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