1072 \end_inset
1073
1074
1075 \end_layout
1076
1077 \begin_layout Description
1078 Categories
1079 \end_layout
1080
1081 \begin_layout Standard
1082 \begin_inset Preview
1083
1084 \begin_layout Standard
1085 \begin_inset ERT
1086 status collapsed
1087
1088 \begin_layout Plain Layout
1089
1090
1091 \backslash
1092 xymatrix{
1093 \end_layout
1094
1095 \begin_layout Plain Layout
1096
1097 (x
1098 \backslash
1099 otimes 1)
1100 \backslash
1101 otimes y
1102 \end_layout
1103
1104 \begin_layout Plain Layout
1105
1106
1107 \backslash
1108 ar[rr]^{a_{x,1,y}}
1109 \end_layout
1110
1111 \begin_layout Plain Layout
1112
1113
1114 \backslash
1115 ar[dr]_{r_x
1116 \backslash
1117 otimes 1_y}
1118 \end_layout
1119
1120 \begin_layout Plain Layout
1121
1122 && x
1123 \backslash
1124 otimes(1
1125 \backslash
1126 otimes y)
1127 \end_layout
1128
1129 \begin_layout Plain Layout
1130
1131
1132 \backslash
1133 ar[dl]^{1_x
1134 \backslash
1135 otimes
1136 \backslash
1137 ell_y }
1138 \backslash
1139
1140 \backslash
1141
1142 \end_layout
1143
1144 \begin_layout Plain Layout
1145
1146 & x
1147 \backslash
1148 otimes y }
1149 \end_layout
1150
1151 \end_inset
1152
1153
1154 \end_layout
1155
1156 \end_inset
1157
1158
1159 \begin_inset Preview
1160
1161 \begin_layout Standard
1162 \begin_inset ERT
1163 status collapsed
1164
1165 \begin_layout Plain Layout
1166
1167
1168 \backslash
1169 xy
1170 \end_layout
1171
1172 \begin_layout Plain Layout
1173
1174 (-9,0)*+{
1175 \backslash
1176 bullet}="1";
1177 \end_layout
1178
1179 \begin_layout Plain Layout
1180
1181 (0,0)*+{
1182 \backslash
1183 bullet}="2";
1184 \end_layout
1185
1186 \begin_layout Plain Layout
1187
1188 {
1189 \backslash
1190 ar@/^.9pc/ "1";"2"};
1191 \end_layout
1192
1193 \begin_layout Plain Layout
1194
1195 {
1196 \backslash
1197 ar@/_.9pc/ "1";"2"};
1198 \end_layout
1199
1200 \begin_layout Plain Layout
1201
1202 {
1203 \backslash
1204 ar@/^2pc/ "1";"2"};
1205 \end_layout
1206
1207 \begin_layout Plain Layout
1208
1209 {
1210 \backslash
1211 ar@/_2pc/ "1";"2"};
1212 \end_layout
1213
1214 \begin_layout Plain Layout
1215
1216 {
1217 \backslash
1218 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1219 \end_layout
1220
1221 \begin_layout Plain Layout
1222
1223 {
1224 \backslash
1225 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1226 \end_layout
1227
1228 \begin_layout Plain Layout
1229
1230 {
1231 \backslash
1232 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1233 \end_layout
1234
1235 \begin_layout Plain Layout
1236
1237 (0,0)*+{
1238 \backslash
1239 bullet}="1";
1240 \end_layout
1241
1242 \begin_layout Plain Layout
1243
1244 (9,0)*+{
1245 \backslash
1246 bullet}="2";
1247 \end_layout
1248
1249 \begin_layout Plain Layout
1250
1251 (18,0)*+{
1252 \backslash
1253 bullet}="3";
1254 \end_layout
1255
1256 \begin_layout Plain Layout
1257
1258 {
1259 \backslash
1260 ar "1";"2"};
1261 \end_layout
1262
1263 \begin_layout Plain Layout
1264
1265 {
1266 \backslash
1267 ar "2";"3"};
1268 \end_layout
1269
1270 \begin_layout Plain Layout
1271
1272 {
1273 \backslash
1274 ar@/^1pc/ "1";"2"};
1275 \end_layout
1276
1277 \begin_layout Plain Layout
1278
1279 {
1280 \backslash
1281 ar@/_1pc/ "1";"2"};
1282 \end_layout
1283
1284 \begin_layout Plain Layout
1285
1286 {
1287 \backslash
1288 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1289 \end_layout
1290
1291 \begin_layout Plain Layout
1292
1293 {
1294 \backslash
1295 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1296 \end_layout
1297
1298 \begin_layout Plain Layout
1299
1300
1301 \backslash
1302 endxy
1303 \end_layout
1304
1305 \end_inset
1306
1307
1308 \end_layout
1309
1310 \end_inset
1311
1312
1313 \end_layout
1314
1315 \begin_layout Description
1316 Transformations
1317 \end_layout
1318
1319 \begin_layout Standard
1320 \begin_inset Preview
1321
1322 \begin_layout Standard
1323 \begin_inset ERT
1324 status collapsed
1325
1326 \begin_layout Plain Layout
1327
1328
1329 \backslash
1330 xy %FIG.19.
1331  Natural transformation between functors.
1332 \end_layout
1333
1334 \begin_layout Plain Layout
1335
1336 (-26,-2)*+{
1337 \backslash
1338 bullet}="a";
1339 \end_layout
1340
1341 \begin_layout Plain Layout
1342
1343 (-12,3)*+{
1344 \backslash
1345 bullet}="b";
1346 \end_layout
1347
1348 \begin_layout Plain Layout
1349
1350 (-16,-5)*+{
1351 \backslash
1352 bullet}="c";
1353 \end_layout
1354
1355 \begin_layout Plain Layout
1356
1357 {
1358 \backslash
1359 ar@/^.25pc/ "a";"b"};
1360 \end_layout
1361
1362 \begin_layout Plain Layout
1363
1364 {
1365 \backslash
1366 ar@/_.25pc/"a";"c"};
1367 \end_layout
1368
1369 \begin_layout Plain Layout
1370
1371 {
1372 \backslash
1373 ar@/_.15pc/ "b";"c"};
1374 \end_layout
1375
1376 \begin_layout Plain Layout
1377
1378 %START TOP
1379 \end_layout
1380
1381 \begin_layout Plain Layout
1382
1383 (12,10)*+{
1384 \backslash
1385 bullet}="ta";
1386 \end_layout
1387
1388 \begin_layout Plain Layout
1389
1390 (26,15)*+{
1391 \backslash
1392 bullet}="tb";
1393 \end_layout
1394
1395 \begin_layout Plain Layout
1396
1397 (22,8)*+{
1398 \backslash
1399 bullet}="tc";
1400 \end_layout
1401
1402 \begin_layout Plain Layout
1403
1404 {
1405 \backslash
1406 ar@/^.25pc/ "ta";"tb"};
1407 \end_layout
1408
1409 \begin_layout Plain Layout
1410
1411 {
1412 \backslash
1413 ar@/_.25pc/ "ta";"tc"};
1414 \end_layout
1415
1416 \begin_layout Plain Layout
1417
1418 {
1419 \backslash
1420 ar@/_.15pc/ "tb";"tc"};
1421 \end_layout
1422
1423 \begin_layout Plain Layout
1424
1425 %START bottom
1426 \end_layout
1427
1428 \begin_layout Plain Layout
1429
1430 (12,-10)*+{
1431 \backslash
1432 bullet}="ba";
1433 \end_layout
1434
1435 \begin_layout Plain Layout
1436
1437 (26,-5)*+{
1438 \backslash
1439 bullet}="bb";
1440 \end_layout
1441
1442 \begin_layout Plain Layout
1443
1444 (22,-12)*+{
1445 \backslash
1446 bullet}="bc";
1447 \end_layout
1448
1449 \begin_layout Plain Layout
1450
1451 {
1452 \backslash
1453 ar@/^.25pc/@{.>} "ba";"bb"};
1454 \end_layout
1455
1456 \begin_layout Plain Layout
1457
1458 {
1459 \backslash
1460 ar@/_.25pc/ "ba";"bc"};
1461 \end_layout
1462
1463 \begin_layout Plain Layout
1464
1465 {
1466 \backslash
1467 ar@/_.15pc/ "bb";"bc"};
1468 \end_layout
1469
1470 \begin_layout Plain Layout
1471
1472 %START CONNECT
1473 \end_layout
1474
1475 \begin_layout Plain Layout
1476
1477 {
1478 \backslash
1479 ar@/_.15pc/ "ta";"ba"};
1480 \end_layout
1481
1482 \begin_layout Plain Layout
1483
1484 {
1485 \backslash
1486 ar@/_.15pc/ "tb";"bb"};
1487 \end_layout
1488
1489 \begin_layout Plain Layout
1490
1491 {
1492 \backslash
1493 ar@/_.15pc/ "tc";"bc"};
1494 \end_layout
1495
1496 \begin_layout Plain Layout
1497
1498 %START ARROWS AND LABELS
1499 \end_layout
1500
1501 \begin_layout Plain Layout
1502
1503 (-12,6)*{}="DF";
1504 \end_layout
1505
1506 \begin_layout Plain Layout
1507
1508 (6,10)*{}="CF";
1509 \end_layout
1510
1511 \begin_layout Plain Layout
1512
1513 {
1514 \backslash
1515 ar@/^.35pc/^F "DF";"CF"};
1516 \end_layout
1517
1518 \begin_layout Plain Layout
1519
1520 (-12,-6)*{}="DF";
1521 \end_layout
1522
1523 \begin_layout Plain Layout
1524
1525 (6,-10)*{}="CF";
1526 \end_layout
1527
1528 \begin_layout Plain Layout
1529
1530 {
1531 \backslash
1532 ar@/_.35pc/_G "DF";"CF"};
1533 \end_layout
1534
1535 \begin_layout Plain Layout
1536
1537 (-2,5)*{}="DF";
1538 \end_layout
1539
1540 \begin_layout Plain Layout
1541
1542 (-2,-5)*{}="CF";
1543 \end_layout
1544
1545 \begin_layout Plain Layout
1546
1547 {
1548 \backslash
1549 ar@{=>}^{
1550 \backslash
1551 alpha} "DF";"CF"};
1552 \end_layout
1553
1554 \begin_layout Plain Layout
1555
1556 (29,3)*{D};
1557 \end_layout
1558
1559 \begin_layout Plain Layout
1560
1561 (-23,3)*{C};
1562 \end_layout
1563
1564 \begin_layout Plain Layout
1565
1566
1567 \backslash
1568 endxy
1569 \end_layout
1570
1571 \end_inset
1572
1573
1574 \end_layout
1575
1576 \end_inset
1577
1578
1579 \end_layout
1580
1581 \begin_layout Section
1582 IPA
1583 \end_layout
1584
1585 \begin_layout Standard
1586 \begin_inset Preview
1587
1588 \begin_layout Standard
1589 \begin_inset ERT
1590 status collapsed
1591
1592 \begin_layout Plain Layout
1593
1594
1595 \backslash
1596 textipa{Ekspl@"neIS@n}
1597 \end_layout
1598
1599 \end_inset
1600
1601
1602 \end_layout
1603
1604 \end_inset
1605
1606
1607 \end_layout
1608
1609 \begin_layout Section
1610 QTree
1611 \end_layout
1612
1613 \begin_layout Standard
1614 \begin_inset Preview
1615
1616 \begin_layout Standard
1617 \begin_inset ERT
1618 status collapsed
1619
1620 \begin_layout Plain Layout
1621
1622
1623 \backslash
1624 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1625 \end_layout
1626
1627 \end_inset
1628
1629
1630 \end_layout
1631
1632 \end_inset
1633
1634
1635 \begin_inset Preview
1636
1637 \begin_layout Standard
1638 \begin_inset ERT
1639 status collapsed
1640
1641 \begin_layout Plain Layout
1642
1643
1644 \backslash
1645 Tree [.$
1646 \backslash
1647 sigma$ $
1648 \backslash
1649 mu$ $
1650 \backslash
1651 mu$ ]
1652 \end_layout
1653
1654 \end_inset
1655
1656
1657 \end_layout
1658
1659 \end_inset
1660
1661
1662 \end_layout
1663
1664 \begin_layout Section
1665 PSTricks
1666 \begin_inset CommandInset label
1667 LatexCommand label
1668 name "sec:PSTricks"
1669
1670 \end_inset
1671
1672
1673 \end_layout
1674
1675 \begin_layout Standard
1676 Some simple graphing examples.
1677 \end_layout
1678
1679 \begin_layout Subsection
1680 Function plotting
1681 \end_layout
1682
1683 \begin_layout Standard
1684 \begin_inset Preview
1685
1686 \begin_layout Standard
1687 \begin_inset ERT
1688 status open
1689
1690 \begin_layout Plain Layout
1691
1692
1693 \backslash
1694 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1695 \end_layout
1696
1697 \begin_layout Plain Layout
1698
1699
1700 \backslash
1701 psaxes{->}(0,0)(0,-3)(10,3)
1702 \end_layout
1703
1704 \begin_layout Plain Layout
1705
1706
1707 \backslash
1708 uput[-90](10,0){$x$}
1709 \backslash
1710 uput[0](0,3){$f(x)$}
1711 \end_layout
1712
1713 \begin_layout Plain Layout
1714
1715
1716 \backslash
1717 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1718 \end_layout
1719
1720 \begin_layout Plain Layout
1721
1722
1723 \backslash
1724 end{pspicture*}
1725 \end_layout
1726
1727 \end_inset
1728
1729
1730 \end_layout
1731
1732 \end_inset
1733
1734
1735 \end_layout
1736
1737 \begin_layout Subsection
1738 Inline data plotting
1739 \end_layout
1740
1741 \begin_layout Standard
1742 \align center
1743 \begin_inset Preview
1744
1745 \begin_layout Standard
1746 \align center
1747 \begin_inset ERT
1748 status open
1749
1750 \begin_layout Plain Layout
1751
1752
1753 \backslash
1754 begin{pspicture*}(-1.5,-1.5)(11,5)
1755 \end_layout
1756
1757 \begin_layout Plain Layout
1758
1759
1760 \backslash
1761 psaxes{->}(0,0)(0,0)(10,5)
1762 \end_layout
1763
1764 \begin_layout Plain Layout
1765
1766
1767 \backslash
1768 psset{linewidth=2.5pt}
1769 \end_layout
1770
1771 \begin_layout Plain Layout
1772
1773
1774 \backslash
1775 rput(5.0,-1.0){Speed [MPH]}
1776 \end_layout
1777
1778 \begin_layout Plain Layout
1779
1780
1781 \backslash
1782 rput(-1.0,1.0){
1783 \backslash
1784 begin{rotate}{90}Cost [Dollars]
1785 \backslash
1786 end{rotate}}
1787 \end_layout
1788
1789 \begin_layout Plain Layout
1790
1791
1792 \backslash
1793 savedata{
1794 \backslash
1795 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1796 \end_layout
1797
1798 \begin_layout Plain Layout
1799
1800
1801 \backslash
1802 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1803 \backslash
1804 mydata}
1805 \end_layout
1806
1807 \begin_layout Plain Layout
1808
1809
1810 \backslash
1811 end{pspicture*}
1812 \end_layout
1813
1814 \end_inset
1815
1816
1817 \end_layout
1818
1819 \end_inset
1820
1821
1822 \end_layout
1823
1824 \begin_layout Subsection
1825 Lissajous curves
1826 \end_layout
1827
1828 \begin_layout Standard
1829 \begin_inset Preview
1830
1831 \begin_layout Standard
1832 \begin_inset ERT
1833 status open
1834
1835 \begin_layout Plain Layout
1836
1837
1838 \backslash
1839 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1840 \end_layout
1841
1842 \begin_layout Plain Layout
1843
1844
1845 \backslash
1846 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1847  cos 100 t mul sin}
1848 \end_layout
1849
1850 \begin_layout Plain Layout
1851
1852
1853 \backslash
1854 end{pspicture*}
1855 \end_layout
1856
1857 \end_inset
1858
1859
1860 \end_layout
1861
1862 \end_inset
1863
1864
1865 \begin_inset space \hfill{}
1866 \end_inset
1867
1868
1869 \begin_inset Preview
1870
1871 \begin_layout Standard
1872 \begin_inset ERT
1873 status open
1874
1875 \begin_layout Plain Layout
1876
1877
1878 \backslash
1879 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1880 \end_layout
1881
1882 \begin_layout Plain Layout
1883
1884
1885 \backslash
1886 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1887  mul cos 100 t mul sin}
1888 \end_layout
1889
1890 \begin_layout Plain Layout
1891
1892
1893 \backslash
1894 end{pspicture*}
1895 \end_layout
1896
1897 \end_inset
1898
1899
1900 \end_layout
1901
1902 \end_inset
1903
1904
1905 \begin_inset space \hfill{}
1906 \end_inset
1907
1908
1909 \begin_inset Preview
1910
1911 \begin_layout Standard
1912 \begin_inset ERT
1913 status open
1914
1915 \begin_layout Plain Layout
1916
1917
1918 \backslash
1919 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1920 \end_layout
1921
1922 \begin_layout Plain Layout
1923
1924
1925 \backslash
1926 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1927  mul cos 200 t mul sin}
1928 \end_layout
1929
1930 \begin_layout Plain Layout
1931
1932
1933 \backslash
1934 end{pspicture*}
1935 \end_layout
1936
1937 \end_inset
1938
1939
1940 \end_layout
1941
1942 \end_inset
1943
1944
1945 \begin_inset space \hfill{}
1946 \end_inset
1947
1948
1949 \begin_inset Preview
1950
1951 \begin_layout Standard
1952 \begin_inset ERT
1953 status open
1954
1955 \begin_layout Plain Layout
1956
1957
1958 \backslash
1959 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1960 \end_layout
1961
1962 \begin_layout Plain Layout
1963
1964
1965 \backslash
1966 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1967  mul cos 200 t mul sin}
1968 \end_layout
1969
1970 \begin_layout Plain Layout
1971
1972
1973 \backslash
1974 end{pspicture*}
1975 \end_layout
1976
1977 \end_inset
1978
1979
1980 \end_layout
1981
1982 \end_inset
1983
1984
1985 \end_layout
1986
1987 \begin_layout Section
1988 TikZ
1989 \end_layout
1990
1991 \begin_layout Standard
1992 \begin_inset Flex URL
1993 status collapsed
1994
1995 \begin_layout Plain Layout
1996
1997 http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
1998 \end_layout
1999
2000 \end_inset
2001
2002
2003 \end_layout
2004
2005 \begin_layout Standard
2006 \begin_inset Preview
2007
2008 \begin_layout Standard
2009 \begin_inset ERT
2010 status collapsed
2011
2012 \begin_layout Plain Layout
2013
2014
2015 \backslash
2016 def
2017 \backslash
2018 iangle{35} % Angle of the inclined plane
2019 \end_layout
2020
2021 \begin_layout Plain Layout
2022
2023
2024 \backslash
2025 def
2026 \backslash
2027 down{-90}
2028 \end_layout
2029
2030 \begin_layout Plain Layout
2031
2032
2033 \backslash
2034 def
2035 \backslash
2036 arcr{0.5cm} % Radius of the arc used to indicate angles
2037 \end_layout
2038
2039 \begin_layout Plain Layout
2040
2041 \end_layout
2042
2043 \begin_layout Plain Layout
2044
2045
2046 \backslash
2047 begin{tikzpicture}[
2048 \end_layout
2049
2050 \begin_layout Plain Layout
2051
2052     force/.style={>=latex,draw=blue,fill=blue},
2053 \end_layout
2054
2055 \begin_layout Plain Layout
2056
2057     axis/.style={densely dashed,gray,font=
2058 \backslash
2059 small},
2060 \end_layout
2061
2062 \begin_layout Plain Layout
2063
2064     M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2065 \end_layout
2066
2067 \begin_layout Plain Layout
2068
2069     m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2070 \end_layout
2071
2072 \begin_layout Plain Layout
2073
2074     plane/.style={draw=black,fill=blue!10},
2075 \end_layout
2076
2077 \begin_layout Plain Layout
2078
2079     string/.style={draw=red, thick},
2080 \end_layout
2081
2082 \begin_layout Plain Layout
2083
2084     pulley/.style={thick},
2085 \end_layout
2086
2087 \begin_layout Plain Layout
2088
2089 ]
2090 \end_layout
2091
2092 \begin_layout Plain Layout
2093
2094 \end_layout
2095
2096 \begin_layout Plain Layout
2097
2098
2099 \backslash
2100 matrix[column sep=1cm] {
2101 \end_layout
2102
2103 \begin_layout Plain Layout
2104
2105     %% Sketch
2106 \end_layout
2107
2108 \begin_layout Plain Layout
2109
2110
2111 \backslash
2112 draw[plane] (0,-1) coordinate (base)
2113 \end_layout
2114
2115 \begin_layout Plain Layout
2116
2117                      -- coordinate[pos=0.5] (mid) ++(
2118 \backslash
2119 iangle:3) coordinate (top)
2120 \end_layout
2121
2122 \begin_layout Plain Layout
2123
2124                      |- (base) -- cycle;
2125 \end_layout
2126
2127 \begin_layout Plain Layout
2128
2129
2130 \backslash
2131 path (mid) node[M,rotate=
2132 \backslash
2133 iangle,yshift=0.25cm] (M) {};
2134 \end_layout
2135
2136 \begin_layout Plain Layout
2137
2138
2139 \backslash
2140 draw[pulley] (top) -- ++(
2141 \backslash
2142 iangle:0.25) circle (0.25cm)
2143 \end_layout
2144
2145 \begin_layout Plain Layout
2146
2147                    ++ (90-
2148 \backslash
2149 iangle:0.5) coordinate (pulley);
2150 \end_layout
2151
2152 \begin_layout Plain Layout
2153
2154
2155 \backslash
2156 draw[string] (M.east) -- ++(
2157 \backslash
2158 iangle:1.5cm) arc (90+
2159 \backslash
2160 iangle:0:0.25)
2161 \end_layout
2162
2163 \begin_layout Plain Layout
2164
2165                   -- ++(0,-1) node[m] {};
2166 \end_layout
2167
2168 \begin_layout Plain Layout
2169
2170 \end_layout
2171
2172 \begin_layout Plain Layout
2173
2174
2175 \backslash
2176 draw[->] (base)++(
2177 \backslash
2178 arcr,0) arc (0:
2179 \backslash
2180 iangle:
2181 \backslash
2182 arcr);
2183 \end_layout
2184
2185 \begin_layout Plain Layout
2186
2187
2188 \backslash
2189 path (base)++(
2190 \backslash
2191 iangle*0.5:
2192 \backslash
2193 arcr+5pt) node {$
2194 \backslash
2195 alpha$};
2196 \end_layout
2197
2198 \begin_layout Plain Layout
2199
2200     %%
2201 \end_layout
2202
2203 \begin_layout Plain Layout
2204
2205 \end_layout
2206
2207 \begin_layout Plain Layout
2208
2209 &
2210 \end_layout
2211
2212 \begin_layout Plain Layout
2213
2214     %% Free body diagram of M
2215 \end_layout
2216
2217 \begin_layout Plain Layout
2218
2219
2220 \backslash
2221 begin{scope}[rotate=
2222 \backslash
2223 iangle]
2224 \end_layout
2225
2226 \begin_layout Plain Layout
2227
2228
2229 \backslash
2230 node[M,transform shape] (M) {};
2231 \end_layout
2232
2233 \begin_layout Plain Layout
2234
2235         % Draw axes and help lines
2236 \end_layout
2237
2238 \begin_layout Plain Layout
2239
2240 \end_layout
2241
2242 \begin_layout Plain Layout
2243
2244         {[axis,->]
2245 \end_layout
2246
2247 \begin_layout Plain Layout
2248
2249
2250 \backslash
2251 draw (0,-1) -- (0,2) node[right] {$+y$};
2252 \end_layout
2253
2254 \begin_layout Plain Layout
2255
2256
2257 \backslash
2258 draw (M) -- ++(2,0) node[right] {$+x$};
2259 \end_layout
2260
2261 \begin_layout Plain Layout
2262
2263             % Indicate angle.
2264  The code is a bit awkward.
2265 \end_layout
2266
2267 \begin_layout Plain Layout
2268
2269 \end_layout
2270
2271 \begin_layout Plain Layout
2272
2273
2274 \backslash
2275 draw[solid,shorten >=0.5pt] (
2276 \backslash
2277 down-
2278 \backslash
2279 iangle:
2280 \backslash
2281 arcr)
2282 \end_layout
2283
2284 \begin_layout Plain Layout
2285
2286                 arc(
2287 \backslash
2288 down-
2289 \backslash
2290 iangle:
2291 \backslash
2292 down:
2293 \backslash
2294 arcr);
2295 \end_layout
2296
2297 \begin_layout Plain Layout
2298
2299
2300 \backslash
2301 node at (
2302 \backslash
2303 down-0.5*
2304 \backslash
2305 iangle:1.3*
2306 \backslash
2307 arcr) {$
2308 \backslash
2309 alpha$};
2310 \end_layout
2311
2312 \begin_layout Plain Layout
2313
2314         }
2315 \end_layout
2316
2317 \begin_layout Plain Layout
2318
2319 \end_layout
2320
2321 \begin_layout Plain Layout
2322
2323         % Forces
2324 \end_layout
2325
2326 \begin_layout Plain Layout
2327
2328         {[force,->]
2329 \end_layout
2330
2331 \begin_layout Plain Layout
2332
2333             % Assuming that Mg = 1.
2334  The normal force will therefore be cos(alpha)
2335 \end_layout
2336
2337 \begin_layout Plain Layout
2338
2339
2340 \backslash
2341 draw (M.center) -- ++(0,{cos(
2342 \backslash
2343 iangle)}) node[above right] {$N$};
2344 \end_layout
2345
2346 \begin_layout Plain Layout
2347
2348
2349 \backslash
2350 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2351 \end_layout
2352
2353 \begin_layout Plain Layout
2354
2355
2356 \backslash
2357 draw (M.east) -- ++(1,0) node[above] {$T$};
2358 \end_layout
2359
2360 \begin_layout Plain Layout
2361
2362         }
2363 \end_layout
2364
2365 \begin_layout Plain Layout
2366
2367 \end_layout
2368
2369 \begin_layout Plain Layout
2370
2371
2372 \backslash
2373 end{scope}
2374 \end_layout
2375
2376 \begin_layout Plain Layout
2377
2378     % Draw gravity force.
2379  The code is put outside the rotated
2380 \end_layout
2381
2382 \begin_layout Plain Layout
2383
2384     % scope for simplicity.
2385  No need to do any angle calculations.
2386
2387 \end_layout
2388
2389 \begin_layout Plain Layout
2390
2391
2392 \backslash
2393 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2394 \end_layout
2395
2396 \begin_layout Plain Layout
2397
2398     %%
2399 \end_layout
2400
2401 \begin_layout Plain Layout
2402
2403 \end_layout
2404
2405 \begin_layout Plain Layout
2406
2407 &
2408 \end_layout
2409
2410 \begin_layout Plain Layout
2411
2412     %%%
2413 \end_layout
2414
2415 \begin_layout Plain Layout
2416
2417     % Free body diagram of m
2418 \end_layout
2419
2420 \begin_layout Plain Layout
2421
2422
2423 \backslash
2424 node[m] (m) {};
2425 \end_layout
2426
2427 \begin_layout Plain Layout
2428
2429
2430 \backslash
2431 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2432 \end_layout
2433
2434 \begin_layout Plain Layout
2435
2436     {[force,->]
2437 \end_layout
2438
2439 \begin_layout Plain Layout
2440
2441
2442 \backslash
2443 draw (m.north) -- ++(0,1) node[above] {$T'$};
2444 \end_layout
2445
2446 \begin_layout Plain Layout
2447
2448
2449 \backslash
2450 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2451 \end_layout
2452
2453 \begin_layout Plain Layout
2454
2455     }
2456 \end_layout
2457
2458 \begin_layout Plain Layout
2459
2460 \end_layout
2461
2462 \begin_layout Plain Layout
2463
2464
2465 \backslash
2466
2467 \backslash
2468
2469 \end_layout
2470
2471 \begin_layout Plain Layout
2472
2473 };
2474 \end_layout
2475
2476 \begin_layout Plain Layout
2477
2478
2479 \backslash
2480 end{tikzpicture}
2481 \end_layout
2482
2483 \begin_layout Plain Layout
2484
2485 \end_layout
2486
2487 \end_inset
2488
2489
2490 \end_layout
2491
2492 \end_inset
2493
2494
2495 \end_layout
2496
2497 \end_body
2498 \end_document