lib/examples/instant_preview.lyx

   1 #LyX 2.0.0svn created this file. For more info see http://www.lyx.org/
   2 \lyxformat 410
   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 \inputencoding auto
  21 \fontencoding global
  22 \font_roman lmodern
  23 \font_sans default
  24 \font_typewriter default
  25 \font_default_family default
  26 \use_non_tex_fonts false
  27 \font_sc false
  28 \font_osf false
  29 \font_sf_scale 100
  30 \font_tt_scale 100
  31
  32 \graphics default
  33 \default_output_format default
  34 \output_sync 0
  35 \bibtex_command default
  36 \index_command default
  37 \paperfontsize default
  38 \spacing single
  39 \use_hyperref false
  40 \papersize default
  41 \use_geometry false
  42 \use_amsmath 1
  43 \use_esint 1
  44 \use_mhchem 1
  45 \use_mathdots 1
  46 \cite_engine basic
  47 \use_bibtopic false
  48 \use_indices false
  49 \paperorientation portrait
  50 \suppress_date false
  51 \use_refstyle 0
  52 \index Index
  53 \shortcut idx
  54 \color #008000
  55 \end_index
  56 \secnumdepth 3
  57 \tocdepth 3
  58 \paragraph_separation indent
  59 \paragraph_indentation default
  60 \quotes_language english
  61 \papercolumns 1
  62 \papersides 1
  63 \paperpagestyle default
  64 \tracking_changes false
  65 \output_changes false
  66 \html_math_output 0
  67 \html_be_strict true
  68 \end_header
  69
  70 \begin_body
  71
  72 \begin_layout Section
  73 Introduction
  74 \end_layout
  75
  76 \begin_layout Standard
  77 In order to properly typeset the document and have instant preview working,
  78  the following packages have to be installed:
  79 \end_layout
  80
  81 \begin_layout LyX-Code
  82 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf
  83 \end_layout
  84
  85 \begin_layout Standard
  86 Due to the use of postscript specials in Section
  87 \begin_inset CommandInset ref
  88 LatexCommand ref
  89 reference "sec:PSTricks"
  90
  91 \end_inset
  92
  93 , only the Postscript or PDF (ps2pdf) output formats will correctly render
  94  the included images.
  95  However, the PDF (XeTeX) output seems to also work, while trying to typeset
  96  the document with
  97 \family typewriter
  98 pdflatex
  99 \family default
 100  or
 101 \family typewriter
 102 pdflualatex
 103 \family default
 104  will generate errors.
 105 \end_layout
 106
 107 \begin_layout Section
 108 Diagrams by XY(-pic)
 109 \end_layout
 110
 111 \begin_layout Standard
 112 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
 113  examples, see
 114 \begin_inset Flex URL
 115 status collapsed
 116
 117 \begin_layout Plain Layout
 118
 119 http://www.math.columbia.edu/~lauda/xy/
 120 \end_layout
 121
 122 \end_inset
 123
 124 .
 125 \end_layout
 126
 127 \begin_layout Description
 128 Braid
 129 \end_layout
 130
 131 \begin_layout Standard
 132 \begin_inset Preview
 133
 134 \begin_layout Standard
 135 \begin_inset ERT
 136 status collapsed
 137
 138 \begin_layout Plain Layout
 139
 140
 141 \backslash
 142 xy
 143 \end_layout
 144
 145 \begin_layout Plain Layout
 146
 147 (5,10)*{}; (-10,-10)*{} **
 148 \backslash
 149 crv{(6,-2)&(-12,4)}
 150 \end_layout
 151
 152 \begin_layout Plain Layout
 153
 154
 155 \backslash
 156 POS?(.25)*{
 157 \backslash
 158 hole}="x"
 159 \backslash
 160 POS?(.45)*{
 161 \backslash
 162 hole}="y"
 163 \backslash
 164 POS?(.6)*{
 165 \backslash
 166 hole}="z";
 167 \end_layout
 168
 169 \begin_layout Plain Layout
 170
 171 "y"+(0,-1); (2,-10)*{} **
 172 \backslash
 173 crv{}
 174 \backslash
 175 POS?(.2)*{
 176 \backslash
 177 hole}="M";
 178 \end_layout
 179
 180 \begin_layout Plain Layout
 181
 182 (-10,10)*{}; "z" **
 183 \backslash
 184 crv{(-9,0)};
 185 \end_layout
 186
 187 \begin_layout Plain Layout
 188
 189 "z"; "M" **
 190 \backslash
 191 crv{};
 192 \end_layout
 193
 194 \begin_layout Plain Layout
 195
 196 "M"; "x" **
 197 \backslash
 198 crv{(5,0)};
 199 \end_layout
 200
 201 \begin_layout Plain Layout
 202
 203 "x"; "y" **
 204 \backslash
 205 crv{(0,7) & (-5,6)};
 206 \end_layout
 207
 208 \begin_layout Plain Layout
 209
 210
 211 \backslash
 212 endxy
 213 \end_layout
 214
 215 \end_inset
 216
 217
 218 \end_layout
 219
 220 \end_inset
 221
 222
 223 \end_layout
 224
 225 \begin_layout Description
 226 Knots
 227 \end_layout
 228
 229 \begin_layout Standard
 230 \begin_inset Preview
 231
 232 \begin_layout Standard
 233 \begin_inset ERT
 234 status collapsed
 235
 236 \begin_layout Plain Layout
 237
 238
 239 \backslash
 240 xy
 241 \end_layout
 242
 243 \begin_layout Plain Layout
 244
 245 (6,9)*{}="1";
 246 \end_layout
 247
 248 \begin_layout Plain Layout
 249
 250 (-8.5,-1)*{}="2";
 251 \end_layout
 252
 253 \begin_layout Plain Layout
 254
 255 "1";"2" **
 256 \backslash
 257 crv{~*=<.5pt>{.} (0,30)}?(.75)*
 258 \backslash
 259 dir{>}+(-2,2)*{z};
 260 \end_layout
 261
 262 \begin_layout Plain Layout
 263
 264 (-6.5,8)*{}="1";
 265 \end_layout
 266
 267 \begin_layout Plain Layout
 268
 269 (-.5,-9)*{}="2";
 270 \end_layout
 271
 272 \begin_layout Plain Layout
 273
 274 "1";"2" **
 275 \backslash
 276 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
 277 \backslash
 278 dir{>}+(-2,-2)*{u};
 279 \end_layout
 280
 281 \begin_layout Plain Layout
 282
 283 (-9.5,-3.35)*{}="1";
 284 \end_layout
 285
 286 \begin_layout Plain Layout
 287
 288 (8.5,-3)*{}="2";
 289 \end_layout
 290
 291 \begin_layout Plain Layout
 292
 293 "1";"2" **
 294 \backslash
 295 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
 296 \backslash
 297 dir{>}+(-1,-3)*{x};
 298 \end_layout
 299
 300 \begin_layout Plain Layout
 301
 302 (1,-10)*{}="1";
 303 \end_layout
 304
 305 \begin_layout Plain Layout
 306
 307 (6.5,7.13)*{}="2";
 308 \end_layout
 309
 310 \begin_layout Plain Layout
 311
 312 "1";"2" **
 313 \backslash
 314 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
 315 \backslash
 316 dir{>}+(3,-1)*{y};
 317 \end_layout
 318
 319 \begin_layout Plain Layout
 320
 321 (11,-1)*{}="1";
 322 \end_layout
 323
 324 \begin_layout Plain Layout
 325
 326 (-4,8)*{}="2";
 327 \end_layout
 328
 329 \begin_layout Plain Layout
 330
 331 "1";"2" **
 332 \backslash
 333 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
 334 \backslash
 335 dir{>}+(1,2)*{w};
 336 \end_layout
 337
 338 \begin_layout Plain Layout
 339
 340
 341 \backslash
 342 endxy
 343 \end_layout
 344
 345 \end_inset
 346
 347
 348 \end_layout
 349
 350 \end_inset
 351
 352
 353 \end_layout
 354
 355 \begin_layout Description
 356 Circles
 357 \end_layout
 358
 359 \begin_layout Standard
 360 \begin_inset Preview
 361
 362 \begin_layout Standard
 363 \begin_inset ERT
 364 status collapsed
 365
 366 \begin_layout Plain Layout
 367
 368
 369 \backslash
 370 xy
 371 \end_layout
 372
 373 \begin_layout Plain Layout
 374
 375 (0,0)*
 376 \backslash
 377 xycircle(14,8){++
 378 \backslash
 379 dir{<}};
 380 \end_layout
 381
 382 \begin_layout Plain Layout
 383
 384 (0,0)*
 385 \backslash
 386 xycircle<10pt>{{.}};
 387 \end_layout
 388
 389 \begin_layout Plain Layout
 390
 391 (0,0)*
 392 \backslash
 393 xycircle(5,2){:};
 394 \end_layout
 395
 396 \begin_layout Plain Layout
 397
 398 (0,15)*
 399 \backslash
 400 xycircle(10,4){--};
 401 \end_layout
 402
 403 \begin_layout Plain Layout
 404
 405
 406 \backslash
 407 endxy
 408 \end_layout
 409
 410 \end_inset
 411
 412
 413 \end_layout
 414
 415 \end_inset
 416
 417
 418 \end_layout
 419
 420 \begin_layout Description
 421 Cobordism
 422 \end_layout
 423
 424 \begin_layout Standard
 425 \begin_inset Preview
 426
 427 \begin_layout Standard
 428 \begin_inset ERT
 429 status collapsed
 430
 431 \begin_layout Plain Layout
 432
 433
 434 \backslash
 435 xy
 436 \end_layout
 437
 438 \begin_layout Plain Layout
 439
 440 (0,0)*
 441 \backslash
 442 ellipse(3,1){.};
 443 \end_layout
 444
 445 \begin_layout Plain Layout
 446
 447 (0,0)*
 448 \backslash
 449 ellipse(3,1)__,=:a(-180){-};
 450 \end_layout
 451
 452 \begin_layout Plain Layout
 453
 454 (-6,-8)*
 455 \backslash
 456 ellipse(3,1){.};
 457 \end_layout
 458
 459 \begin_layout Plain Layout
 460
 461 (6,-8)*
 462 \backslash
 463 ellipse(3,1){.};
 464 \end_layout
 465
 466 \begin_layout Plain Layout
 467
 468 (0,-8)*
 469 \backslash
 470 ellipse(3,1){.};
 471 \end_layout
 472
 473 \begin_layout Plain Layout
 474
 475 (-6,-8)*
 476 \backslash
 477 ellipse(3,1)__,=:a(-180){-};
 478 \end_layout
 479
 480 \begin_layout Plain Layout
 481
 482 (6,-8)*
 483 \backslash
 484 ellipse(3,1)__,=:a(-180){-};
 485 \end_layout
 486
 487 \begin_layout Plain Layout
 488
 489 (0,-8)*
 490 \backslash
 491 ellipse(3,1)__,=:a(180){-};
 492 \end_layout
 493
 494 \begin_layout Plain Layout
 495
 496 (-3,6)*
 497 \backslash
 498 ellipse(3,1){-};
 499 \end_layout
 500
 501 \begin_layout Plain Layout
 502
 503 (3,6)*
 504 \backslash
 505 ellipse(3,1){-};
 506 \end_layout
 507
 508 \begin_layout Plain Layout
 509
 510 (-3,12)*{}="1";
 511 \end_layout
 512
 513 \begin_layout Plain Layout
 514
 515 (3,12)*{}="2";
 516 \end_layout
 517
 518 \begin_layout Plain Layout
 519
 520 (-9,12)*{}="A2";
 521 \end_layout
 522
 523 \begin_layout Plain Layout
 524
 525 (9,12)*{}="B2";
 526 \end_layout
 527
 528 \begin_layout Plain Layout
 529
 530 "1";"2" **
 531 \backslash
 532 crv{(-3,7) & (3,7)};
 533 \end_layout
 534
 535 \begin_layout Plain Layout
 536
 537 (-3,0)*{}="A";
 538 \end_layout
 539
 540 \begin_layout Plain Layout
 541
 542 (3,0)*{}="B";
 543 \end_layout
 544
 545 \begin_layout Plain Layout
 546
 547 (-3,1)*{}="A1";
 548 \end_layout
 549
 550 \begin_layout Plain Layout
 551
 552 (3,1)*{}="B1";
 553 \end_layout
 554
 555 \begin_layout Plain Layout
 556
 557 "A";"A1" **
 558 \backslash
 559 dir{-};
 560 \end_layout
 561
 562 \begin_layout Plain Layout
 563
 564 "B";"B1" **
 565 \backslash
 566 dir{-};
 567 \end_layout
 568
 569 \begin_layout Plain Layout
 570
 571 "B2";"B1" **
 572 \backslash
 573 crv{(8,7) & (3,5)};
 574 \end_layout
 575
 576 \begin_layout Plain Layout
 577
 578 "A2";"A1" **
 579 \backslash
 580 crv{(-8,7) & (-3,5)};
 581 \end_layout
 582
 583 \begin_layout Plain Layout
 584
 585 %REFLECT
 586 \end_layout
 587
 588 \begin_layout Plain Layout
 589
 590 (3,-16)*{}="1";
 591 \end_layout
 592
 593 \begin_layout Plain Layout
 594
 595 (9,-16)*{}="2";
 596 \end_layout
 597
 598 \begin_layout Plain Layout
 599
 600 "1";"2" **
 601 \backslash
 602 crv{(3,-10) & (9,-10)};
 603 \end_layout
 604
 605 \begin_layout Plain Layout
 606
 607 (-3,-16)*{}="1";
 608 \end_layout
 609
 610 \begin_layout Plain Layout
 611
 612 (-9,-16)*{}="2";
 613 \end_layout
 614
 615 \begin_layout Plain Layout
 616
 617 "1";"2" **
 618 \backslash
 619 crv{(-3,-10) & (-9,-10)};
 620 \end_layout
 621
 622 \begin_layout Plain Layout
 623
 624 (-15,-16)*{}="A2";
 625 \end_layout
 626
 627 \begin_layout Plain Layout
 628
 629 (15,-16)*{}="B2";
 630 \end_layout
 631
 632 \begin_layout Plain Layout
 633
 634 (-3,0)*{}="A";
 635 \end_layout
 636
 637 \begin_layout Plain Layout
 638
 639 (3,0)*{}="B";
 640 \end_layout
 641
 642 \begin_layout Plain Layout
 643
 644 (-3,-1)*{}="A1";
 645 \end_layout
 646
 647 \begin_layout Plain Layout
 648
 649 (3,-1)*{}="B1";
 650 \end_layout
 651
 652 \begin_layout Plain Layout
 653
 654 "A";"A1" **
 655 \backslash
 656 dir{-};
 657 \end_layout
 658
 659 \begin_layout Plain Layout
 660
 661 "B";"B1" **
 662 \backslash
 663 dir{-};
 664 \end_layout
 665
 666 \begin_layout Plain Layout
 667
 668 "B2";"B1" **
 669 \backslash
 670 crv{(13,-6) & (2,-8)};
 671 \end_layout
 672
 673 \begin_layout Plain Layout
 674
 675 "A2";"A1" **
 676 \backslash
 677 crv{(-13,-6) & (-2,-8)};
 678 \end_layout
 679
 680 \begin_layout Plain Layout
 681
 682
 683 \backslash
 684 endxy
 685 \end_layout
 686
 687 \end_inset
 688
 689
 690 \end_layout
 691
 692 \end_inset
 693
 694
 695 \begin_inset Preview
 696
 697 \begin_layout Standard
 698 \begin_inset ERT
 699 status collapsed
 700
 701 \begin_layout Plain Layout
 702
 703
 704 \backslash
 705 xy 0;/r.18pc/:
 706 \end_layout
 707
 708 \begin_layout Plain Layout
 709
 710 (20,2)*{
 711 \backslash
 712 bullet}="RU"+(1,3)*{x^{
 713 \backslash
 714 ast}};
 715 \end_layout
 716
 717 \begin_layout Plain Layout
 718
 719 (16,-3)*{
 720 \backslash
 721 bullet}="RD"+(2.5,2)*{x^{
 722 \backslash
 723 ast}};
 724 \end_layout
 725
 726 \begin_layout Plain Layout
 727
 728 (-16,2)*{
 729 \backslash
 730 bullet}="LU"+(-1,2)*{x};
 731 \end_layout
 732
 733 \begin_layout Plain Layout
 734
 735 (-20,-3)*{
 736 \backslash
 737 bullet}="LD"+(-1,2)*{x};
 738 \end_layout
 739
 740 \begin_layout Plain Layout
 741
 742 "RU";"RD" **
 743 \backslash
 744 crv{(4,2) & (4,-1)}; ?(.1)*
 745 \backslash
 746 dir{<}; ?(.85)*
 747 \backslash
 748 dir{<};
 749 \end_layout
 750
 751 \begin_layout Plain Layout
 752
 753 "LD";"LU" **
 754 \backslash
 755 crv{(-4,-2) & (-4,1)};
 756 \end_layout
 757
 758 \begin_layout Plain Layout
 759
 760 ?(.08)*
 761 \backslash
 762 dir{<}; ?(.85)*
 763 \backslash
 764 dir{<};
 765 \end_layout
 766
 767 \begin_layout Plain Layout
 768
 769 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
 770 \end_layout
 771
 772 \begin_layout Plain Layout
 773
 774 "x1"; "x2" **
 775 \backslash
 776 crv{(7,-10) & (-7,-10)};
 777 \end_layout
 778
 779 \begin_layout Plain Layout
 780
 781 (16,-20)*{
 782 \backslash
 783 bullet}="RDD"+(2.5,-1)*{x^{
 784 \backslash
 785 ast}};
 786 \end_layout
 787
 788 \begin_layout Plain Layout
 789
 790 (-20,-20)*{
 791 \backslash
 792 bullet}="LDD"+(-1,-3)*{x};
 793 \end_layout
 794
 795 \begin_layout Plain Layout
 796
 797 (20,-12.5)*{
 798 \backslash
 799 bullet}="RUD"+(3.5,1)*{x^{
 800 \backslash
 801 ast}};
 802 \end_layout
 803
 804 \begin_layout Plain Layout
 805
 806 (-16,-15)*{
 807 \backslash
 808 bullet}="LUD";
 809 \end_layout
 810
 811 \begin_layout Plain Layout
 812
 813 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
 814 \end_layout
 815
 816 \begin_layout Plain Layout
 817
 818 "RD"; "RDD" **
 819 \backslash
 820 dir{-};
 821 \end_layout
 822
 823 \begin_layout Plain Layout
 824
 825 "LD"; "LDD" **
 826 \backslash
 827 dir{-};
 828 \end_layout
 829
 830 \begin_layout Plain Layout
 831
 832 "A"; "LUD" **
 833 \backslash
 834 dir{.};
 835 \end_layout
 836
 837 \begin_layout Plain Layout
 838
 839 "RDD"; "LDD" **
 840 \backslash
 841 crv{(0,-17)}; ?(.57)*
 842 \backslash
 843 dir{>};
 844 \end_layout
 845
 846 \begin_layout Plain Layout
 847
 848 "RU"; "RUD" **
 849 \backslash
 850 dir{-};
 851 \end_layout
 852
 853 \begin_layout Plain Layout
 854
 855 "LU"; "A" **
 856 \backslash
 857 dir{-};
 858 \end_layout
 859
 860 \begin_layout Plain Layout
 861
 862 "B"; "RUD" **
 863 \backslash
 864 crv{(18,-14.15)};
 865 \end_layout
 866
 867 \begin_layout Plain Layout
 868
 869 "B"; "LUD" **
 870 \backslash
 871 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
 872 \backslash
 873 dir{<};
 874 \end_layout
 875
 876 \begin_layout Plain Layout
 877
 878
 879 \backslash
 880 endxy
 881 \end_layout
 882
 883 \end_inset
 884
 885
 886 \end_layout
 887
 888 \end_inset
 889
 890
 891 \end_layout
 892
 893 \begin_layout Description
 894 Strings
 895 \end_layout
 896
 897 \begin_layout Standard
 898 \begin_inset Preview
 899
 900 \begin_layout Standard
 901 \begin_inset ERT
 902 status open
 903
 904 \begin_layout Plain Layout
 905
 906
 907 \backslash
 908 xy (-15,0)*{};(15,0)*{};
 909 \end_layout
 910
 911 \begin_layout Plain Layout
 912
 913
 914 \backslash
 915 endxy
 916 \end_layout
 917
 918 \begin_layout Plain Layout
 919
 920
 921 \backslash
 922 qquad =
 923 \backslash
 924 qquad
 925 \backslash
 926 xy
 927 \end_layout
 928
 929 \begin_layout Plain Layout
 930
 931 (-10,12)*{}; (-10,-12)*{}; **
 932 \backslash
 933 dir{-}?(.5)*
 934 \backslash
 935 dir{<}+(-4,0)*{F(x)};
 936 \end_layout
 937
 938 \begin_layout Plain Layout
 939
 940 (-2,12)*{}="1";
 941 \end_layout
 942
 943 \begin_layout Plain Layout
 944
 945 (6,-7) *{}="2";
 946 \end_layout
 947
 948 \begin_layout Plain Layout
 949
 950 (14,-7) *{}="3";
 951 \end_layout
 952
 953 \begin_layout Plain Layout
 954
 955 (14,-13)*{}="3'";
 956 \end_layout
 957
 958 \begin_layout Plain Layout
 959
 960 (18,0) *={}="";
 961 \end_layout
 962
 963 \begin_layout Plain Layout
 964
 965 "1";"2" **
 966 \backslash
 967 crv{(-4,-21)&(5,-15)};
 968 \end_layout
 969
 970 \begin_layout Plain Layout
 971
 972 ?(.15)*
 973 \backslash
 974 dir{<}+(5,10)*{
 975 \backslash
 976 overline{F(x)}};
 977 \end_layout
 978
 979 \begin_layout Plain Layout
 980
 981 "2";"3" **
 982 \backslash
 983 crv{(6,1)&(14,1)};
 984 \end_layout
 985
 986 \begin_layout Plain Layout
 987
 988 ?(0)*
 989 \backslash
 990 dir{<}+(4,8)*{
 991 \backslash
 992 widetilde{F(i_x)}} ;
 993 \end_layout
 994
 995 \begin_layout Plain Layout
 996
 997 ?(.95)*
 998 \backslash
 999 dir{<}+(5,-2)*{F(
1000 \backslash
1001 overline x)};
1002 \end_layout
1003
1004 \begin_layout Plain Layout
1005
1006 "3";"3'" **
1007 \backslash
1008 dir{-};
1009 \end_layout
1010
1011 \begin_layout Plain Layout
1012
1013 (-2,6)*{}="X1";
1014 \end_layout
1015
1016 \begin_layout Plain Layout
1017
1018 (-10,6)*{}="X2";
1019 \end_layout
1020
1021 \begin_layout Plain Layout
1022
1023 "X1";"X2" **
1024 \backslash
1025 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1026 \end_layout
1027
1028 \begin_layout Plain Layout
1029
1030 (-2,-6)*{}="XA";
1031 \end_layout
1032
1033 \begin_layout Plain Layout
1034
1035 (-10,-6)*{}="XB";
1036 \end_layout
1037
1038 \begin_layout Plain Layout
1039
1040 "XA";"XB" **
1041 \backslash
1042 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1043 \end_layout
1044
1045 \begin_layout Plain Layout
1046
1047
1048 \backslash
1049 endxy
1050 \end_layout
1051
1052 \end_inset
1053
1054
1055 \end_layout
1056
1057 \end_inset
1058
1059
1060 \end_layout
1061
1062 \begin_layout Description
1063 Categories
1064 \end_layout
1065
1066 \begin_layout Standard
1067 \begin_inset Preview
1068
1069 \begin_layout Standard
1070 \begin_inset ERT
1071 status collapsed
1072
1073 \begin_layout Plain Layout
1074
1075
1076 \backslash
1077 xymatrix{
1078 \end_layout
1079
1080 \begin_layout Plain Layout
1081
1082 (x
1083 \backslash
1084 otimes 1)
1085 \backslash
1086 otimes y
1087 \end_layout
1088
1089 \begin_layout Plain Layout
1090
1091
1092 \backslash
1093 ar[rr]^{a_{x,1,y}}
1094 \end_layout
1095
1096 \begin_layout Plain Layout
1097
1098
1099 \backslash
1100 ar[dr]_{r_x
1101 \backslash
1102 otimes 1_y}
1103 \end_layout
1104
1105 \begin_layout Plain Layout
1106
1107 && x
1108 \backslash
1109 otimes(1
1110 \backslash
1111 otimes y)
1112 \end_layout
1113
1114 \begin_layout Plain Layout
1115
1116
1117 \backslash
1118 ar[dl]^{1_x
1119 \backslash
1120 otimes
1121 \backslash
1122 ell_y }
1123 \backslash
1124
1125 \backslash
1126
1127 \end_layout
1128
1129 \begin_layout Plain Layout
1130
1131 & x
1132 \backslash
1133 otimes y }
1134 \end_layout
1135
1136 \end_inset
1137
1138
1139 \end_layout
1140
1141 \end_inset
1142
1143
1144 \begin_inset Preview
1145
1146 \begin_layout Standard
1147 \begin_inset ERT
1148 status collapsed
1149
1150 \begin_layout Plain Layout
1151
1152
1153 \backslash
1154 xy
1155 \end_layout
1156
1157 \begin_layout Plain Layout
1158
1159 (-9,0)*+{
1160 \backslash
1161 bullet}="1";
1162 \end_layout
1163
1164 \begin_layout Plain Layout
1165
1166 (0,0)*+{
1167 \backslash
1168 bullet}="2";
1169 \end_layout
1170
1171 \begin_layout Plain Layout
1172
1173 {
1174 \backslash
1175 ar@/^.9pc/ "1";"2"};
1176 \end_layout
1177
1178 \begin_layout Plain Layout
1179
1180 {
1181 \backslash
1182 ar@/_.9pc/ "1";"2"};
1183 \end_layout
1184
1185 \begin_layout Plain Layout
1186
1187 {
1188 \backslash
1189 ar@/^2pc/ "1";"2"};
1190 \end_layout
1191
1192 \begin_layout Plain Layout
1193
1194 {
1195 \backslash
1196 ar@/_2pc/ "1";"2"};
1197 \end_layout
1198
1199 \begin_layout Plain Layout
1200
1201 {
1202 \backslash
1203 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1204 \end_layout
1205
1206 \begin_layout Plain Layout
1207
1208 {
1209 \backslash
1210 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1211 \end_layout
1212
1213 \begin_layout Plain Layout
1214
1215 {
1216 \backslash
1217 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1218 \end_layout
1219
1220 \begin_layout Plain Layout
1221
1222 (0,0)*+{
1223 \backslash
1224 bullet}="1";
1225 \end_layout
1226
1227 \begin_layout Plain Layout
1228
1229 (9,0)*+{
1230 \backslash
1231 bullet}="2";
1232 \end_layout
1233
1234 \begin_layout Plain Layout
1235
1236 (18,0)*+{
1237 \backslash
1238 bullet}="3";
1239 \end_layout
1240
1241 \begin_layout Plain Layout
1242
1243 {
1244 \backslash
1245 ar "1";"2"};
1246 \end_layout
1247
1248 \begin_layout Plain Layout
1249
1250 {
1251 \backslash
1252 ar "2";"3"};
1253 \end_layout
1254
1255 \begin_layout Plain Layout
1256
1257 {
1258 \backslash
1259 ar@/^1pc/ "1";"2"};
1260 \end_layout
1261
1262 \begin_layout Plain Layout
1263
1264 {
1265 \backslash
1266 ar@/_1pc/ "1";"2"};
1267 \end_layout
1268
1269 \begin_layout Plain Layout
1270
1271 {
1272 \backslash
1273 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1274 \end_layout
1275
1276 \begin_layout Plain Layout
1277
1278 {
1279 \backslash
1280 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1281 \end_layout
1282
1283 \begin_layout Plain Layout
1284
1285
1286 \backslash
1287 endxy
1288 \end_layout
1289
1290 \end_inset
1291
1292
1293 \end_layout
1294
1295 \end_inset
1296
1297
1298 \end_layout
1299
1300 \begin_layout Description
1301 Transformations
1302 \end_layout
1303
1304 \begin_layout Standard
1305 \begin_inset Preview
1306
1307 \begin_layout Standard
1308 \begin_inset ERT
1309 status collapsed
1310
1311 \begin_layout Plain Layout
1312
1313
1314 \backslash
1315 xy %FIG.19.
1316  Natural transformation between functors.
1317 \end_layout
1318
1319 \begin_layout Plain Layout
1320
1321 (-26,-2)*+{
1322 \backslash
1323 bullet}="a";
1324 \end_layout
1325
1326 \begin_layout Plain Layout
1327
1328 (-12,3)*+{
1329 \backslash
1330 bullet}="b";
1331 \end_layout
1332
1333 \begin_layout Plain Layout
1334
1335 (-16,-5)*+{
1336 \backslash
1337 bullet}="c";
1338 \end_layout
1339
1340 \begin_layout Plain Layout
1341
1342 {
1343 \backslash
1344 ar@/^.25pc/ "a";"b"};
1345 \end_layout
1346
1347 \begin_layout Plain Layout
1348
1349 {
1350 \backslash
1351 ar@/_.25pc/"a";"c"};
1352 \end_layout
1353
1354 \begin_layout Plain Layout
1355
1356 {
1357 \backslash
1358 ar@/_.15pc/ "b";"c"};
1359 \end_layout
1360
1361 \begin_layout Plain Layout
1362
1363 %START TOP
1364 \end_layout
1365
1366 \begin_layout Plain Layout
1367
1368 (12,10)*+{
1369 \backslash
1370 bullet}="ta";
1371 \end_layout
1372
1373 \begin_layout Plain Layout
1374
1375 (26,15)*+{
1376 \backslash
1377 bullet}="tb";
1378 \end_layout
1379
1380 \begin_layout Plain Layout
1381
1382 (22,8)*+{
1383 \backslash
1384 bullet}="tc";
1385 \end_layout
1386
1387 \begin_layout Plain Layout
1388
1389 {
1390 \backslash
1391 ar@/^.25pc/ "ta";"tb"};
1392 \end_layout
1393
1394 \begin_layout Plain Layout
1395
1396 {
1397 \backslash
1398 ar@/_.25pc/ "ta";"tc"};
1399 \end_layout
1400
1401 \begin_layout Plain Layout
1402
1403 {
1404 \backslash
1405 ar@/_.15pc/ "tb";"tc"};
1406 \end_layout
1407
1408 \begin_layout Plain Layout
1409
1410 %START bottom
1411 \end_layout
1412
1413 \begin_layout Plain Layout
1414
1415 (12,-10)*+{
1416 \backslash
1417 bullet}="ba";
1418 \end_layout
1419
1420 \begin_layout Plain Layout
1421
1422 (26,-5)*+{
1423 \backslash
1424 bullet}="bb";
1425 \end_layout
1426
1427 \begin_layout Plain Layout
1428
1429 (22,-12)*+{
1430 \backslash
1431 bullet}="bc";
1432 \end_layout
1433
1434 \begin_layout Plain Layout
1435
1436 {
1437 \backslash
1438 ar@/^.25pc/@{.>} "ba";"bb"};
1439 \end_layout
1440
1441 \begin_layout Plain Layout
1442
1443 {
1444 \backslash
1445 ar@/_.25pc/ "ba";"bc"};
1446 \end_layout
1447
1448 \begin_layout Plain Layout
1449
1450 {
1451 \backslash
1452 ar@/_.15pc/ "bb";"bc"};
1453 \end_layout
1454
1455 \begin_layout Plain Layout
1456
1457 %START CONNECT
1458 \end_layout
1459
1460 \begin_layout Plain Layout
1461
1462 {
1463 \backslash
1464 ar@/_.15pc/ "ta";"ba"};
1465 \end_layout
1466
1467 \begin_layout Plain Layout
1468
1469 {
1470 \backslash
1471 ar@/_.15pc/ "tb";"bb"};
1472 \end_layout
1473
1474 \begin_layout Plain Layout
1475
1476 {
1477 \backslash
1478 ar@/_.15pc/ "tc";"bc"};
1479 \end_layout
1480
1481 \begin_layout Plain Layout
1482
1483 %START ARROWS AND LABELS
1484 \end_layout
1485
1486 \begin_layout Plain Layout
1487
1488 (-12,6)*{}="DF";
1489 \end_layout
1490
1491 \begin_layout Plain Layout
1492
1493 (6,10)*{}="CF";
1494 \end_layout
1495
1496 \begin_layout Plain Layout
1497
1498 {
1499 \backslash
1500 ar@/^.35pc/^F "DF";"CF"};
1501 \end_layout
1502
1503 \begin_layout Plain Layout
1504
1505 (-12,-6)*{}="DF";
1506 \end_layout
1507
1508 \begin_layout Plain Layout
1509
1510 (6,-10)*{}="CF";
1511 \end_layout
1512
1513 \begin_layout Plain Layout
1514
1515 {
1516 \backslash
1517 ar@/_.35pc/_G "DF";"CF"};
1518 \end_layout
1519
1520 \begin_layout Plain Layout
1521
1522 (-2,5)*{}="DF";
1523 \end_layout
1524
1525 \begin_layout Plain Layout
1526
1527 (-2,-5)*{}="CF";
1528 \end_layout
1529
1530 \begin_layout Plain Layout
1531
1532 {
1533 \backslash
1534 ar@{=>}^{
1535 \backslash
1536 alpha} "DF";"CF"};
1537 \end_layout
1538
1539 \begin_layout Plain Layout
1540
1541 (29,3)*{D};
1542 \end_layout
1543
1544 \begin_layout Plain Layout
1545
1546 (-23,3)*{C};
1547 \end_layout
1548
1549 \begin_layout Plain Layout
1550
1551
1552 \backslash
1553 endxy
1554 \end_layout
1555
1556 \end_inset
1557
1558
1559 \end_layout
1560
1561 \end_inset
1562
1563
1564 \end_layout
1565
1566 \begin_layout Section
1567 IPA
1568 \end_layout
1569
1570 \begin_layout Standard
1571 \begin_inset Preview
1572
1573 \begin_layout Standard
1574 \begin_inset ERT
1575 status collapsed
1576
1577 \begin_layout Plain Layout
1578
1579
1580 \backslash
1581 textipa{Ekspl@"neIS@n}
1582 \end_layout
1583
1584 \end_inset
1585
1586
1587 \end_layout
1588
1589 \end_inset
1590
1591
1592 \end_layout
1593
1594 \begin_layout Section
1595 QTree
1596 \end_layout
1597
1598 \begin_layout Standard
1599 \begin_inset Preview
1600
1601 \begin_layout Standard
1602 \begin_inset ERT
1603 status collapsed
1604
1605 \begin_layout Plain Layout
1606
1607
1608 \backslash
1609 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1610 \end_layout
1611
1612 \end_inset
1613
1614
1615 \end_layout
1616
1617 \end_inset
1618
1619
1620 \begin_inset Preview
1621
1622 \begin_layout Standard
1623 \begin_inset ERT
1624 status collapsed
1625
1626 \begin_layout Plain Layout
1627
1628
1629 \backslash
1630 Tree [.$
1631 \backslash
1632 sigma$ $
1633 \backslash
1634 mu$ $
1635 \backslash
1636 mu$ ]
1637 \end_layout
1638
1639 \end_inset
1640
1641
1642 \end_layout
1643
1644 \end_inset
1645
1646
1647 \end_layout
1648
1649 \begin_layout Section
1650 PSTricks
1651 \begin_inset CommandInset label
1652 LatexCommand label
1653 name "sec:PSTricks"
1654
1655 \end_inset
1656
1657
1658 \end_layout
1659
1660 \begin_layout Standard
1661 Some simple graphing examples.
1662 \end_layout
1663
1664 \begin_layout Subsection
1665 Function plotting
1666 \end_layout
1667
1668 \begin_layout Standard
1669 \begin_inset Preview
1670
1671 \begin_layout Standard
1672 \begin_inset ERT
1673 status open
1674
1675 \begin_layout Plain Layout
1676
1677
1678 \backslash
1679 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1680 \end_layout
1681
1682 \begin_layout Plain Layout
1683
1684
1685 \backslash
1686 psaxes{->}(0,0)(0,-3)(10,3)
1687 \end_layout
1688
1689 \begin_layout Plain Layout
1690
1691
1692 \backslash
1693 uput[-90](10,0){$x$}
1694 \backslash
1695 uput[0](0,3){$f(x)$}
1696 \end_layout
1697
1698 \begin_layout Plain Layout
1699
1700
1701 \backslash
1702 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1703 \end_layout
1704
1705 \begin_layout Plain Layout
1706
1707
1708 \backslash
1709 end{pspicture*}
1710 \end_layout
1711
1712 \end_inset
1713
1714
1715 \end_layout
1716
1717 \end_inset
1718
1719
1720 \end_layout
1721
1722 \begin_layout Subsection
1723 Inline data plotting
1724 \end_layout
1725
1726 \begin_layout Standard
1727 \align center
1728 \begin_inset Preview
1729
1730 \begin_layout Standard
1731 \align center
1732 \begin_inset ERT
1733 status open
1734
1735 \begin_layout Plain Layout
1736
1737
1738 \backslash
1739 begin{pspicture*}(-1.5,-1.5)(11,5)
1740 \end_layout
1741
1742 \begin_layout Plain Layout
1743
1744
1745 \backslash
1746 psaxes{->}(0,0)(0,0)(10,5)
1747 \end_layout
1748
1749 \begin_layout Plain Layout
1750
1751
1752 \backslash
1753 psset{linewidth=2.5pt}
1754 \end_layout
1755
1756 \begin_layout Plain Layout
1757
1758
1759 \backslash
1760 rput(5.0,-1.0){Speed [MPH]}
1761 \end_layout
1762
1763 \begin_layout Plain Layout
1764
1765
1766 \backslash
1767 rput(-1.0,1.0){
1768 \backslash
1769 begin{rotate}{90}Cost [Dollars]
1770 \backslash
1771 end{rotate}}
1772 \end_layout
1773
1774 \begin_layout Plain Layout
1775
1776
1777 \backslash
1778 savedata{
1779 \backslash
1780 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1781 \end_layout
1782
1783 \begin_layout Plain Layout
1784
1785
1786 \backslash
1787 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1788 \backslash
1789 mydata}
1790 \end_layout
1791
1792 \begin_layout Plain Layout
1793
1794
1795 \backslash
1796 end{pspicture*}
1797 \end_layout
1798
1799 \end_inset
1800
1801
1802 \end_layout
1803
1804 \end_inset
1805
1806
1807 \end_layout
1808
1809 \begin_layout Subsection
1810 Lissajous curves
1811 \end_layout
1812
1813 \begin_layout Standard
1814 \begin_inset Preview
1815
1816 \begin_layout Standard
1817 \begin_inset ERT
1818 status open
1819
1820 \begin_layout Plain Layout
1821
1822
1823 \backslash
1824 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1825 \end_layout
1826
1827 \begin_layout Plain Layout
1828
1829
1830 \backslash
1831 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1832  cos 100 t mul sin}
1833 \end_layout
1834
1835 \begin_layout Plain Layout
1836
1837
1838 \backslash
1839 end{pspicture*}
1840 \end_layout
1841
1842 \end_inset
1843
1844
1845 \end_layout
1846
1847 \end_inset
1848
1849
1850 \begin_inset space \hfill{}
1851 \end_inset
1852
1853
1854 \begin_inset Preview
1855
1856 \begin_layout Standard
1857 \begin_inset ERT
1858 status open
1859
1860 \begin_layout Plain Layout
1861
1862
1863 \backslash
1864 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1865 \end_layout
1866
1867 \begin_layout Plain Layout
1868
1869
1870 \backslash
1871 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1872  mul cos 100 t mul sin}
1873 \end_layout
1874
1875 \begin_layout Plain Layout
1876
1877
1878 \backslash
1879 end{pspicture*}
1880 \end_layout
1881
1882 \end_inset
1883
1884
1885 \end_layout
1886
1887 \end_inset
1888
1889
1890 \begin_inset space \hfill{}
1891 \end_inset
1892
1893
1894 \begin_inset Preview
1895
1896 \begin_layout Standard
1897 \begin_inset ERT
1898 status open
1899
1900 \begin_layout Plain Layout
1901
1902
1903 \backslash
1904 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1905 \end_layout
1906
1907 \begin_layout Plain Layout
1908
1909
1910 \backslash
1911 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1912  mul cos 200 t mul sin}
1913 \end_layout
1914
1915 \begin_layout Plain Layout
1916
1917
1918 \backslash
1919 end{pspicture*}
1920 \end_layout
1921
1922 \end_inset
1923
1924
1925 \end_layout
1926
1927 \end_inset
1928
1929
1930 \begin_inset space \hfill{}
1931 \end_inset
1932
1933
1934 \begin_inset Preview
1935
1936 \begin_layout Standard
1937 \begin_inset ERT
1938 status open
1939
1940 \begin_layout Plain Layout
1941
1942
1943 \backslash
1944 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1945 \end_layout
1946
1947 \begin_layout Plain Layout
1948
1949
1950 \backslash
1951 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1952  mul cos 200 t mul sin}
1953 \end_layout
1954
1955 \begin_layout Plain Layout
1956
1957
1958 \backslash
1959 end{pspicture*}
1960 \end_layout
1961
1962 \end_inset
1963
1964
1965 \end_layout
1966
1967 \end_inset
1968
1969
1970 \end_layout
1971
1972 \begin_layout Section
1973 TikZ
1974 \end_layout
1975
1976 \begin_layout Standard
1977 \begin_inset Flex URL
1978 status collapsed
1979
1980 \begin_layout Plain Layout
1981
1982 http://media.texample.net/tikz/examples/TEX/free-body-diagrams.tex
1983 \end_layout
1984
1985 \end_inset
1986
1987
1988 \end_layout
1989
1990 \begin_layout Standard
1991 \begin_inset Preview
1992
1993 \begin_layout Standard
1994 \begin_inset ERT
1995 status collapsed
1996
1997 \begin_layout Plain Layout
1998
1999
2000 \backslash
2001 def
2002 \backslash
2003 iangle{35} % Angle of the inclined plane
2004 \end_layout
2005
2006 \begin_layout Plain Layout
2007
2008
2009 \backslash
2010 def
2011 \backslash
2012 down{-90}
2013 \end_layout
2014
2015 \begin_layout Plain Layout
2016
2017
2018 \backslash
2019 def
2020 \backslash
2021 arcr{0.5cm} % Radius of the arc used to indicate angles
2022 \end_layout
2023
2024 \begin_layout Plain Layout
2025
2026 \end_layout
2027
2028 \begin_layout Plain Layout
2029
2030
2031 \backslash
2032 begin{tikzpicture}[
2033 \end_layout
2034
2035 \begin_layout Plain Layout
2036
2037     force/.style={>=latex,draw=blue,fill=blue},
2038 \end_layout
2039
2040 \begin_layout Plain Layout
2041
2042     axis/.style={densely dashed,gray,font=
2043 \backslash
2044 small},
2045 \end_layout
2046
2047 \begin_layout Plain Layout
2048
2049     M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2050 \end_layout
2051
2052 \begin_layout Plain Layout
2053
2054     m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2055 \end_layout
2056
2057 \begin_layout Plain Layout
2058
2059     plane/.style={draw=black,fill=blue!10},
2060 \end_layout
2061
2062 \begin_layout Plain Layout
2063
2064     string/.style={draw=red, thick},
2065 \end_layout
2066
2067 \begin_layout Plain Layout
2068
2069     pulley/.style={thick},
2070 \end_layout
2071
2072 \begin_layout Plain Layout
2073
2074 ]
2075 \end_layout
2076
2077 \begin_layout Plain Layout
2078
2079 \end_layout
2080
2081 \begin_layout Plain Layout
2082
2083
2084 \backslash
2085 matrix[column sep=1cm] {
2086 \end_layout
2087
2088 \begin_layout Plain Layout
2089
2090     %% Sketch
2091 \end_layout
2092
2093 \begin_layout Plain Layout
2094
2095
2096 \backslash
2097 draw[plane] (0,-1) coordinate (base)
2098 \end_layout
2099
2100 \begin_layout Plain Layout
2101
2102                      -- coordinate[pos=0.5] (mid) ++(
2103 \backslash
2104 iangle:3) coordinate (top)
2105 \end_layout
2106
2107 \begin_layout Plain Layout
2108
2109                      |- (base) -- cycle;
2110 \end_layout
2111
2112 \begin_layout Plain Layout
2113
2114
2115 \backslash
2116 path (mid) node[M,rotate=
2117 \backslash
2118 iangle,yshift=0.25cm] (M) {};
2119 \end_layout
2120
2121 \begin_layout Plain Layout
2122
2123
2124 \backslash
2125 draw[pulley] (top) -- ++(
2126 \backslash
2127 iangle:0.25) circle (0.25cm)
2128 \end_layout
2129
2130 \begin_layout Plain Layout
2131
2132                    ++ (90-
2133 \backslash
2134 iangle:0.5) coordinate (pulley);
2135 \end_layout
2136
2137 \begin_layout Plain Layout
2138
2139
2140 \backslash
2141 draw[string] (M.east) -- ++(
2142 \backslash
2143 iangle:1.5cm) arc (90+
2144 \backslash
2145 iangle:0:0.25)
2146 \end_layout
2147
2148 \begin_layout Plain Layout
2149
2150                   -- ++(0,-1) node[m] {};
2151 \end_layout
2152
2153 \begin_layout Plain Layout
2154
2155 \end_layout
2156
2157 \begin_layout Plain Layout
2158
2159
2160 \backslash
2161 draw[->] (base)++(
2162 \backslash
2163 arcr,0) arc (0:
2164 \backslash
2165 iangle:
2166 \backslash
2167 arcr);
2168 \end_layout
2169
2170 \begin_layout Plain Layout
2171
2172
2173 \backslash
2174 path (base)++(
2175 \backslash
2176 iangle*0.5:
2177 \backslash
2178 arcr+5pt) node {$
2179 \backslash
2180 alpha$};
2181 \end_layout
2182
2183 \begin_layout Plain Layout
2184
2185     %%
2186 \end_layout
2187
2188 \begin_layout Plain Layout
2189
2190 \end_layout
2191
2192 \begin_layout Plain Layout
2193
2194 &
2195 \end_layout
2196
2197 \begin_layout Plain Layout
2198
2199     %% Free body diagram of M
2200 \end_layout
2201
2202 \begin_layout Plain Layout
2203
2204
2205 \backslash
2206 begin{scope}[rotate=
2207 \backslash
2208 iangle]
2209 \end_layout
2210
2211 \begin_layout Plain Layout
2212
2213
2214 \backslash
2215 node[M,transform shape] (M) {};
2216 \end_layout
2217
2218 \begin_layout Plain Layout
2219
2220         % Draw axes and help lines
2221 \end_layout
2222
2223 \begin_layout Plain Layout
2224
2225 \end_layout
2226
2227 \begin_layout Plain Layout
2228
2229         {[axis,->]
2230 \end_layout
2231
2232 \begin_layout Plain Layout
2233
2234
2235 \backslash
2236 draw (0,-1) -- (0,2) node[right] {$+y$};
2237 \end_layout
2238
2239 \begin_layout Plain Layout
2240
2241
2242 \backslash
2243 draw (M) -- ++(2,0) node[right] {$+x$};
2244 \end_layout
2245
2246 \begin_layout Plain Layout
2247
2248             % Indicate angle.
2249  The code is a bit awkward.
2250 \end_layout
2251
2252 \begin_layout Plain Layout
2253
2254 \end_layout
2255
2256 \begin_layout Plain Layout
2257
2258
2259 \backslash
2260 draw[solid,shorten >=0.5pt] (
2261 \backslash
2262 down-
2263 \backslash
2264 iangle:
2265 \backslash
2266 arcr)
2267 \end_layout
2268
2269 \begin_layout Plain Layout
2270
2271                 arc(
2272 \backslash
2273 down-
2274 \backslash
2275 iangle:
2276 \backslash
2277 down:
2278 \backslash
2279 arcr);
2280 \end_layout
2281
2282 \begin_layout Plain Layout
2283
2284
2285 \backslash
2286 node at (
2287 \backslash
2288 down-0.5*
2289 \backslash
2290 iangle:1.3*
2291 \backslash
2292 arcr) {$
2293 \backslash
2294 alpha$};
2295 \end_layout
2296
2297 \begin_layout Plain Layout
2298
2299         }
2300 \end_layout
2301
2302 \begin_layout Plain Layout
2303
2304 \end_layout
2305
2306 \begin_layout Plain Layout
2307
2308         % Forces
2309 \end_layout
2310
2311 \begin_layout Plain Layout
2312
2313         {[force,->]
2314 \end_layout
2315
2316 \begin_layout Plain Layout
2317
2318             % Assuming that Mg = 1.
2319  The normal force will therefore be cos(alpha)
2320 \end_layout
2321
2322 \begin_layout Plain Layout
2323
2324
2325 \backslash
2326 draw (M.center) -- ++(0,{cos(
2327 \backslash
2328 iangle)}) node[above right] {$N$};
2329 \end_layout
2330
2331 \begin_layout Plain Layout
2332
2333
2334 \backslash
2335 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2336 \end_layout
2337
2338 \begin_layout Plain Layout
2339
2340
2341 \backslash
2342 draw (M.east) -- ++(1,0) node[above] {$T$};
2343 \end_layout
2344
2345 \begin_layout Plain Layout
2346
2347         }
2348 \end_layout
2349
2350 \begin_layout Plain Layout
2351
2352 \end_layout
2353
2354 \begin_layout Plain Layout
2355
2356
2357 \backslash
2358 end{scope}
2359 \end_layout
2360
2361 \begin_layout Plain Layout
2362
2363     % Draw gravity force.
2364  The code is put outside the rotated
2365 \end_layout
2366
2367 \begin_layout Plain Layout
2368
2369     % scope for simplicity.
2370  No need to do any angle calculations.
2371
2372 \end_layout
2373
2374 \begin_layout Plain Layout
2375
2376
2377 \backslash
2378 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2379 \end_layout
2380
2381 \begin_layout Plain Layout
2382
2383     %%
2384 \end_layout
2385
2386 \begin_layout Plain Layout
2387
2388 \end_layout
2389
2390 \begin_layout Plain Layout
2391
2392 &
2393 \end_layout
2394
2395 \begin_layout Plain Layout
2396
2397     %%%
2398 \end_layout
2399
2400 \begin_layout Plain Layout
2401
2402     % Free body diagram of m
2403 \end_layout
2404
2405 \begin_layout Plain Layout
2406
2407
2408 \backslash
2409 node[m] (m) {};
2410 \end_layout
2411
2412 \begin_layout Plain Layout
2413
2414
2415 \backslash
2416 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2417 \end_layout
2418
2419 \begin_layout Plain Layout
2420
2421     {[force,->]
2422 \end_layout
2423
2424 \begin_layout Plain Layout
2425
2426
2427 \backslash
2428 draw (m.north) -- ++(0,1) node[above] {$T'$};
2429 \end_layout
2430
2431 \begin_layout Plain Layout
2432
2433
2434 \backslash
2435 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2436 \end_layout
2437
2438 \begin_layout Plain Layout
2439
2440     }
2441 \end_layout
2442
2443 \begin_layout Plain Layout
2444
2445 \end_layout
2446
2447 \begin_layout Plain Layout
2448
2449
2450 \backslash
2451
2452 \backslash
2453
2454 \end_layout
2455
2456 \begin_layout Plain Layout
2457
2458 };
2459 \end_layout
2460
2461 \begin_layout Plain Layout
2462
2463
2464 \backslash
2465 end{tikzpicture}
2466 \end_layout
2467
2468 \begin_layout Plain Layout
2469
2470 \end_layout
2471
2472 \end_inset
2473
2474
2475 \end_layout
2476
2477 \end_inset
2478
2479
2480 \end_layout
2481
2482 \end_body
2483 \end_document