lib/examples/instant_preview.lyx

   1 #LyX 2.0 created this file. For more info see http://www.lyx.org/
   2 \lyxformat 413
   3 \begin_document
   4 \begin_header
   5 \textclass article
   6 \begin_preamble
   7 \usepackage[all, knot]{xy}
   8 \xyoption{arc}
   9 \usepackage{qtree}
  10 \usepackage{tipa}
  11 \usepackage{pstricks}
  12 \usepackage{pst-plot}
  13 \usepackage{rotating}
  14 \usepackage{tikz}
  15 \usetikzlibrary{scopes}
  16 \end_preamble
  17 \use_default_options false
  18 \maintain_unincluded_children false
  19 \language english
  20 \language_package default
  21 \inputencoding auto
  22 \fontencoding global
  23 \font_roman lmodern
  24 \font_sans default
  25 \font_typewriter default
  26 \font_default_family default
  27 \use_non_tex_fonts false
  28 \font_sc false
  29 \font_osf false
  30 \font_sf_scale 100
  31 \font_tt_scale 100
  32
  33 \graphics default
  34 \default_output_format default
  35 \output_sync 0
  36 \bibtex_command default
  37 \index_command default
  38 \paperfontsize default
  39 \spacing single
  40 \use_hyperref false
  41 \papersize default
  42 \use_geometry false
  43 \use_amsmath 1
  44 \use_esint 1
  45 \use_mhchem 1
  46 \use_mathdots 1
  47 \cite_engine basic
  48 \use_bibtopic false
  49 \use_indices false
  50 \paperorientation portrait
  51 \suppress_date false
  52 \use_refstyle 0
  53 \index Index
  54 \shortcut idx
  55 \color #008000
  56 \end_index
  57 \secnumdepth 3
  58 \tocdepth 3
  59 \paragraph_separation indent
  60 \paragraph_indentation default
  61 \quotes_language english
  62 \papercolumns 1
  63 \papersides 1
  64 \paperpagestyle default
  65 \tracking_changes false
  66 \output_changes false
  67 \html_math_output 0
  68 \html_css_as_file 0
  69 \html_be_strict true
  70 \end_header
  71
  72 \begin_body
  73
  74 \begin_layout Section
  75 Introduction
  76 \end_layout
  77
  78 \begin_layout Standard
  79 In order to properly typeset the document and have instant preview working,
  80  the following packages have to be installed:
  81 \end_layout
  82
  83 \begin_layout LyX-Code
  84 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf
  85 \end_layout
  86
  87 \begin_layout Standard
  88 Due to the use of postscript specials in Section
  89 \begin_inset CommandInset ref
  90 LatexCommand ref
  91 reference "sec:PSTricks"
  92
  93 \end_inset
  94
  95 , only the Postscript or PDF (ps2pdf) output formats will correctly render
  96  the included images.
  97  However, the PDF (XeTeX) output seems to also work, while trying to typeset
  98  the document with
  99 \family typewriter
 100 pdflatex
 101 \family default
 102  or
 103 \family typewriter
 104 pdflualatex
 105 \family default
 106  will generate errors.
 107 \end_layout
 108
 109 \begin_layout Section
 110 Diagrams by XY(-pic)
 111 \end_layout
 112
 113 \begin_layout Standard
 114 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
 115  examples, see
 116 \begin_inset Flex URL
 117 status collapsed
 118
 119 \begin_layout Plain Layout
 120
 121 http://www.math.columbia.edu/~lauda/xy/
 122 \end_layout
 123
 124 \end_inset
 125
 126 .
 127 \end_layout
 128
 129 \begin_layout Description
 130 Braid
 131 \end_layout
 132
 133 \begin_layout Standard
 134 \begin_inset Preview
 135
 136 \begin_layout Standard
 137 \begin_inset ERT
 138 status collapsed
 139
 140 \begin_layout Plain Layout
 141
 142
 143 \backslash
 144 xy
 145 \end_layout
 146
 147 \begin_layout Plain Layout
 148
 149 (5,10)*{}; (-10,-10)*{} **
 150 \backslash
 151 crv{(6,-2)&(-12,4)}
 152 \end_layout
 153
 154 \begin_layout Plain Layout
 155
 156
 157 \backslash
 158 POS?(.25)*{
 159 \backslash
 160 hole}="x"
 161 \backslash
 162 POS?(.45)*{
 163 \backslash
 164 hole}="y"
 165 \backslash
 166 POS?(.6)*{
 167 \backslash
 168 hole}="z";
 169 \end_layout
 170
 171 \begin_layout Plain Layout
 172
 173 "y"+(0,-1); (2,-10)*{} **
 174 \backslash
 175 crv{}
 176 \backslash
 177 POS?(.2)*{
 178 \backslash
 179 hole}="M";
 180 \end_layout
 181
 182 \begin_layout Plain Layout
 183
 184 (-10,10)*{}; "z" **
 185 \backslash
 186 crv{(-9,0)};
 187 \end_layout
 188
 189 \begin_layout Plain Layout
 190
 191 "z"; "M" **
 192 \backslash
 193 crv{};
 194 \end_layout
 195
 196 \begin_layout Plain Layout
 197
 198 "M"; "x" **
 199 \backslash
 200 crv{(5,0)};
 201 \end_layout
 202
 203 \begin_layout Plain Layout
 204
 205 "x"; "y" **
 206 \backslash
 207 crv{(0,7) & (-5,6)};
 208 \end_layout
 209
 210 \begin_layout Plain Layout
 211
 212
 213 \backslash
 214 endxy
 215 \end_layout
 216
 217 \end_inset
 218
 219
 220 \end_layout
 221
 222 \end_inset
 223
 224
 225 \end_layout
 226
 227 \begin_layout Description
 228 Knots
 229 \end_layout
 230
 231 \begin_layout Standard
 232 \begin_inset Preview
 233
 234 \begin_layout Standard
 235 \begin_inset ERT
 236 status collapsed
 237
 238 \begin_layout Plain Layout
 239
 240
 241 \backslash
 242 xy
 243 \end_layout
 244
 245 \begin_layout Plain Layout
 246
 247 (6,9)*{}="1";
 248 \end_layout
 249
 250 \begin_layout Plain Layout
 251
 252 (-8.5,-1)*{}="2";
 253 \end_layout
 254
 255 \begin_layout Plain Layout
 256
 257 "1";"2" **
 258 \backslash
 259 crv{~*=<.5pt>{.} (0,30)}?(.75)*
 260 \backslash
 261 dir{>}+(-2,2)*{z};
 262 \end_layout
 263
 264 \begin_layout Plain Layout
 265
 266 (-6.5,8)*{}="1";
 267 \end_layout
 268
 269 \begin_layout Plain Layout
 270
 271 (-.5,-9)*{}="2";
 272 \end_layout
 273
 274 \begin_layout Plain Layout
 275
 276 "1";"2" **
 277 \backslash
 278 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
 279 \backslash
 280 dir{>}+(-2,-2)*{u};
 281 \end_layout
 282
 283 \begin_layout Plain Layout
 284
 285 (-9.5,-3.35)*{}="1";
 286 \end_layout
 287
 288 \begin_layout Plain Layout
 289
 290 (8.5,-3)*{}="2";
 291 \end_layout
 292
 293 \begin_layout Plain Layout
 294
 295 "1";"2" **
 296 \backslash
 297 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
 298 \backslash
 299 dir{>}+(-1,-3)*{x};
 300 \end_layout
 301
 302 \begin_layout Plain Layout
 303
 304 (1,-10)*{}="1";
 305 \end_layout
 306
 307 \begin_layout Plain Layout
 308
 309 (6.5,7.13)*{}="2";
 310 \end_layout
 311
 312 \begin_layout Plain Layout
 313
 314 "1";"2" **
 315 \backslash
 316 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
 317 \backslash
 318 dir{>}+(3,-1)*{y};
 319 \end_layout
 320
 321 \begin_layout Plain Layout
 322
 323 (11,-1)*{}="1";
 324 \end_layout
 325
 326 \begin_layout Plain Layout
 327
 328 (-4,8)*{}="2";
 329 \end_layout
 330
 331 \begin_layout Plain Layout
 332
 333 "1";"2" **
 334 \backslash
 335 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
 336 \backslash
 337 dir{>}+(1,2)*{w};
 338 \end_layout
 339
 340 \begin_layout Plain Layout
 341
 342
 343 \backslash
 344 endxy
 345 \end_layout
 346
 347 \end_inset
 348
 349
 350 \end_layout
 351
 352 \end_inset
 353
 354
 355 \end_layout
 356
 357 \begin_layout Description
 358 Circles
 359 \end_layout
 360
 361 \begin_layout Standard
 362 \begin_inset Preview
 363
 364 \begin_layout Standard
 365 \begin_inset ERT
 366 status collapsed
 367
 368 \begin_layout Plain Layout
 369
 370
 371 \backslash
 372 xy
 373 \end_layout
 374
 375 \begin_layout Plain Layout
 376
 377 (0,0)*
 378 \backslash
 379 xycircle(14,8){++
 380 \backslash
 381 dir{<}};
 382 \end_layout
 383
 384 \begin_layout Plain Layout
 385
 386 (0,0)*
 387 \backslash
 388 xycircle<10pt>{{.}};
 389 \end_layout
 390
 391 \begin_layout Plain Layout
 392
 393 (0,0)*
 394 \backslash
 395 xycircle(5,2){:};
 396 \end_layout
 397
 398 \begin_layout Plain Layout
 399
 400 (0,15)*
 401 \backslash
 402 xycircle(10,4){--};
 403 \end_layout
 404
 405 \begin_layout Plain Layout
 406
 407
 408 \backslash
 409 endxy
 410 \end_layout
 411
 412 \end_inset
 413
 414
 415 \end_layout
 416
 417 \end_inset
 418
 419
 420 \end_layout
 421
 422 \begin_layout Description
 423 Cobordism
 424 \end_layout
 425
 426 \begin_layout Standard
 427 \begin_inset Preview
 428
 429 \begin_layout Standard
 430 \begin_inset ERT
 431 status collapsed
 432
 433 \begin_layout Plain Layout
 434
 435
 436 \backslash
 437 xy
 438 \end_layout
 439
 440 \begin_layout Plain Layout
 441
 442 (0,0)*
 443 \backslash
 444 ellipse(3,1){.};
 445 \end_layout
 446
 447 \begin_layout Plain Layout
 448
 449 (0,0)*
 450 \backslash
 451 ellipse(3,1)__,=:a(-180){-};
 452 \end_layout
 453
 454 \begin_layout Plain Layout
 455
 456 (-6,-8)*
 457 \backslash
 458 ellipse(3,1){.};
 459 \end_layout
 460
 461 \begin_layout Plain Layout
 462
 463 (6,-8)*
 464 \backslash
 465 ellipse(3,1){.};
 466 \end_layout
 467
 468 \begin_layout Plain Layout
 469
 470 (0,-8)*
 471 \backslash
 472 ellipse(3,1){.};
 473 \end_layout
 474
 475 \begin_layout Plain Layout
 476
 477 (-6,-8)*
 478 \backslash
 479 ellipse(3,1)__,=:a(-180){-};
 480 \end_layout
 481
 482 \begin_layout Plain Layout
 483
 484 (6,-8)*
 485 \backslash
 486 ellipse(3,1)__,=:a(-180){-};
 487 \end_layout
 488
 489 \begin_layout Plain Layout
 490
 491 (0,-8)*
 492 \backslash
 493 ellipse(3,1)__,=:a(180){-};
 494 \end_layout
 495
 496 \begin_layout Plain Layout
 497
 498 (-3,6)*
 499 \backslash
 500 ellipse(3,1){-};
 501 \end_layout
 502
 503 \begin_layout Plain Layout
 504
 505 (3,6)*
 506 \backslash
 507 ellipse(3,1){-};
 508 \end_layout
 509
 510 \begin_layout Plain Layout
 511
 512 (-3,12)*{}="1";
 513 \end_layout
 514
 515 \begin_layout Plain Layout
 516
 517 (3,12)*{}="2";
 518 \end_layout
 519
 520 \begin_layout Plain Layout
 521
 522 (-9,12)*{}="A2";
 523 \end_layout
 524
 525 \begin_layout Plain Layout
 526
 527 (9,12)*{}="B2";
 528 \end_layout
 529
 530 \begin_layout Plain Layout
 531
 532 "1";"2" **
 533 \backslash
 534 crv{(-3,7) & (3,7)};
 535 \end_layout
 536
 537 \begin_layout Plain Layout
 538
 539 (-3,0)*{}="A";
 540 \end_layout
 541
 542 \begin_layout Plain Layout
 543
 544 (3,0)*{}="B";
 545 \end_layout
 546
 547 \begin_layout Plain Layout
 548
 549 (-3,1)*{}="A1";
 550 \end_layout
 551
 552 \begin_layout Plain Layout
 553
 554 (3,1)*{}="B1";
 555 \end_layout
 556
 557 \begin_layout Plain Layout
 558
 559 "A";"A1" **
 560 \backslash
 561 dir{-};
 562 \end_layout
 563
 564 \begin_layout Plain Layout
 565
 566 "B";"B1" **
 567 \backslash
 568 dir{-};
 569 \end_layout
 570
 571 \begin_layout Plain Layout
 572
 573 "B2";"B1" **
 574 \backslash
 575 crv{(8,7) & (3,5)};
 576 \end_layout
 577
 578 \begin_layout Plain Layout
 579
 580 "A2";"A1" **
 581 \backslash
 582 crv{(-8,7) & (-3,5)};
 583 \end_layout
 584
 585 \begin_layout Plain Layout
 586
 587 %REFLECT
 588 \end_layout
 589
 590 \begin_layout Plain Layout
 591
 592 (3,-16)*{}="1";
 593 \end_layout
 594
 595 \begin_layout Plain Layout
 596
 597 (9,-16)*{}="2";
 598 \end_layout
 599
 600 \begin_layout Plain Layout
 601
 602 "1";"2" **
 603 \backslash
 604 crv{(3,-10) & (9,-10)};
 605 \end_layout
 606
 607 \begin_layout Plain Layout
 608
 609 (-3,-16)*{}="1";
 610 \end_layout
 611
 612 \begin_layout Plain Layout
 613
 614 (-9,-16)*{}="2";
 615 \end_layout
 616
 617 \begin_layout Plain Layout
 618
 619 "1";"2" **
 620 \backslash
 621 crv{(-3,-10) & (-9,-10)};
 622 \end_layout
 623
 624 \begin_layout Plain Layout
 625
 626 (-15,-16)*{}="A2";
 627 \end_layout
 628
 629 \begin_layout Plain Layout
 630
 631 (15,-16)*{}="B2";
 632 \end_layout
 633
 634 \begin_layout Plain Layout
 635
 636 (-3,0)*{}="A";
 637 \end_layout
 638
 639 \begin_layout Plain Layout
 640
 641 (3,0)*{}="B";
 642 \end_layout
 643
 644 \begin_layout Plain Layout
 645
 646 (-3,-1)*{}="A1";
 647 \end_layout
 648
 649 \begin_layout Plain Layout
 650
 651 (3,-1)*{}="B1";
 652 \end_layout
 653
 654 \begin_layout Plain Layout
 655
 656 "A";"A1" **
 657 \backslash
 658 dir{-};
 659 \end_layout
 660
 661 \begin_layout Plain Layout
 662
 663 "B";"B1" **
 664 \backslash
 665 dir{-};
 666 \end_layout
 667
 668 \begin_layout Plain Layout
 669
 670 "B2";"B1" **
 671 \backslash
 672 crv{(13,-6) & (2,-8)};
 673 \end_layout
 674
 675 \begin_layout Plain Layout
 676
 677 "A2";"A1" **
 678 \backslash
 679 crv{(-13,-6) & (-2,-8)};
 680 \end_layout
 681
 682 \begin_layout Plain Layout
 683
 684
 685 \backslash
 686 endxy
 687 \end_layout
 688
 689 \end_inset
 690
 691
 692 \end_layout
 693
 694 \end_inset
 695
 696
 697 \begin_inset Preview
 698
 699 \begin_layout Standard
 700 \begin_inset ERT
 701 status collapsed
 702
 703 \begin_layout Plain Layout
 704
 705
 706 \backslash
 707 xy 0;/r.18pc/:
 708 \end_layout
 709
 710 \begin_layout Plain Layout
 711
 712 (20,2)*{
 713 \backslash
 714 bullet}="RU"+(1,3)*{x^{
 715 \backslash
 716 ast}};
 717 \end_layout
 718
 719 \begin_layout Plain Layout
 720
 721 (16,-3)*{
 722 \backslash
 723 bullet}="RD"+(2.5,2)*{x^{
 724 \backslash
 725 ast}};
 726 \end_layout
 727
 728 \begin_layout Plain Layout
 729
 730 (-16,2)*{
 731 \backslash
 732 bullet}="LU"+(-1,2)*{x};
 733 \end_layout
 734
 735 \begin_layout Plain Layout
 736
 737 (-20,-3)*{
 738 \backslash
 739 bullet}="LD"+(-1,2)*{x};
 740 \end_layout
 741
 742 \begin_layout Plain Layout
 743
 744 "RU";"RD" **
 745 \backslash
 746 crv{(4,2) & (4,-1)}; ?(.1)*
 747 \backslash
 748 dir{<}; ?(.85)*
 749 \backslash
 750 dir{<};
 751 \end_layout
 752
 753 \begin_layout Plain Layout
 754
 755 "LD";"LU" **
 756 \backslash
 757 crv{(-4,-2) & (-4,1)};
 758 \end_layout
 759
 760 \begin_layout Plain Layout
 761
 762 ?(.08)*
 763 \backslash
 764 dir{<}; ?(.85)*
 765 \backslash
 766 dir{<};
 767 \end_layout
 768
 769 \begin_layout Plain Layout
 770
 771 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
 772 \end_layout
 773
 774 \begin_layout Plain Layout
 775
 776 "x1"; "x2" **
 777 \backslash
 778 crv{(7,-10) & (-7,-10)};
 779 \end_layout
 780
 781 \begin_layout Plain Layout
 782
 783 (16,-20)*{
 784 \backslash
 785 bullet}="RDD"+(2.5,-1)*{x^{
 786 \backslash
 787 ast}};
 788 \end_layout
 789
 790 \begin_layout Plain Layout
 791
 792 (-20,-20)*{
 793 \backslash
 794 bullet}="LDD"+(-1,-3)*{x};
 795 \end_layout
 796
 797 \begin_layout Plain Layout
 798
 799 (20,-12.5)*{
 800 \backslash
 801 bullet}="RUD"+(3.5,1)*{x^{
 802 \backslash
 803 ast}};
 804 \end_layout
 805
 806 \begin_layout Plain Layout
 807
 808 (-16,-15)*{
 809 \backslash
 810 bullet}="LUD";
 811 \end_layout
 812
 813 \begin_layout Plain Layout
 814
 815 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
 816 \end_layout
 817
 818 \begin_layout Plain Layout
 819
 820 "RD"; "RDD" **
 821 \backslash
 822 dir{-};
 823 \end_layout
 824
 825 \begin_layout Plain Layout
 826
 827 "LD"; "LDD" **
 828 \backslash
 829 dir{-};
 830 \end_layout
 831
 832 \begin_layout Plain Layout
 833
 834 "A"; "LUD" **
 835 \backslash
 836 dir{.};
 837 \end_layout
 838
 839 \begin_layout Plain Layout
 840
 841 "RDD"; "LDD" **
 842 \backslash
 843 crv{(0,-17)}; ?(.57)*
 844 \backslash
 845 dir{>};
 846 \end_layout
 847
 848 \begin_layout Plain Layout
 849
 850 "RU"; "RUD" **
 851 \backslash
 852 dir{-};
 853 \end_layout
 854
 855 \begin_layout Plain Layout
 856
 857 "LU"; "A" **
 858 \backslash
 859 dir{-};
 860 \end_layout
 861
 862 \begin_layout Plain Layout
 863
 864 "B"; "RUD" **
 865 \backslash
 866 crv{(18,-14.15)};
 867 \end_layout
 868
 869 \begin_layout Plain Layout
 870
 871 "B"; "LUD" **
 872 \backslash
 873 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
 874 \backslash
 875 dir{<};
 876 \end_layout
 877
 878 \begin_layout Plain Layout
 879
 880
 881 \backslash
 882 endxy
 883 \end_layout
 884
 885 \end_inset
 886
 887
 888 \end_layout
 889
 890 \end_inset
 891
 892
 893 \end_layout
 894
 895 \begin_layout Description
 896 Strings
 897 \end_layout
 898
 899 \begin_layout Standard
 900 \begin_inset Preview
 901
 902 \begin_layout Standard
 903 \begin_inset ERT
 904 status open
 905
 906 \begin_layout Plain Layout
 907
 908
 909 \backslash
 910 xy (-15,0)*{};(15,0)*{};
 911 \end_layout
 912
 913 \begin_layout Plain Layout
 914
 915
 916 \backslash
 917 endxy
 918 \end_layout
 919
 920 \begin_layout Plain Layout
 921
 922
 923 \backslash
 924 qquad =
 925 \backslash
 926 qquad
 927 \backslash
 928 xy
 929 \end_layout
 930
 931 \begin_layout Plain Layout
 932
 933 (-10,12)*{}; (-10,-12)*{}; **
 934 \backslash
 935 dir{-}?(.5)*
 936 \backslash
 937 dir{<}+(-4,0)*{F(x)};
 938 \end_layout
 939
 940 \begin_layout Plain Layout
 941
 942 (-2,12)*{}="1";
 943 \end_layout
 944
 945 \begin_layout Plain Layout
 946
 947 (6,-7) *{}="2";
 948 \end_layout
 949
 950 \begin_layout Plain Layout
 951
 952 (14,-7) *{}="3";
 953 \end_layout
 954
 955 \begin_layout Plain Layout
 956
 957 (14,-13)*{}="3'";
 958 \end_layout
 959
 960 \begin_layout Plain Layout
 961
 962 (18,0) *={}="";
 963 \end_layout
 964
 965 \begin_layout Plain Layout
 966
 967 "1";"2" **
 968 \backslash
 969 crv{(-4,-21)&(5,-15)};
 970 \end_layout
 971
 972 \begin_layout Plain Layout
 973
 974 ?(.15)*
 975 \backslash
 976 dir{<}+(5,10)*{
 977 \backslash
 978 overline{F(x)}};
 979 \end_layout
 980
 981 \begin_layout Plain Layout
 982
 983 "2";"3" **
 984 \backslash
 985 crv{(6,1)&(14,1)};
 986 \end_layout
 987
 988 \begin_layout Plain Layout
 989
 990 ?(0)*
 991 \backslash
 992 dir{<}+(4,8)*{
 993 \backslash
 994 widetilde{F(i_x)}} ;
 995 \end_layout
 996
 997 \begin_layout Plain Layout
 998
 999 ?(.95)*
1000 \backslash
1001 dir{<}+(5,-2)*{F(
1002 \backslash
1003 overline x)};
1004 \end_layout
1005
1006 \begin_layout Plain Layout
1007
1008 "3";"3'" **
1009 \backslash
1010 dir{-};
1011 \end_layout
1012
1013 \begin_layout Plain Layout
1014
1015 (-2,6)*{}="X1";
1016 \end_layout
1017
1018 \begin_layout Plain Layout
1019
1020 (-10,6)*{}="X2";
1021 \end_layout
1022
1023 \begin_layout Plain Layout
1024
1025 "X1";"X2" **
1026 \backslash
1027 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1028 \end_layout
1029
1030 \begin_layout Plain Layout
1031
1032 (-2,-6)*{}="XA";
1033 \end_layout
1034
1035 \begin_layout Plain Layout
1036
1037 (-10,-6)*{}="XB";
1038 \end_layout
1039
1040 \begin_layout Plain Layout
1041
1042 "XA";"XB" **
1043 \backslash
1044 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1045 \end_layout
1046
1047 \begin_layout Plain Layout
1048
1049
1050 \backslash
1051 endxy
1052 \end_layout
1053
1054 \end_inset
1055
1056
1057 \end_layout
1058
1059 \end_inset
1060
1061
1062 \end_layout
1063
1064 \begin_layout Description
1065 Categories
1066 \end_layout
1067
1068 \begin_layout Standard
1069 \begin_inset Preview
1070
1071 \begin_layout Standard
1072 \begin_inset ERT
1073 status collapsed
1074
1075 \begin_layout Plain Layout
1076
1077
1078 \backslash
1079 xymatrix{
1080 \end_layout
1081
1082 \begin_layout Plain Layout
1083
1084 (x
1085 \backslash
1086 otimes 1)
1087 \backslash
1088 otimes y
1089 \end_layout
1090
1091 \begin_layout Plain Layout
1092
1093
1094 \backslash
1095 ar[rr]^{a_{x,1,y}}
1096 \end_layout
1097
1098 \begin_layout Plain Layout
1099
1100
1101 \backslash
1102 ar[dr]_{r_x
1103 \backslash
1104 otimes 1_y}
1105 \end_layout
1106
1107 \begin_layout Plain Layout
1108
1109 && x
1110 \backslash
1111 otimes(1
1112 \backslash
1113 otimes y)
1114 \end_layout
1115
1116 \begin_layout Plain Layout
1117
1118
1119 \backslash
1120 ar[dl]^{1_x
1121 \backslash
1122 otimes
1123 \backslash
1124 ell_y }
1125 \backslash
1126
1127 \backslash
1128
1129 \end_layout
1130
1131 \begin_layout Plain Layout
1132
1133 & x
1134 \backslash
1135 otimes y }
1136 \end_layout
1137
1138 \end_inset
1139
1140
1141 \end_layout
1142
1143 \end_inset
1144
1145
1146 \begin_inset Preview
1147
1148 \begin_layout Standard
1149 \begin_inset ERT
1150 status collapsed
1151
1152 \begin_layout Plain Layout
1153
1154
1155 \backslash
1156 xy
1157 \end_layout
1158
1159 \begin_layout Plain Layout
1160
1161 (-9,0)*+{
1162 \backslash
1163 bullet}="1";
1164 \end_layout
1165
1166 \begin_layout Plain Layout
1167
1168 (0,0)*+{
1169 \backslash
1170 bullet}="2";
1171 \end_layout
1172
1173 \begin_layout Plain Layout
1174
1175 {
1176 \backslash
1177 ar@/^.9pc/ "1";"2"};
1178 \end_layout
1179
1180 \begin_layout Plain Layout
1181
1182 {
1183 \backslash
1184 ar@/_.9pc/ "1";"2"};
1185 \end_layout
1186
1187 \begin_layout Plain Layout
1188
1189 {
1190 \backslash
1191 ar@/^2pc/ "1";"2"};
1192 \end_layout
1193
1194 \begin_layout Plain Layout
1195
1196 {
1197 \backslash
1198 ar@/_2pc/ "1";"2"};
1199 \end_layout
1200
1201 \begin_layout Plain Layout
1202
1203 {
1204 \backslash
1205 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1206 \end_layout
1207
1208 \begin_layout Plain Layout
1209
1210 {
1211 \backslash
1212 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1213 \end_layout
1214
1215 \begin_layout Plain Layout
1216
1217 {
1218 \backslash
1219 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1220 \end_layout
1221
1222 \begin_layout Plain Layout
1223
1224 (0,0)*+{
1225 \backslash
1226 bullet}="1";
1227 \end_layout
1228
1229 \begin_layout Plain Layout
1230
1231 (9,0)*+{
1232 \backslash
1233 bullet}="2";
1234 \end_layout
1235
1236 \begin_layout Plain Layout
1237
1238 (18,0)*+{
1239 \backslash
1240 bullet}="3";
1241 \end_layout
1242
1243 \begin_layout Plain Layout
1244
1245 {
1246 \backslash
1247 ar "1";"2"};
1248 \end_layout
1249
1250 \begin_layout Plain Layout
1251
1252 {
1253 \backslash
1254 ar "2";"3"};
1255 \end_layout
1256
1257 \begin_layout Plain Layout
1258
1259 {
1260 \backslash
1261 ar@/^1pc/ "1";"2"};
1262 \end_layout
1263
1264 \begin_layout Plain Layout
1265
1266 {
1267 \backslash
1268 ar@/_1pc/ "1";"2"};
1269 \end_layout
1270
1271 \begin_layout Plain Layout
1272
1273 {
1274 \backslash
1275 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1276 \end_layout
1277
1278 \begin_layout Plain Layout
1279
1280 {
1281 \backslash
1282 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1283 \end_layout
1284
1285 \begin_layout Plain Layout
1286
1287
1288 \backslash
1289 endxy
1290 \end_layout
1291
1292 \end_inset
1293
1294
1295 \end_layout
1296
1297 \end_inset
1298
1299
1300 \end_layout
1301
1302 \begin_layout Description
1303 Transformations
1304 \end_layout
1305
1306 \begin_layout Standard
1307 \begin_inset Preview
1308
1309 \begin_layout Standard
1310 \begin_inset ERT
1311 status collapsed
1312
1313 \begin_layout Plain Layout
1314
1315
1316 \backslash
1317 xy %FIG.19.
1318  Natural transformation between functors.
1319 \end_layout
1320
1321 \begin_layout Plain Layout
1322
1323 (-26,-2)*+{
1324 \backslash
1325 bullet}="a";
1326 \end_layout
1327
1328 \begin_layout Plain Layout
1329
1330 (-12,3)*+{
1331 \backslash
1332 bullet}="b";
1333 \end_layout
1334
1335 \begin_layout Plain Layout
1336
1337 (-16,-5)*+{
1338 \backslash
1339 bullet}="c";
1340 \end_layout
1341
1342 \begin_layout Plain Layout
1343
1344 {
1345 \backslash
1346 ar@/^.25pc/ "a";"b"};
1347 \end_layout
1348
1349 \begin_layout Plain Layout
1350
1351 {
1352 \backslash
1353 ar@/_.25pc/"a";"c"};
1354 \end_layout
1355
1356 \begin_layout Plain Layout
1357
1358 {
1359 \backslash
1360 ar@/_.15pc/ "b";"c"};
1361 \end_layout
1362
1363 \begin_layout Plain Layout
1364
1365 %START TOP
1366 \end_layout
1367
1368 \begin_layout Plain Layout
1369
1370 (12,10)*+{
1371 \backslash
1372 bullet}="ta";
1373 \end_layout
1374
1375 \begin_layout Plain Layout
1376
1377 (26,15)*+{
1378 \backslash
1379 bullet}="tb";
1380 \end_layout
1381
1382 \begin_layout Plain Layout
1383
1384 (22,8)*+{
1385 \backslash
1386 bullet}="tc";
1387 \end_layout
1388
1389 \begin_layout Plain Layout
1390
1391 {
1392 \backslash
1393 ar@/^.25pc/ "ta";"tb"};
1394 \end_layout
1395
1396 \begin_layout Plain Layout
1397
1398 {
1399 \backslash
1400 ar@/_.25pc/ "ta";"tc"};
1401 \end_layout
1402
1403 \begin_layout Plain Layout
1404
1405 {
1406 \backslash
1407 ar@/_.15pc/ "tb";"tc"};
1408 \end_layout
1409
1410 \begin_layout Plain Layout
1411
1412 %START bottom
1413 \end_layout
1414
1415 \begin_layout Plain Layout
1416
1417 (12,-10)*+{
1418 \backslash
1419 bullet}="ba";
1420 \end_layout
1421
1422 \begin_layout Plain Layout
1423
1424 (26,-5)*+{
1425 \backslash
1426 bullet}="bb";
1427 \end_layout
1428
1429 \begin_layout Plain Layout
1430
1431 (22,-12)*+{
1432 \backslash
1433 bullet}="bc";
1434 \end_layout
1435
1436 \begin_layout Plain Layout
1437
1438 {
1439 \backslash
1440 ar@/^.25pc/@{.>} "ba";"bb"};
1441 \end_layout
1442
1443 \begin_layout Plain Layout
1444
1445 {
1446 \backslash
1447 ar@/_.25pc/ "ba";"bc"};
1448 \end_layout
1449
1450 \begin_layout Plain Layout
1451
1452 {
1453 \backslash
1454 ar@/_.15pc/ "bb";"bc"};
1455 \end_layout
1456
1457 \begin_layout Plain Layout
1458
1459 %START CONNECT
1460 \end_layout
1461
1462 \begin_layout Plain Layout
1463
1464 {
1465 \backslash
1466 ar@/_.15pc/ "ta";"ba"};
1467 \end_layout
1468
1469 \begin_layout Plain Layout
1470
1471 {
1472 \backslash
1473 ar@/_.15pc/ "tb";"bb"};
1474 \end_layout
1475
1476 \begin_layout Plain Layout
1477
1478 {
1479 \backslash
1480 ar@/_.15pc/ "tc";"bc"};
1481 \end_layout
1482
1483 \begin_layout Plain Layout
1484
1485 %START ARROWS AND LABELS
1486 \end_layout
1487
1488 \begin_layout Plain Layout
1489
1490 (-12,6)*{}="DF";
1491 \end_layout
1492
1493 \begin_layout Plain Layout
1494
1495 (6,10)*{}="CF";
1496 \end_layout
1497
1498 \begin_layout Plain Layout
1499
1500 {
1501 \backslash
1502 ar@/^.35pc/^F "DF";"CF"};
1503 \end_layout
1504
1505 \begin_layout Plain Layout
1506
1507 (-12,-6)*{}="DF";
1508 \end_layout
1509
1510 \begin_layout Plain Layout
1511
1512 (6,-10)*{}="CF";
1513 \end_layout
1514
1515 \begin_layout Plain Layout
1516
1517 {
1518 \backslash
1519 ar@/_.35pc/_G "DF";"CF"};
1520 \end_layout
1521
1522 \begin_layout Plain Layout
1523
1524 (-2,5)*{}="DF";
1525 \end_layout
1526
1527 \begin_layout Plain Layout
1528
1529 (-2,-5)*{}="CF";
1530 \end_layout
1531
1532 \begin_layout Plain Layout
1533
1534 {
1535 \backslash
1536 ar@{=>}^{
1537 \backslash
1538 alpha} "DF";"CF"};
1539 \end_layout
1540
1541 \begin_layout Plain Layout
1542
1543 (29,3)*{D};
1544 \end_layout
1545
1546 \begin_layout Plain Layout
1547
1548 (-23,3)*{C};
1549 \end_layout
1550
1551 \begin_layout Plain Layout
1552
1553
1554 \backslash
1555 endxy
1556 \end_layout
1557
1558 \end_inset
1559
1560
1561 \end_layout
1562
1563 \end_inset
1564
1565
1566 \end_layout
1567
1568 \begin_layout Section
1569 IPA
1570 \end_layout
1571
1572 \begin_layout Standard
1573 \begin_inset Preview
1574
1575 \begin_layout Standard
1576 \begin_inset ERT
1577 status collapsed
1578
1579 \begin_layout Plain Layout
1580
1581
1582 \backslash
1583 textipa{Ekspl@"neIS@n}
1584 \end_layout
1585
1586 \end_inset
1587
1588
1589 \end_layout
1590
1591 \end_inset
1592
1593
1594 \end_layout
1595
1596 \begin_layout Section
1597 QTree
1598 \end_layout
1599
1600 \begin_layout Standard
1601 \begin_inset Preview
1602
1603 \begin_layout Standard
1604 \begin_inset ERT
1605 status collapsed
1606
1607 \begin_layout Plain Layout
1608
1609
1610 \backslash
1611 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1612 \end_layout
1613
1614 \end_inset
1615
1616
1617 \end_layout
1618
1619 \end_inset
1620
1621
1622 \begin_inset Preview
1623
1624 \begin_layout Standard
1625 \begin_inset ERT
1626 status collapsed
1627
1628 \begin_layout Plain Layout
1629
1630
1631 \backslash
1632 Tree [.$
1633 \backslash
1634 sigma$ $
1635 \backslash
1636 mu$ $
1637 \backslash
1638 mu$ ]
1639 \end_layout
1640
1641 \end_inset
1642
1643
1644 \end_layout
1645
1646 \end_inset
1647
1648
1649 \end_layout
1650
1651 \begin_layout Section
1652 PSTricks
1653 \begin_inset CommandInset label
1654 LatexCommand label
1655 name "sec:PSTricks"
1656
1657 \end_inset
1658
1659
1660 \end_layout
1661
1662 \begin_layout Standard
1663 Some simple graphing examples.
1664 \end_layout
1665
1666 \begin_layout Subsection
1667 Function plotting
1668 \end_layout
1669
1670 \begin_layout Standard
1671 \begin_inset Preview
1672
1673 \begin_layout Standard
1674 \begin_inset ERT
1675 status open
1676
1677 \begin_layout Plain Layout
1678
1679
1680 \backslash
1681 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1682 \end_layout
1683
1684 \begin_layout Plain Layout
1685
1686
1687 \backslash
1688 psaxes{->}(0,0)(0,-3)(10,3)
1689 \end_layout
1690
1691 \begin_layout Plain Layout
1692
1693
1694 \backslash
1695 uput[-90](10,0){$x$}
1696 \backslash
1697 uput[0](0,3){$f(x)$}
1698 \end_layout
1699
1700 \begin_layout Plain Layout
1701
1702
1703 \backslash
1704 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1705 \end_layout
1706
1707 \begin_layout Plain Layout
1708
1709
1710 \backslash
1711 end{pspicture*}
1712 \end_layout
1713
1714 \end_inset
1715
1716
1717 \end_layout
1718
1719 \end_inset
1720
1721
1722 \end_layout
1723
1724 \begin_layout Subsection
1725 Inline data plotting
1726 \end_layout
1727
1728 \begin_layout Standard
1729 \align center
1730 \begin_inset Preview
1731
1732 \begin_layout Standard
1733 \align center
1734 \begin_inset ERT
1735 status open
1736
1737 \begin_layout Plain Layout
1738
1739
1740 \backslash
1741 begin{pspicture*}(-1.5,-1.5)(11,5)
1742 \end_layout
1743
1744 \begin_layout Plain Layout
1745
1746
1747 \backslash
1748 psaxes{->}(0,0)(0,0)(10,5)
1749 \end_layout
1750
1751 \begin_layout Plain Layout
1752
1753
1754 \backslash
1755 psset{linewidth=2.5pt}
1756 \end_layout
1757
1758 \begin_layout Plain Layout
1759
1760
1761 \backslash
1762 rput(5.0,-1.0){Speed [MPH]}
1763 \end_layout
1764
1765 \begin_layout Plain Layout
1766
1767
1768 \backslash
1769 rput(-1.0,1.0){
1770 \backslash
1771 begin{rotate}{90}Cost [Dollars]
1772 \backslash
1773 end{rotate}}
1774 \end_layout
1775
1776 \begin_layout Plain Layout
1777
1778
1779 \backslash
1780 savedata{
1781 \backslash
1782 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1783 \end_layout
1784
1785 \begin_layout Plain Layout
1786
1787
1788 \backslash
1789 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1790 \backslash
1791 mydata}
1792 \end_layout
1793
1794 \begin_layout Plain Layout
1795
1796
1797 \backslash
1798 end{pspicture*}
1799 \end_layout
1800
1801 \end_inset
1802
1803
1804 \end_layout
1805
1806 \end_inset
1807
1808
1809 \end_layout
1810
1811 \begin_layout Subsection
1812 Lissajous curves
1813 \end_layout
1814
1815 \begin_layout Standard
1816 \begin_inset Preview
1817
1818 \begin_layout Standard
1819 \begin_inset ERT
1820 status open
1821
1822 \begin_layout Plain Layout
1823
1824
1825 \backslash
1826 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1827 \end_layout
1828
1829 \begin_layout Plain Layout
1830
1831
1832 \backslash
1833 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1834  cos 100 t mul sin}
1835 \end_layout
1836
1837 \begin_layout Plain Layout
1838
1839
1840 \backslash
1841 end{pspicture*}
1842 \end_layout
1843
1844 \end_inset
1845
1846
1847 \end_layout
1848
1849 \end_inset
1850
1851
1852 \begin_inset space \hfill{}
1853 \end_inset
1854
1855
1856 \begin_inset Preview
1857
1858 \begin_layout Standard
1859 \begin_inset ERT
1860 status open
1861
1862 \begin_layout Plain Layout
1863
1864
1865 \backslash
1866 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1867 \end_layout
1868
1869 \begin_layout Plain Layout
1870
1871
1872 \backslash
1873 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1874  mul cos 100 t mul sin}
1875 \end_layout
1876
1877 \begin_layout Plain Layout
1878
1879
1880 \backslash
1881 end{pspicture*}
1882 \end_layout
1883
1884 \end_inset
1885
1886
1887 \end_layout
1888
1889 \end_inset
1890
1891
1892 \begin_inset space \hfill{}
1893 \end_inset
1894
1895
1896 \begin_inset Preview
1897
1898 \begin_layout Standard
1899 \begin_inset ERT
1900 status open
1901
1902 \begin_layout Plain Layout
1903
1904
1905 \backslash
1906 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1907 \end_layout
1908
1909 \begin_layout Plain Layout
1910
1911
1912 \backslash
1913 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1914  mul cos 200 t mul sin}
1915 \end_layout
1916
1917 \begin_layout Plain Layout
1918
1919
1920 \backslash
1921 end{pspicture*}
1922 \end_layout
1923
1924 \end_inset
1925
1926
1927 \end_layout
1928
1929 \end_inset
1930
1931
1932 \begin_inset space \hfill{}
1933 \end_inset
1934
1935
1936 \begin_inset Preview
1937
1938 \begin_layout Standard
1939 \begin_inset ERT
1940 status open
1941
1942 \begin_layout Plain Layout
1943
1944
1945 \backslash
1946 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1947 \end_layout
1948
1949 \begin_layout Plain Layout
1950
1951
1952 \backslash
1953 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1954  mul cos 200 t mul sin}
1955 \end_layout
1956
1957 \begin_layout Plain Layout
1958
1959
1960 \backslash
1961 end{pspicture*}
1962 \end_layout
1963
1964 \end_inset
1965
1966
1967 \end_layout
1968
1969 \end_inset
1970
1971
1972 \end_layout
1973
1974 \begin_layout Section
1975 TikZ
1976 \end_layout
1977
1978 \begin_layout Standard
1979 \begin_inset Flex URL
1980 status collapsed
1981
1982 \begin_layout Plain Layout
1983
1984 http://media.texample.net/tikz/examples/TEX/free-body-diagrams.tex
1985 \end_layout
1986
1987 \end_inset
1988
1989
1990 \end_layout
1991
1992 \begin_layout Standard
1993 \begin_inset Preview
1994
1995 \begin_layout Standard
1996 \begin_inset ERT
1997 status collapsed
1998
1999 \begin_layout Plain Layout
2000
2001
2002 \backslash
2003 def
2004 \backslash
2005 iangle{35} % Angle of the inclined plane
2006 \end_layout
2007
2008 \begin_layout Plain Layout
2009
2010
2011 \backslash
2012 def
2013 \backslash
2014 down{-90}
2015 \end_layout
2016
2017 \begin_layout Plain Layout
2018
2019
2020 \backslash
2021 def
2022 \backslash
2023 arcr{0.5cm} % Radius of the arc used to indicate angles
2024 \end_layout
2025
2026 \begin_layout Plain Layout
2027
2028 \end_layout
2029
2030 \begin_layout Plain Layout
2031
2032
2033 \backslash
2034 begin{tikzpicture}[
2035 \end_layout
2036
2037 \begin_layout Plain Layout
2038
2039     force/.style={>=latex,draw=blue,fill=blue},
2040 \end_layout
2041
2042 \begin_layout Plain Layout
2043
2044     axis/.style={densely dashed,gray,font=
2045 \backslash
2046 small},
2047 \end_layout
2048
2049 \begin_layout Plain Layout
2050
2051     M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2052 \end_layout
2053
2054 \begin_layout Plain Layout
2055
2056     m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2057 \end_layout
2058
2059 \begin_layout Plain Layout
2060
2061     plane/.style={draw=black,fill=blue!10},
2062 \end_layout
2063
2064 \begin_layout Plain Layout
2065
2066     string/.style={draw=red, thick},
2067 \end_layout
2068
2069 \begin_layout Plain Layout
2070
2071     pulley/.style={thick},
2072 \end_layout
2073
2074 \begin_layout Plain Layout
2075
2076 ]
2077 \end_layout
2078
2079 \begin_layout Plain Layout
2080
2081 \end_layout
2082
2083 \begin_layout Plain Layout
2084
2085
2086 \backslash
2087 matrix[column sep=1cm] {
2088 \end_layout
2089
2090 \begin_layout Plain Layout
2091
2092     %% Sketch
2093 \end_layout
2094
2095 \begin_layout Plain Layout
2096
2097
2098 \backslash
2099 draw[plane] (0,-1) coordinate (base)
2100 \end_layout
2101
2102 \begin_layout Plain Layout
2103
2104                      -- coordinate[pos=0.5] (mid) ++(
2105 \backslash
2106 iangle:3) coordinate (top)
2107 \end_layout
2108
2109 \begin_layout Plain Layout
2110
2111                      |- (base) -- cycle;
2112 \end_layout
2113
2114 \begin_layout Plain Layout
2115
2116
2117 \backslash
2118 path (mid) node[M,rotate=
2119 \backslash
2120 iangle,yshift=0.25cm] (M) {};
2121 \end_layout
2122
2123 \begin_layout Plain Layout
2124
2125
2126 \backslash
2127 draw[pulley] (top) -- ++(
2128 \backslash
2129 iangle:0.25) circle (0.25cm)
2130 \end_layout
2131
2132 \begin_layout Plain Layout
2133
2134                    ++ (90-
2135 \backslash
2136 iangle:0.5) coordinate (pulley);
2137 \end_layout
2138
2139 \begin_layout Plain Layout
2140
2141
2142 \backslash
2143 draw[string] (M.east) -- ++(
2144 \backslash
2145 iangle:1.5cm) arc (90+
2146 \backslash
2147 iangle:0:0.25)
2148 \end_layout
2149
2150 \begin_layout Plain Layout
2151
2152                   -- ++(0,-1) node[m] {};
2153 \end_layout
2154
2155 \begin_layout Plain Layout
2156
2157 \end_layout
2158
2159 \begin_layout Plain Layout
2160
2161
2162 \backslash
2163 draw[->] (base)++(
2164 \backslash
2165 arcr,0) arc (0:
2166 \backslash
2167 iangle:
2168 \backslash
2169 arcr);
2170 \end_layout
2171
2172 \begin_layout Plain Layout
2173
2174
2175 \backslash
2176 path (base)++(
2177 \backslash
2178 iangle*0.5:
2179 \backslash
2180 arcr+5pt) node {$
2181 \backslash
2182 alpha$};
2183 \end_layout
2184
2185 \begin_layout Plain Layout
2186
2187     %%
2188 \end_layout
2189
2190 \begin_layout Plain Layout
2191
2192 \end_layout
2193
2194 \begin_layout Plain Layout
2195
2196 &
2197 \end_layout
2198
2199 \begin_layout Plain Layout
2200
2201     %% Free body diagram of M
2202 \end_layout
2203
2204 \begin_layout Plain Layout
2205
2206
2207 \backslash
2208 begin{scope}[rotate=
2209 \backslash
2210 iangle]
2211 \end_layout
2212
2213 \begin_layout Plain Layout
2214
2215
2216 \backslash
2217 node[M,transform shape] (M) {};
2218 \end_layout
2219
2220 \begin_layout Plain Layout
2221
2222         % Draw axes and help lines
2223 \end_layout
2224
2225 \begin_layout Plain Layout
2226
2227 \end_layout
2228
2229 \begin_layout Plain Layout
2230
2231         {[axis,->]
2232 \end_layout
2233
2234 \begin_layout Plain Layout
2235
2236
2237 \backslash
2238 draw (0,-1) -- (0,2) node[right] {$+y$};
2239 \end_layout
2240
2241 \begin_layout Plain Layout
2242
2243
2244 \backslash
2245 draw (M) -- ++(2,0) node[right] {$+x$};
2246 \end_layout
2247
2248 \begin_layout Plain Layout
2249
2250             % Indicate angle.
2251  The code is a bit awkward.
2252 \end_layout
2253
2254 \begin_layout Plain Layout
2255
2256 \end_layout
2257
2258 \begin_layout Plain Layout
2259
2260
2261 \backslash
2262 draw[solid,shorten >=0.5pt] (
2263 \backslash
2264 down-
2265 \backslash
2266 iangle:
2267 \backslash
2268 arcr)
2269 \end_layout
2270
2271 \begin_layout Plain Layout
2272
2273                 arc(
2274 \backslash
2275 down-
2276 \backslash
2277 iangle:
2278 \backslash
2279 down:
2280 \backslash
2281 arcr);
2282 \end_layout
2283
2284 \begin_layout Plain Layout
2285
2286
2287 \backslash
2288 node at (
2289 \backslash
2290 down-0.5*
2291 \backslash
2292 iangle:1.3*
2293 \backslash
2294 arcr) {$
2295 \backslash
2296 alpha$};
2297 \end_layout
2298
2299 \begin_layout Plain Layout
2300
2301         }
2302 \end_layout
2303
2304 \begin_layout Plain Layout
2305
2306 \end_layout
2307
2308 \begin_layout Plain Layout
2309
2310         % Forces
2311 \end_layout
2312
2313 \begin_layout Plain Layout
2314
2315         {[force,->]
2316 \end_layout
2317
2318 \begin_layout Plain Layout
2319
2320             % Assuming that Mg = 1.
2321  The normal force will therefore be cos(alpha)
2322 \end_layout
2323
2324 \begin_layout Plain Layout
2325
2326
2327 \backslash
2328 draw (M.center) -- ++(0,{cos(
2329 \backslash
2330 iangle)}) node[above right] {$N$};
2331 \end_layout
2332
2333 \begin_layout Plain Layout
2334
2335
2336 \backslash
2337 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2338 \end_layout
2339
2340 \begin_layout Plain Layout
2341
2342
2343 \backslash
2344 draw (M.east) -- ++(1,0) node[above] {$T$};
2345 \end_layout
2346
2347 \begin_layout Plain Layout
2348
2349         }
2350 \end_layout
2351
2352 \begin_layout Plain Layout
2353
2354 \end_layout
2355
2356 \begin_layout Plain Layout
2357
2358
2359 \backslash
2360 end{scope}
2361 \end_layout
2362
2363 \begin_layout Plain Layout
2364
2365     % Draw gravity force.
2366  The code is put outside the rotated
2367 \end_layout
2368
2369 \begin_layout Plain Layout
2370
2371     % scope for simplicity.
2372  No need to do any angle calculations.
2373
2374 \end_layout
2375
2376 \begin_layout Plain Layout
2377
2378
2379 \backslash
2380 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2381 \end_layout
2382
2383 \begin_layout Plain Layout
2384
2385     %%
2386 \end_layout
2387
2388 \begin_layout Plain Layout
2389
2390 \end_layout
2391
2392 \begin_layout Plain Layout
2393
2394 &
2395 \end_layout
2396
2397 \begin_layout Plain Layout
2398
2399     %%%
2400 \end_layout
2401
2402 \begin_layout Plain Layout
2403
2404     % Free body diagram of m
2405 \end_layout
2406
2407 \begin_layout Plain Layout
2408
2409
2410 \backslash
2411 node[m] (m) {};
2412 \end_layout
2413
2414 \begin_layout Plain Layout
2415
2416
2417 \backslash
2418 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2419 \end_layout
2420
2421 \begin_layout Plain Layout
2422
2423     {[force,->]
2424 \end_layout
2425
2426 \begin_layout Plain Layout
2427
2428
2429 \backslash
2430 draw (m.north) -- ++(0,1) node[above] {$T'$};
2431 \end_layout
2432
2433 \begin_layout Plain Layout
2434
2435
2436 \backslash
2437 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2438 \end_layout
2439
2440 \begin_layout Plain Layout
2441
2442     }
2443 \end_layout
2444
2445 \begin_layout Plain Layout
2446
2447 \end_layout
2448
2449 \begin_layout Plain Layout
2450
2451
2452 \backslash
2453
2454 \backslash
2455
2456 \end_layout
2457
2458 \begin_layout Plain Layout
2459
2460 };
2461 \end_layout
2462
2463 \begin_layout Plain Layout
2464
2465
2466 \backslash
2467 end{tikzpicture}
2468 \end_layout
2469
2470 \begin_layout Plain Layout
2471
2472 \end_layout
2473
2474 \end_inset
2475
2476
2477 \end_layout
2478
2479 \end_inset
2480
2481
2482 \end_layout
2483
2484 \end_body
2485 \end_document