lib/examples/instant_preview.lyx

   1 #LyX 2.1 created this file. For more info see http://www.lyx.org/
   2 \lyxformat 474
   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_math auto
  27 \font_default_family default
  28 \use_non_tex_fonts false
  29 \font_sc false
  30 \font_osf false
  31 \font_sf_scale 100
  32 \font_tt_scale 100
  33 \graphics default
  34 \default_output_format pdf
  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_package amsmath 1
  44 \use_package amssymb 1
  45 \use_package cancel 0
  46 \use_package esint 1
  47 \use_package mathdots 1
  48 \use_package mathtools 0
  49 \use_package mhchem 1
  50 \use_package stackrel 0
  51 \use_package stmaryrd 0
  52 \use_package undertilde 0
  53 \cite_engine basic
  54 \cite_engine_type default
  55 \biblio_style plain
  56 \use_bibtopic false
  57 \use_indices false
  58 \paperorientation portrait
  59 \suppress_date false
  60 \justification true
  61 \use_refstyle 0
  62 \index Index
  63 \shortcut idx
  64 \color #008000
  65 \end_index
  66 \secnumdepth 3
  67 \tocdepth 3
  68 \paragraph_separation indent
  69 \paragraph_indentation default
  70 \quotes_language english
  71 \papercolumns 1
  72 \papersides 1
  73 \paperpagestyle default
  74 \tracking_changes false
  75 \output_changes false
  76 \html_math_output 0
  77 \html_css_as_file 0
  78 \html_be_strict true
  79 \end_header
  80
  81 \begin_body
  82
  83 \begin_layout Section
  84 Introduction
  85 \end_layout
  86
  87 \begin_layout Standard
  88 In order to properly typeset the document and have instant preview working,
  89  the following packages have to be installed:
  90 \end_layout
  91
  92 \begin_layout LyX-Code
  93 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf
  94 \end_layout
  95
  96 \begin_layout Standard
  97 Due to the use of postscript specials in Section
  98 \begin_inset CommandInset ref
  99 LatexCommand ref
 100 reference "sec:PSTricks"
 101
 102 \end_inset
 103
 104 , only the Postscript or PDF (ps2pdf) output formats will correctly render
 105  the included images.
 106  However, the PDF (XeTeX) output seems to also work, while trying to typeset
 107  the document with
 108 \family typewriter
 109 pdflatex
 110 \family default
 111  or
 112 \family typewriter
 113 pdflualatex
 114 \family default
 115  will generate errors.
 116 \end_layout
 117
 118 \begin_layout Section
 119 Diagrams by XY(-pic)
 120 \end_layout
 121
 122 \begin_layout Standard
 123 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
 124  examples, see
 125 \begin_inset Flex URL
 126 status collapsed
 127
 128 \begin_layout Plain Layout
 129
 130 http://www.math.columbia.edu/~lauda/xy/
 131 \end_layout
 132
 133 \end_inset
 134
 135 .
 136 \end_layout
 137
 138 \begin_layout Description
 139 Braid
 140 \end_layout
 141
 142 \begin_layout Standard
 143 \begin_inset Preview
 144
 145 \begin_layout Standard
 146 \begin_inset ERT
 147 status collapsed
 148
 149 \begin_layout Plain Layout
 150
 151
 152 \backslash
 153 xy
 154 \end_layout
 155
 156 \begin_layout Plain Layout
 157
 158 (5,10)*{}; (-10,-10)*{} **
 159 \backslash
 160 crv{(6,-2)&(-12,4)}
 161 \end_layout
 162
 163 \begin_layout Plain Layout
 164
 165
 166 \backslash
 167 POS?(.25)*{
 168 \backslash
 169 hole}="x"
 170 \backslash
 171 POS?(.45)*{
 172 \backslash
 173 hole}="y"
 174 \backslash
 175 POS?(.6)*{
 176 \backslash
 177 hole}="z";
 178 \end_layout
 179
 180 \begin_layout Plain Layout
 181
 182 "y"+(0,-1); (2,-10)*{} **
 183 \backslash
 184 crv{}
 185 \backslash
 186 POS?(.2)*{
 187 \backslash
 188 hole}="M";
 189 \end_layout
 190
 191 \begin_layout Plain Layout
 192
 193 (-10,10)*{}; "z" **
 194 \backslash
 195 crv{(-9,0)};
 196 \end_layout
 197
 198 \begin_layout Plain Layout
 199
 200 "z"; "M" **
 201 \backslash
 202 crv{};
 203 \end_layout
 204
 205 \begin_layout Plain Layout
 206
 207 "M"; "x" **
 208 \backslash
 209 crv{(5,0)};
 210 \end_layout
 211
 212 \begin_layout Plain Layout
 213
 214 "x"; "y" **
 215 \backslash
 216 crv{(0,7) & (-5,6)};
 217 \end_layout
 218
 219 \begin_layout Plain Layout
 220
 221
 222 \backslash
 223 endxy
 224 \end_layout
 225
 226 \end_inset
 227
 228
 229 \end_layout
 230
 231 \end_inset
 232
 233
 234 \end_layout
 235
 236 \begin_layout Description
 237 Knots
 238 \end_layout
 239
 240 \begin_layout Standard
 241 \begin_inset Preview
 242
 243 \begin_layout Standard
 244 \begin_inset ERT
 245 status collapsed
 246
 247 \begin_layout Plain Layout
 248
 249
 250 \backslash
 251 xy
 252 \end_layout
 253
 254 \begin_layout Plain Layout
 255
 256 (6,9)*{}="1";
 257 \end_layout
 258
 259 \begin_layout Plain Layout
 260
 261 (-8.5,-1)*{}="2";
 262 \end_layout
 263
 264 \begin_layout Plain Layout
 265
 266 "1";"2" **
 267 \backslash
 268 crv{~*=<.5pt>{.} (0,30)}?(.75)*
 269 \backslash
 270 dir{>}+(-2,2)*{z};
 271 \end_layout
 272
 273 \begin_layout Plain Layout
 274
 275 (-6.5,8)*{}="1";
 276 \end_layout
 277
 278 \begin_layout Plain Layout
 279
 280 (-.5,-9)*{}="2";
 281 \end_layout
 282
 283 \begin_layout Plain Layout
 284
 285 "1";"2" **
 286 \backslash
 287 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
 288 \backslash
 289 dir{>}+(-2,-2)*{u};
 290 \end_layout
 291
 292 \begin_layout Plain Layout
 293
 294 (-9.5,-3.35)*{}="1";
 295 \end_layout
 296
 297 \begin_layout Plain Layout
 298
 299 (8.5,-3)*{}="2";
 300 \end_layout
 301
 302 \begin_layout Plain Layout
 303
 304 "1";"2" **
 305 \backslash
 306 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
 307 \backslash
 308 dir{>}+(-1,-3)*{x};
 309 \end_layout
 310
 311 \begin_layout Plain Layout
 312
 313 (1,-10)*{}="1";
 314 \end_layout
 315
 316 \begin_layout Plain Layout
 317
 318 (6.5,7.13)*{}="2";
 319 \end_layout
 320
 321 \begin_layout Plain Layout
 322
 323 "1";"2" **
 324 \backslash
 325 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
 326 \backslash
 327 dir{>}+(3,-1)*{y};
 328 \end_layout
 329
 330 \begin_layout Plain Layout
 331
 332 (11,-1)*{}="1";
 333 \end_layout
 334
 335 \begin_layout Plain Layout
 336
 337 (-4,8)*{}="2";
 338 \end_layout
 339
 340 \begin_layout Plain Layout
 341
 342 "1";"2" **
 343 \backslash
 344 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
 345 \backslash
 346 dir{>}+(1,2)*{w};
 347 \end_layout
 348
 349 \begin_layout Plain Layout
 350
 351
 352 \backslash
 353 endxy
 354 \end_layout
 355
 356 \end_inset
 357
 358
 359 \end_layout
 360
 361 \end_inset
 362
 363
 364 \end_layout
 365
 366 \begin_layout Description
 367 Circles
 368 \end_layout
 369
 370 \begin_layout Standard
 371 \begin_inset Preview
 372
 373 \begin_layout Standard
 374 \begin_inset ERT
 375 status collapsed
 376
 377 \begin_layout Plain Layout
 378
 379
 380 \backslash
 381 xy
 382 \end_layout
 383
 384 \begin_layout Plain Layout
 385
 386 (0,0)*
 387 \backslash
 388 xycircle(14,8){++
 389 \backslash
 390 dir{<}};
 391 \end_layout
 392
 393 \begin_layout Plain Layout
 394
 395 (0,0)*
 396 \backslash
 397 xycircle<10pt>{{.}};
 398 \end_layout
 399
 400 \begin_layout Plain Layout
 401
 402 (0,0)*
 403 \backslash
 404 xycircle(5,2){:};
 405 \end_layout
 406
 407 \begin_layout Plain Layout
 408
 409 (0,15)*
 410 \backslash
 411 xycircle(10,4){--};
 412 \end_layout
 413
 414 \begin_layout Plain Layout
 415
 416
 417 \backslash
 418 endxy
 419 \end_layout
 420
 421 \end_inset
 422
 423
 424 \end_layout
 425
 426 \end_inset
 427
 428
 429 \end_layout
 430
 431 \begin_layout Description
 432 Cobordism
 433 \end_layout
 434
 435 \begin_layout Standard
 436 \begin_inset Preview
 437
 438 \begin_layout Standard
 439 \begin_inset ERT
 440 status collapsed
 441
 442 \begin_layout Plain Layout
 443
 444
 445 \backslash
 446 xy
 447 \end_layout
 448
 449 \begin_layout Plain Layout
 450
 451 (0,0)*
 452 \backslash
 453 ellipse(3,1){.};
 454 \end_layout
 455
 456 \begin_layout Plain Layout
 457
 458 (0,0)*
 459 \backslash
 460 ellipse(3,1)__,=:a(-180){-};
 461 \end_layout
 462
 463 \begin_layout Plain Layout
 464
 465 (-6,-8)*
 466 \backslash
 467 ellipse(3,1){.};
 468 \end_layout
 469
 470 \begin_layout Plain Layout
 471
 472 (6,-8)*
 473 \backslash
 474 ellipse(3,1){.};
 475 \end_layout
 476
 477 \begin_layout Plain Layout
 478
 479 (0,-8)*
 480 \backslash
 481 ellipse(3,1){.};
 482 \end_layout
 483
 484 \begin_layout Plain Layout
 485
 486 (-6,-8)*
 487 \backslash
 488 ellipse(3,1)__,=:a(-180){-};
 489 \end_layout
 490
 491 \begin_layout Plain Layout
 492
 493 (6,-8)*
 494 \backslash
 495 ellipse(3,1)__,=:a(-180){-};
 496 \end_layout
 497
 498 \begin_layout Plain Layout
 499
 500 (0,-8)*
 501 \backslash
 502 ellipse(3,1)__,=:a(180){-};
 503 \end_layout
 504
 505 \begin_layout Plain Layout
 506
 507 (-3,6)*
 508 \backslash
 509 ellipse(3,1){-};
 510 \end_layout
 511
 512 \begin_layout Plain Layout
 513
 514 (3,6)*
 515 \backslash
 516 ellipse(3,1){-};
 517 \end_layout
 518
 519 \begin_layout Plain Layout
 520
 521 (-3,12)*{}="1";
 522 \end_layout
 523
 524 \begin_layout Plain Layout
 525
 526 (3,12)*{}="2";
 527 \end_layout
 528
 529 \begin_layout Plain Layout
 530
 531 (-9,12)*{}="A2";
 532 \end_layout
 533
 534 \begin_layout Plain Layout
 535
 536 (9,12)*{}="B2";
 537 \end_layout
 538
 539 \begin_layout Plain Layout
 540
 541 "1";"2" **
 542 \backslash
 543 crv{(-3,7) & (3,7)};
 544 \end_layout
 545
 546 \begin_layout Plain Layout
 547
 548 (-3,0)*{}="A";
 549 \end_layout
 550
 551 \begin_layout Plain Layout
 552
 553 (3,0)*{}="B";
 554 \end_layout
 555
 556 \begin_layout Plain Layout
 557
 558 (-3,1)*{}="A1";
 559 \end_layout
 560
 561 \begin_layout Plain Layout
 562
 563 (3,1)*{}="B1";
 564 \end_layout
 565
 566 \begin_layout Plain Layout
 567
 568 "A";"A1" **
 569 \backslash
 570 dir{-};
 571 \end_layout
 572
 573 \begin_layout Plain Layout
 574
 575 "B";"B1" **
 576 \backslash
 577 dir{-};
 578 \end_layout
 579
 580 \begin_layout Plain Layout
 581
 582 "B2";"B1" **
 583 \backslash
 584 crv{(8,7) & (3,5)};
 585 \end_layout
 586
 587 \begin_layout Plain Layout
 588
 589 "A2";"A1" **
 590 \backslash
 591 crv{(-8,7) & (-3,5)};
 592 \end_layout
 593
 594 \begin_layout Plain Layout
 595
 596 %REFLECT
 597 \end_layout
 598
 599 \begin_layout Plain Layout
 600
 601 (3,-16)*{}="1";
 602 \end_layout
 603
 604 \begin_layout Plain Layout
 605
 606 (9,-16)*{}="2";
 607 \end_layout
 608
 609 \begin_layout Plain Layout
 610
 611 "1";"2" **
 612 \backslash
 613 crv{(3,-10) & (9,-10)};
 614 \end_layout
 615
 616 \begin_layout Plain Layout
 617
 618 (-3,-16)*{}="1";
 619 \end_layout
 620
 621 \begin_layout Plain Layout
 622
 623 (-9,-16)*{}="2";
 624 \end_layout
 625
 626 \begin_layout Plain Layout
 627
 628 "1";"2" **
 629 \backslash
 630 crv{(-3,-10) & (-9,-10)};
 631 \end_layout
 632
 633 \begin_layout Plain Layout
 634
 635 (-15,-16)*{}="A2";
 636 \end_layout
 637
 638 \begin_layout Plain Layout
 639
 640 (15,-16)*{}="B2";
 641 \end_layout
 642
 643 \begin_layout Plain Layout
 644
 645 (-3,0)*{}="A";
 646 \end_layout
 647
 648 \begin_layout Plain Layout
 649
 650 (3,0)*{}="B";
 651 \end_layout
 652
 653 \begin_layout Plain Layout
 654
 655 (-3,-1)*{}="A1";
 656 \end_layout
 657
 658 \begin_layout Plain Layout
 659
 660 (3,-1)*{}="B1";
 661 \end_layout
 662
 663 \begin_layout Plain Layout
 664
 665 "A";"A1" **
 666 \backslash
 667 dir{-};
 668 \end_layout
 669
 670 \begin_layout Plain Layout
 671
 672 "B";"B1" **
 673 \backslash
 674 dir{-};
 675 \end_layout
 676
 677 \begin_layout Plain Layout
 678
 679 "B2";"B1" **
 680 \backslash
 681 crv{(13,-6) & (2,-8)};
 682 \end_layout
 683
 684 \begin_layout Plain Layout
 685
 686 "A2";"A1" **
 687 \backslash
 688 crv{(-13,-6) & (-2,-8)};
 689 \end_layout
 690
 691 \begin_layout Plain Layout
 692
 693
 694 \backslash
 695 endxy
 696 \end_layout
 697
 698 \end_inset
 699
 700
 701 \end_layout
 702
 703 \end_inset
 704
 705
 706 \begin_inset Preview
 707
 708 \begin_layout Standard
 709 \begin_inset ERT
 710 status collapsed
 711
 712 \begin_layout Plain Layout
 713
 714
 715 \backslash
 716 xy 0;/r.18pc/:
 717 \end_layout
 718
 719 \begin_layout Plain Layout
 720
 721 (20,2)*{
 722 \backslash
 723 bullet}="RU"+(1,3)*{x^{
 724 \backslash
 725 ast}};
 726 \end_layout
 727
 728 \begin_layout Plain Layout
 729
 730 (16,-3)*{
 731 \backslash
 732 bullet}="RD"+(2.5,2)*{x^{
 733 \backslash
 734 ast}};
 735 \end_layout
 736
 737 \begin_layout Plain Layout
 738
 739 (-16,2)*{
 740 \backslash
 741 bullet}="LU"+(-1,2)*{x};
 742 \end_layout
 743
 744 \begin_layout Plain Layout
 745
 746 (-20,-3)*{
 747 \backslash
 748 bullet}="LD"+(-1,2)*{x};
 749 \end_layout
 750
 751 \begin_layout Plain Layout
 752
 753 "RU";"RD" **
 754 \backslash
 755 crv{(4,2) & (4,-1)}; ?(.1)*
 756 \backslash
 757 dir{<}; ?(.85)*
 758 \backslash
 759 dir{<};
 760 \end_layout
 761
 762 \begin_layout Plain Layout
 763
 764 "LD";"LU" **
 765 \backslash
 766 crv{(-4,-2) & (-4,1)};
 767 \end_layout
 768
 769 \begin_layout Plain Layout
 770
 771 ?(.08)*
 772 \backslash
 773 dir{<}; ?(.85)*
 774 \backslash
 775 dir{<};
 776 \end_layout
 777
 778 \begin_layout Plain Layout
 779
 780 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
 781 \end_layout
 782
 783 \begin_layout Plain Layout
 784
 785 "x1"; "x2" **
 786 \backslash
 787 crv{(7,-10) & (-7,-10)};
 788 \end_layout
 789
 790 \begin_layout Plain Layout
 791
 792 (16,-20)*{
 793 \backslash
 794 bullet}="RDD"+(2.5,-1)*{x^{
 795 \backslash
 796 ast}};
 797 \end_layout
 798
 799 \begin_layout Plain Layout
 800
 801 (-20,-20)*{
 802 \backslash
 803 bullet}="LDD"+(-1,-3)*{x};
 804 \end_layout
 805
 806 \begin_layout Plain Layout
 807
 808 (20,-12.5)*{
 809 \backslash
 810 bullet}="RUD"+(3.5,1)*{x^{
 811 \backslash
 812 ast}};
 813 \end_layout
 814
 815 \begin_layout Plain Layout
 816
 817 (-16,-15)*{
 818 \backslash
 819 bullet}="LUD";
 820 \end_layout
 821
 822 \begin_layout Plain Layout
 823
 824 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
 825 \end_layout
 826
 827 \begin_layout Plain Layout
 828
 829 "RD"; "RDD" **
 830 \backslash
 831 dir{-};
 832 \end_layout
 833
 834 \begin_layout Plain Layout
 835
 836 "LD"; "LDD" **
 837 \backslash
 838 dir{-};
 839 \end_layout
 840
 841 \begin_layout Plain Layout
 842
 843 "A"; "LUD" **
 844 \backslash
 845 dir{.};
 846 \end_layout
 847
 848 \begin_layout Plain Layout
 849
 850 "RDD"; "LDD" **
 851 \backslash
 852 crv{(0,-17)}; ?(.57)*
 853 \backslash
 854 dir{>};
 855 \end_layout
 856
 857 \begin_layout Plain Layout
 858
 859 "RU"; "RUD" **
 860 \backslash
 861 dir{-};
 862 \end_layout
 863
 864 \begin_layout Plain Layout
 865
 866 "LU"; "A" **
 867 \backslash
 868 dir{-};
 869 \end_layout
 870
 871 \begin_layout Plain Layout
 872
 873 "B"; "RUD" **
 874 \backslash
 875 crv{(18,-14.15)};
 876 \end_layout
 877
 878 \begin_layout Plain Layout
 879
 880 "B"; "LUD" **
 881 \backslash
 882 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
 883 \backslash
 884 dir{<};
 885 \end_layout
 886
 887 \begin_layout Plain Layout
 888
 889
 890 \backslash
 891 endxy
 892 \end_layout
 893
 894 \end_inset
 895
 896
 897 \end_layout
 898
 899 \end_inset
 900
 901
 902 \end_layout
 903
 904 \begin_layout Description
 905 Strings
 906 \end_layout
 907
 908 \begin_layout Standard
 909 \begin_inset Preview
 910
 911 \begin_layout Standard
 912 \begin_inset ERT
 913 status open
 914
 915 \begin_layout Plain Layout
 916
 917
 918 \backslash
 919 xy (-15,0)*{};(15,0)*{};
 920 \end_layout
 921
 922 \begin_layout Plain Layout
 923
 924
 925 \backslash
 926 endxy
 927 \end_layout
 928
 929 \begin_layout Plain Layout
 930
 931
 932 \backslash
 933 qquad =
 934 \backslash
 935 qquad
 936 \backslash
 937 xy
 938 \end_layout
 939
 940 \begin_layout Plain Layout
 941
 942 (-10,12)*{}; (-10,-12)*{}; **
 943 \backslash
 944 dir{-}?(.5)*
 945 \backslash
 946 dir{<}+(-4,0)*{F(x)};
 947 \end_layout
 948
 949 \begin_layout Plain Layout
 950
 951 (-2,12)*{}="1";
 952 \end_layout
 953
 954 \begin_layout Plain Layout
 955
 956 (6,-7) *{}="2";
 957 \end_layout
 958
 959 \begin_layout Plain Layout
 960
 961 (14,-7) *{}="3";
 962 \end_layout
 963
 964 \begin_layout Plain Layout
 965
 966 (14,-13)*{}="3'";
 967 \end_layout
 968
 969 \begin_layout Plain Layout
 970
 971 (18,0) *={}="";
 972 \end_layout
 973
 974 \begin_layout Plain Layout
 975
 976 "1";"2" **
 977 \backslash
 978 crv{(-4,-21)&(5,-15)};
 979 \end_layout
 980
 981 \begin_layout Plain Layout
 982
 983 ?(.15)*
 984 \backslash
 985 dir{<}+(5,10)*{
 986 \backslash
 987 overline{F(x)}};
 988 \end_layout
 989
 990 \begin_layout Plain Layout
 991
 992 "2";"3" **
 993 \backslash
 994 crv{(6,1)&(14,1)};
 995 \end_layout
 996
 997 \begin_layout Plain Layout
 998
 999 ?(0)*
1000 \backslash
1001 dir{<}+(4,8)*{
1002 \backslash
1003 widetilde{F(i_x)}} ;
1004 \end_layout
1005
1006 \begin_layout Plain Layout
1007
1008 ?(.95)*
1009 \backslash
1010 dir{<}+(5,-2)*{F(
1011 \backslash
1012 overline x)};
1013 \end_layout
1014
1015 \begin_layout Plain Layout
1016
1017 "3";"3'" **
1018 \backslash
1019 dir{-};
1020 \end_layout
1021
1022 \begin_layout Plain Layout
1023
1024 (-2,6)*{}="X1";
1025 \end_layout
1026
1027 \begin_layout Plain Layout
1028
1029 (-10,6)*{}="X2";
1030 \end_layout
1031
1032 \begin_layout Plain Layout
1033
1034 "X1";"X2" **
1035 \backslash
1036 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1037 \end_layout
1038
1039 \begin_layout Plain Layout
1040
1041 (-2,-6)*{}="XA";
1042 \end_layout
1043
1044 \begin_layout Plain Layout
1045
1046 (-10,-6)*{}="XB";
1047 \end_layout
1048
1049 \begin_layout Plain Layout
1050
1051 "XA";"XB" **
1052 \backslash
1053 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1054 \end_layout
1055
1056 \begin_layout Plain Layout
1057
1058
1059 \backslash
1060 endxy
1061 \end_layout
1062
1063 \end_inset
1064
1065
1066 \end_layout
1067
1068 \end_inset
1069
1070
1071 \end_layout
1072
1073 \begin_layout Description
1074 Categories
1075 \end_layout
1076
1077 \begin_layout Standard
1078 \begin_inset Preview
1079
1080 \begin_layout Standard
1081 \begin_inset ERT
1082 status collapsed
1083
1084 \begin_layout Plain Layout
1085
1086
1087 \backslash
1088 xymatrix{
1089 \end_layout
1090
1091 \begin_layout Plain Layout
1092
1093 (x
1094 \backslash
1095 otimes 1)
1096 \backslash
1097 otimes y
1098 \end_layout
1099
1100 \begin_layout Plain Layout
1101
1102
1103 \backslash
1104 ar[rr]^{a_{x,1,y}}
1105 \end_layout
1106
1107 \begin_layout Plain Layout
1108
1109
1110 \backslash
1111 ar[dr]_{r_x
1112 \backslash
1113 otimes 1_y}
1114 \end_layout
1115
1116 \begin_layout Plain Layout
1117
1118 && x
1119 \backslash
1120 otimes(1
1121 \backslash
1122 otimes y)
1123 \end_layout
1124
1125 \begin_layout Plain Layout
1126
1127
1128 \backslash
1129 ar[dl]^{1_x
1130 \backslash
1131 otimes
1132 \backslash
1133 ell_y }
1134 \backslash
1135
1136 \backslash
1137
1138 \end_layout
1139
1140 \begin_layout Plain Layout
1141
1142 & x
1143 \backslash
1144 otimes y }
1145 \end_layout
1146
1147 \end_inset
1148
1149
1150 \end_layout
1151
1152 \end_inset
1153
1154
1155 \begin_inset Preview
1156
1157 \begin_layout Standard
1158 \begin_inset ERT
1159 status collapsed
1160
1161 \begin_layout Plain Layout
1162
1163
1164 \backslash
1165 xy
1166 \end_layout
1167
1168 \begin_layout Plain Layout
1169
1170 (-9,0)*+{
1171 \backslash
1172 bullet}="1";
1173 \end_layout
1174
1175 \begin_layout Plain Layout
1176
1177 (0,0)*+{
1178 \backslash
1179 bullet}="2";
1180 \end_layout
1181
1182 \begin_layout Plain Layout
1183
1184 {
1185 \backslash
1186 ar@/^.9pc/ "1";"2"};
1187 \end_layout
1188
1189 \begin_layout Plain Layout
1190
1191 {
1192 \backslash
1193 ar@/_.9pc/ "1";"2"};
1194 \end_layout
1195
1196 \begin_layout Plain Layout
1197
1198 {
1199 \backslash
1200 ar@/^2pc/ "1";"2"};
1201 \end_layout
1202
1203 \begin_layout Plain Layout
1204
1205 {
1206 \backslash
1207 ar@/_2pc/ "1";"2"};
1208 \end_layout
1209
1210 \begin_layout Plain Layout
1211
1212 {
1213 \backslash
1214 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1215 \end_layout
1216
1217 \begin_layout Plain Layout
1218
1219 {
1220 \backslash
1221 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1222 \end_layout
1223
1224 \begin_layout Plain Layout
1225
1226 {
1227 \backslash
1228 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1229 \end_layout
1230
1231 \begin_layout Plain Layout
1232
1233 (0,0)*+{
1234 \backslash
1235 bullet}="1";
1236 \end_layout
1237
1238 \begin_layout Plain Layout
1239
1240 (9,0)*+{
1241 \backslash
1242 bullet}="2";
1243 \end_layout
1244
1245 \begin_layout Plain Layout
1246
1247 (18,0)*+{
1248 \backslash
1249 bullet}="3";
1250 \end_layout
1251
1252 \begin_layout Plain Layout
1253
1254 {
1255 \backslash
1256 ar "1";"2"};
1257 \end_layout
1258
1259 \begin_layout Plain Layout
1260
1261 {
1262 \backslash
1263 ar "2";"3"};
1264 \end_layout
1265
1266 \begin_layout Plain Layout
1267
1268 {
1269 \backslash
1270 ar@/^1pc/ "1";"2"};
1271 \end_layout
1272
1273 \begin_layout Plain Layout
1274
1275 {
1276 \backslash
1277 ar@/_1pc/ "1";"2"};
1278 \end_layout
1279
1280 \begin_layout Plain Layout
1281
1282 {
1283 \backslash
1284 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1285 \end_layout
1286
1287 \begin_layout Plain Layout
1288
1289 {
1290 \backslash
1291 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1292 \end_layout
1293
1294 \begin_layout Plain Layout
1295
1296
1297 \backslash
1298 endxy
1299 \end_layout
1300
1301 \end_inset
1302
1303
1304 \end_layout
1305
1306 \end_inset
1307
1308
1309 \end_layout
1310
1311 \begin_layout Description
1312 Transformations
1313 \end_layout
1314
1315 \begin_layout Standard
1316 \begin_inset Preview
1317
1318 \begin_layout Standard
1319 \begin_inset ERT
1320 status collapsed
1321
1322 \begin_layout Plain Layout
1323
1324
1325 \backslash
1326 xy %FIG.19.
1327  Natural transformation between functors.
1328 \end_layout
1329
1330 \begin_layout Plain Layout
1331
1332 (-26,-2)*+{
1333 \backslash
1334 bullet}="a";
1335 \end_layout
1336
1337 \begin_layout Plain Layout
1338
1339 (-12,3)*+{
1340 \backslash
1341 bullet}="b";
1342 \end_layout
1343
1344 \begin_layout Plain Layout
1345
1346 (-16,-5)*+{
1347 \backslash
1348 bullet}="c";
1349 \end_layout
1350
1351 \begin_layout Plain Layout
1352
1353 {
1354 \backslash
1355 ar@/^.25pc/ "a";"b"};
1356 \end_layout
1357
1358 \begin_layout Plain Layout
1359
1360 {
1361 \backslash
1362 ar@/_.25pc/"a";"c"};
1363 \end_layout
1364
1365 \begin_layout Plain Layout
1366
1367 {
1368 \backslash
1369 ar@/_.15pc/ "b";"c"};
1370 \end_layout
1371
1372 \begin_layout Plain Layout
1373
1374 %START TOP
1375 \end_layout
1376
1377 \begin_layout Plain Layout
1378
1379 (12,10)*+{
1380 \backslash
1381 bullet}="ta";
1382 \end_layout
1383
1384 \begin_layout Plain Layout
1385
1386 (26,15)*+{
1387 \backslash
1388 bullet}="tb";
1389 \end_layout
1390
1391 \begin_layout Plain Layout
1392
1393 (22,8)*+{
1394 \backslash
1395 bullet}="tc";
1396 \end_layout
1397
1398 \begin_layout Plain Layout
1399
1400 {
1401 \backslash
1402 ar@/^.25pc/ "ta";"tb"};
1403 \end_layout
1404
1405 \begin_layout Plain Layout
1406
1407 {
1408 \backslash
1409 ar@/_.25pc/ "ta";"tc"};
1410 \end_layout
1411
1412 \begin_layout Plain Layout
1413
1414 {
1415 \backslash
1416 ar@/_.15pc/ "tb";"tc"};
1417 \end_layout
1418
1419 \begin_layout Plain Layout
1420
1421 %START bottom
1422 \end_layout
1423
1424 \begin_layout Plain Layout
1425
1426 (12,-10)*+{
1427 \backslash
1428 bullet}="ba";
1429 \end_layout
1430
1431 \begin_layout Plain Layout
1432
1433 (26,-5)*+{
1434 \backslash
1435 bullet}="bb";
1436 \end_layout
1437
1438 \begin_layout Plain Layout
1439
1440 (22,-12)*+{
1441 \backslash
1442 bullet}="bc";
1443 \end_layout
1444
1445 \begin_layout Plain Layout
1446
1447 {
1448 \backslash
1449 ar@/^.25pc/@{.>} "ba";"bb"};
1450 \end_layout
1451
1452 \begin_layout Plain Layout
1453
1454 {
1455 \backslash
1456 ar@/_.25pc/ "ba";"bc"};
1457 \end_layout
1458
1459 \begin_layout Plain Layout
1460
1461 {
1462 \backslash
1463 ar@/_.15pc/ "bb";"bc"};
1464 \end_layout
1465
1466 \begin_layout Plain Layout
1467
1468 %START CONNECT
1469 \end_layout
1470
1471 \begin_layout Plain Layout
1472
1473 {
1474 \backslash
1475 ar@/_.15pc/ "ta";"ba"};
1476 \end_layout
1477
1478 \begin_layout Plain Layout
1479
1480 {
1481 \backslash
1482 ar@/_.15pc/ "tb";"bb"};
1483 \end_layout
1484
1485 \begin_layout Plain Layout
1486
1487 {
1488 \backslash
1489 ar@/_.15pc/ "tc";"bc"};
1490 \end_layout
1491
1492 \begin_layout Plain Layout
1493
1494 %START ARROWS AND LABELS
1495 \end_layout
1496
1497 \begin_layout Plain Layout
1498
1499 (-12,6)*{}="DF";
1500 \end_layout
1501
1502 \begin_layout Plain Layout
1503
1504 (6,10)*{}="CF";
1505 \end_layout
1506
1507 \begin_layout Plain Layout
1508
1509 {
1510 \backslash
1511 ar@/^.35pc/^F "DF";"CF"};
1512 \end_layout
1513
1514 \begin_layout Plain Layout
1515
1516 (-12,-6)*{}="DF";
1517 \end_layout
1518
1519 \begin_layout Plain Layout
1520
1521 (6,-10)*{}="CF";
1522 \end_layout
1523
1524 \begin_layout Plain Layout
1525
1526 {
1527 \backslash
1528 ar@/_.35pc/_G "DF";"CF"};
1529 \end_layout
1530
1531 \begin_layout Plain Layout
1532
1533 (-2,5)*{}="DF";
1534 \end_layout
1535
1536 \begin_layout Plain Layout
1537
1538 (-2,-5)*{}="CF";
1539 \end_layout
1540
1541 \begin_layout Plain Layout
1542
1543 {
1544 \backslash
1545 ar@{=>}^{
1546 \backslash
1547 alpha} "DF";"CF"};
1548 \end_layout
1549
1550 \begin_layout Plain Layout
1551
1552 (29,3)*{D};
1553 \end_layout
1554
1555 \begin_layout Plain Layout
1556
1557 (-23,3)*{C};
1558 \end_layout
1559
1560 \begin_layout Plain Layout
1561
1562
1563 \backslash
1564 endxy
1565 \end_layout
1566
1567 \end_inset
1568
1569
1570 \end_layout
1571
1572 \end_inset
1573
1574
1575 \end_layout
1576
1577 \begin_layout Section
1578 IPA
1579 \end_layout
1580
1581 \begin_layout Standard
1582 \begin_inset Preview
1583
1584 \begin_layout Standard
1585 \begin_inset ERT
1586 status collapsed
1587
1588 \begin_layout Plain Layout
1589
1590
1591 \backslash
1592 textipa{Ekspl@"neIS@n}
1593 \end_layout
1594
1595 \end_inset
1596
1597
1598 \end_layout
1599
1600 \end_inset
1601
1602
1603 \end_layout
1604
1605 \begin_layout Section
1606 QTree
1607 \end_layout
1608
1609 \begin_layout Standard
1610 \begin_inset Preview
1611
1612 \begin_layout Standard
1613 \begin_inset ERT
1614 status collapsed
1615
1616 \begin_layout Plain Layout
1617
1618
1619 \backslash
1620 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1621 \end_layout
1622
1623 \end_inset
1624
1625
1626 \end_layout
1627
1628 \end_inset
1629
1630
1631 \begin_inset Preview
1632
1633 \begin_layout Standard
1634 \begin_inset ERT
1635 status collapsed
1636
1637 \begin_layout Plain Layout
1638
1639
1640 \backslash
1641 Tree [.$
1642 \backslash
1643 sigma$ $
1644 \backslash
1645 mu$ $
1646 \backslash
1647 mu$ ]
1648 \end_layout
1649
1650 \end_inset
1651
1652
1653 \end_layout
1654
1655 \end_inset
1656
1657
1658 \end_layout
1659
1660 \begin_layout Section
1661 PSTricks
1662 \begin_inset CommandInset label
1663 LatexCommand label
1664 name "sec:PSTricks"
1665
1666 \end_inset
1667
1668
1669 \end_layout
1670
1671 \begin_layout Standard
1672 Some simple graphing examples.
1673 \end_layout
1674
1675 \begin_layout Subsection
1676 Function plotting
1677 \end_layout
1678
1679 \begin_layout Standard
1680 \begin_inset Preview
1681
1682 \begin_layout Standard
1683 \begin_inset ERT
1684 status open
1685
1686 \begin_layout Plain Layout
1687
1688
1689 \backslash
1690 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1691 \end_layout
1692
1693 \begin_layout Plain Layout
1694
1695
1696 \backslash
1697 psaxes{->}(0,0)(0,-3)(10,3)
1698 \end_layout
1699
1700 \begin_layout Plain Layout
1701
1702
1703 \backslash
1704 uput[-90](10,0){$x$}
1705 \backslash
1706 uput[0](0,3){$f(x)$}
1707 \end_layout
1708
1709 \begin_layout Plain Layout
1710
1711
1712 \backslash
1713 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1714 \end_layout
1715
1716 \begin_layout Plain Layout
1717
1718
1719 \backslash
1720 end{pspicture*}
1721 \end_layout
1722
1723 \end_inset
1724
1725
1726 \end_layout
1727
1728 \end_inset
1729
1730
1731 \end_layout
1732
1733 \begin_layout Subsection
1734 Inline data plotting
1735 \end_layout
1736
1737 \begin_layout Standard
1738 \align center
1739 \begin_inset Preview
1740
1741 \begin_layout Standard
1742 \align center
1743 \begin_inset ERT
1744 status open
1745
1746 \begin_layout Plain Layout
1747
1748
1749 \backslash
1750 begin{pspicture*}(-1.5,-1.5)(11,5)
1751 \end_layout
1752
1753 \begin_layout Plain Layout
1754
1755
1756 \backslash
1757 psaxes{->}(0,0)(0,0)(10,5)
1758 \end_layout
1759
1760 \begin_layout Plain Layout
1761
1762
1763 \backslash
1764 psset{linewidth=2.5pt}
1765 \end_layout
1766
1767 \begin_layout Plain Layout
1768
1769
1770 \backslash
1771 rput(5.0,-1.0){Speed [MPH]}
1772 \end_layout
1773
1774 \begin_layout Plain Layout
1775
1776
1777 \backslash
1778 rput(-1.0,1.0){
1779 \backslash
1780 begin{rotate}{90}Cost [Dollars]
1781 \backslash
1782 end{rotate}}
1783 \end_layout
1784
1785 \begin_layout Plain Layout
1786
1787
1788 \backslash
1789 savedata{
1790 \backslash
1791 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1792 \end_layout
1793
1794 \begin_layout Plain Layout
1795
1796
1797 \backslash
1798 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1799 \backslash
1800 mydata}
1801 \end_layout
1802
1803 \begin_layout Plain Layout
1804
1805
1806 \backslash
1807 end{pspicture*}
1808 \end_layout
1809
1810 \end_inset
1811
1812
1813 \end_layout
1814
1815 \end_inset
1816
1817
1818 \end_layout
1819
1820 \begin_layout Subsection
1821 Lissajous curves
1822 \end_layout
1823
1824 \begin_layout Standard
1825 \begin_inset Preview
1826
1827 \begin_layout Standard
1828 \begin_inset ERT
1829 status open
1830
1831 \begin_layout Plain Layout
1832
1833
1834 \backslash
1835 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1836 \end_layout
1837
1838 \begin_layout Plain Layout
1839
1840
1841 \backslash
1842 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1843  cos 100 t mul sin}
1844 \end_layout
1845
1846 \begin_layout Plain Layout
1847
1848
1849 \backslash
1850 end{pspicture*}
1851 \end_layout
1852
1853 \end_inset
1854
1855
1856 \end_layout
1857
1858 \end_inset
1859
1860
1861 \begin_inset space \hfill{}
1862 \end_inset
1863
1864
1865 \begin_inset Preview
1866
1867 \begin_layout Standard
1868 \begin_inset ERT
1869 status open
1870
1871 \begin_layout Plain Layout
1872
1873
1874 \backslash
1875 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1876 \end_layout
1877
1878 \begin_layout Plain Layout
1879
1880
1881 \backslash
1882 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1883  mul cos 100 t mul sin}
1884 \end_layout
1885
1886 \begin_layout Plain Layout
1887
1888
1889 \backslash
1890 end{pspicture*}
1891 \end_layout
1892
1893 \end_inset
1894
1895
1896 \end_layout
1897
1898 \end_inset
1899
1900
1901 \begin_inset space \hfill{}
1902 \end_inset
1903
1904
1905 \begin_inset Preview
1906
1907 \begin_layout Standard
1908 \begin_inset ERT
1909 status open
1910
1911 \begin_layout Plain Layout
1912
1913
1914 \backslash
1915 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1916 \end_layout
1917
1918 \begin_layout Plain Layout
1919
1920
1921 \backslash
1922 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1923  mul cos 200 t mul sin}
1924 \end_layout
1925
1926 \begin_layout Plain Layout
1927
1928
1929 \backslash
1930 end{pspicture*}
1931 \end_layout
1932
1933 \end_inset
1934
1935
1936 \end_layout
1937
1938 \end_inset
1939
1940
1941 \begin_inset space \hfill{}
1942 \end_inset
1943
1944
1945 \begin_inset Preview
1946
1947 \begin_layout Standard
1948 \begin_inset ERT
1949 status open
1950
1951 \begin_layout Plain Layout
1952
1953
1954 \backslash
1955 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1956 \end_layout
1957
1958 \begin_layout Plain Layout
1959
1960
1961 \backslash
1962 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1963  mul cos 200 t mul sin}
1964 \end_layout
1965
1966 \begin_layout Plain Layout
1967
1968
1969 \backslash
1970 end{pspicture*}
1971 \end_layout
1972
1973 \end_inset
1974
1975
1976 \end_layout
1977
1978 \end_inset
1979
1980
1981 \end_layout
1982
1983 \begin_layout Section
1984 TikZ
1985 \end_layout
1986
1987 \begin_layout Standard
1988 \begin_inset Flex URL
1989 status collapsed
1990
1991 \begin_layout Plain Layout
1992
1993 http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
1994 \end_layout
1995
1996 \end_inset
1997
1998
1999 \end_layout
2000
2001 \begin_layout Standard
2002 \begin_inset Preview
2003
2004 \begin_layout Standard
2005 \begin_inset ERT
2006 status collapsed
2007
2008 \begin_layout Plain Layout
2009
2010
2011 \backslash
2012 def
2013 \backslash
2014 iangle{35} % Angle of the inclined plane
2015 \end_layout
2016
2017 \begin_layout Plain Layout
2018
2019
2020 \backslash
2021 def
2022 \backslash
2023 down{-90}
2024 \end_layout
2025
2026 \begin_layout Plain Layout
2027
2028
2029 \backslash
2030 def
2031 \backslash
2032 arcr{0.5cm} % Radius of the arc used to indicate angles
2033 \end_layout
2034
2035 \begin_layout Plain Layout
2036
2037 \end_layout
2038
2039 \begin_layout Plain Layout
2040
2041
2042 \backslash
2043 begin{tikzpicture}[
2044 \end_layout
2045
2046 \begin_layout Plain Layout
2047
2048     force/.style={>=latex,draw=blue,fill=blue},
2049 \end_layout
2050
2051 \begin_layout Plain Layout
2052
2053     axis/.style={densely dashed,gray,font=
2054 \backslash
2055 small},
2056 \end_layout
2057
2058 \begin_layout Plain Layout
2059
2060     M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2061 \end_layout
2062
2063 \begin_layout Plain Layout
2064
2065     m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2066 \end_layout
2067
2068 \begin_layout Plain Layout
2069
2070     plane/.style={draw=black,fill=blue!10},
2071 \end_layout
2072
2073 \begin_layout Plain Layout
2074
2075     string/.style={draw=red, thick},
2076 \end_layout
2077
2078 \begin_layout Plain Layout
2079
2080     pulley/.style={thick},
2081 \end_layout
2082
2083 \begin_layout Plain Layout
2084
2085 ]
2086 \end_layout
2087
2088 \begin_layout Plain Layout
2089
2090 \end_layout
2091
2092 \begin_layout Plain Layout
2093
2094
2095 \backslash
2096 matrix[column sep=1cm] {
2097 \end_layout
2098
2099 \begin_layout Plain Layout
2100
2101     %% Sketch
2102 \end_layout
2103
2104 \begin_layout Plain Layout
2105
2106
2107 \backslash
2108 draw[plane] (0,-1) coordinate (base)
2109 \end_layout
2110
2111 \begin_layout Plain Layout
2112
2113                      -- coordinate[pos=0.5] (mid) ++(
2114 \backslash
2115 iangle:3) coordinate (top)
2116 \end_layout
2117
2118 \begin_layout Plain Layout
2119
2120                      |- (base) -- cycle;
2121 \end_layout
2122
2123 \begin_layout Plain Layout
2124
2125
2126 \backslash
2127 path (mid) node[M,rotate=
2128 \backslash
2129 iangle,yshift=0.25cm] (M) {};
2130 \end_layout
2131
2132 \begin_layout Plain Layout
2133
2134
2135 \backslash
2136 draw[pulley] (top) -- ++(
2137 \backslash
2138 iangle:0.25) circle (0.25cm)
2139 \end_layout
2140
2141 \begin_layout Plain Layout
2142
2143                    ++ (90-
2144 \backslash
2145 iangle:0.5) coordinate (pulley);
2146 \end_layout
2147
2148 \begin_layout Plain Layout
2149
2150
2151 \backslash
2152 draw[string] (M.east) -- ++(
2153 \backslash
2154 iangle:1.5cm) arc (90+
2155 \backslash
2156 iangle:0:0.25)
2157 \end_layout
2158
2159 \begin_layout Plain Layout
2160
2161                   -- ++(0,-1) node[m] {};
2162 \end_layout
2163
2164 \begin_layout Plain Layout
2165
2166 \end_layout
2167
2168 \begin_layout Plain Layout
2169
2170
2171 \backslash
2172 draw[->] (base)++(
2173 \backslash
2174 arcr,0) arc (0:
2175 \backslash
2176 iangle:
2177 \backslash
2178 arcr);
2179 \end_layout
2180
2181 \begin_layout Plain Layout
2182
2183
2184 \backslash
2185 path (base)++(
2186 \backslash
2187 iangle*0.5:
2188 \backslash
2189 arcr+5pt) node {$
2190 \backslash
2191 alpha$};
2192 \end_layout
2193
2194 \begin_layout Plain Layout
2195
2196     %%
2197 \end_layout
2198
2199 \begin_layout Plain Layout
2200
2201 \end_layout
2202
2203 \begin_layout Plain Layout
2204
2205 &
2206 \end_layout
2207
2208 \begin_layout Plain Layout
2209
2210     %% Free body diagram of M
2211 \end_layout
2212
2213 \begin_layout Plain Layout
2214
2215
2216 \backslash
2217 begin{scope}[rotate=
2218 \backslash
2219 iangle]
2220 \end_layout
2221
2222 \begin_layout Plain Layout
2223
2224
2225 \backslash
2226 node[M,transform shape] (M) {};
2227 \end_layout
2228
2229 \begin_layout Plain Layout
2230
2231         % Draw axes and help lines
2232 \end_layout
2233
2234 \begin_layout Plain Layout
2235
2236 \end_layout
2237
2238 \begin_layout Plain Layout
2239
2240         {[axis,->]
2241 \end_layout
2242
2243 \begin_layout Plain Layout
2244
2245
2246 \backslash
2247 draw (0,-1) -- (0,2) node[right] {$+y$};
2248 \end_layout
2249
2250 \begin_layout Plain Layout
2251
2252
2253 \backslash
2254 draw (M) -- ++(2,0) node[right] {$+x$};
2255 \end_layout
2256
2257 \begin_layout Plain Layout
2258
2259             % Indicate angle.
2260  The code is a bit awkward.
2261 \end_layout
2262
2263 \begin_layout Plain Layout
2264
2265 \end_layout
2266
2267 \begin_layout Plain Layout
2268
2269
2270 \backslash
2271 draw[solid,shorten >=0.5pt] (
2272 \backslash
2273 down-
2274 \backslash
2275 iangle:
2276 \backslash
2277 arcr)
2278 \end_layout
2279
2280 \begin_layout Plain Layout
2281
2282                 arc(
2283 \backslash
2284 down-
2285 \backslash
2286 iangle:
2287 \backslash
2288 down:
2289 \backslash
2290 arcr);
2291 \end_layout
2292
2293 \begin_layout Plain Layout
2294
2295
2296 \backslash
2297 node at (
2298 \backslash
2299 down-0.5*
2300 \backslash
2301 iangle:1.3*
2302 \backslash
2303 arcr) {$
2304 \backslash
2305 alpha$};
2306 \end_layout
2307
2308 \begin_layout Plain Layout
2309
2310         }
2311 \end_layout
2312
2313 \begin_layout Plain Layout
2314
2315 \end_layout
2316
2317 \begin_layout Plain Layout
2318
2319         % Forces
2320 \end_layout
2321
2322 \begin_layout Plain Layout
2323
2324         {[force,->]
2325 \end_layout
2326
2327 \begin_layout Plain Layout
2328
2329             % Assuming that Mg = 1.
2330  The normal force will therefore be cos(alpha)
2331 \end_layout
2332
2333 \begin_layout Plain Layout
2334
2335
2336 \backslash
2337 draw (M.center) -- ++(0,{cos(
2338 \backslash
2339 iangle)}) node[above right] {$N$};
2340 \end_layout
2341
2342 \begin_layout Plain Layout
2343
2344
2345 \backslash
2346 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2347 \end_layout
2348
2349 \begin_layout Plain Layout
2350
2351
2352 \backslash
2353 draw (M.east) -- ++(1,0) node[above] {$T$};
2354 \end_layout
2355
2356 \begin_layout Plain Layout
2357
2358         }
2359 \end_layout
2360
2361 \begin_layout Plain Layout
2362
2363 \end_layout
2364
2365 \begin_layout Plain Layout
2366
2367
2368 \backslash
2369 end{scope}
2370 \end_layout
2371
2372 \begin_layout Plain Layout
2373
2374     % Draw gravity force.
2375  The code is put outside the rotated
2376 \end_layout
2377
2378 \begin_layout Plain Layout
2379
2380     % scope for simplicity.
2381  No need to do any angle calculations.
2382
2383 \end_layout
2384
2385 \begin_layout Plain Layout
2386
2387
2388 \backslash
2389 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2390 \end_layout
2391
2392 \begin_layout Plain Layout
2393
2394     %%
2395 \end_layout
2396
2397 \begin_layout Plain Layout
2398
2399 \end_layout
2400
2401 \begin_layout Plain Layout
2402
2403 &
2404 \end_layout
2405
2406 \begin_layout Plain Layout
2407
2408     %%%
2409 \end_layout
2410
2411 \begin_layout Plain Layout
2412
2413     % Free body diagram of m
2414 \end_layout
2415
2416 \begin_layout Plain Layout
2417
2418
2419 \backslash
2420 node[m] (m) {};
2421 \end_layout
2422
2423 \begin_layout Plain Layout
2424
2425
2426 \backslash
2427 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2428 \end_layout
2429
2430 \begin_layout Plain Layout
2431
2432     {[force,->]
2433 \end_layout
2434
2435 \begin_layout Plain Layout
2436
2437
2438 \backslash
2439 draw (m.north) -- ++(0,1) node[above] {$T'$};
2440 \end_layout
2441
2442 \begin_layout Plain Layout
2443
2444
2445 \backslash
2446 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2447 \end_layout
2448
2449 \begin_layout Plain Layout
2450
2451     }
2452 \end_layout
2453
2454 \begin_layout Plain Layout
2455
2456 \end_layout
2457
2458 \begin_layout Plain Layout
2459
2460
2461 \backslash
2462
2463 \backslash
2464
2465 \end_layout
2466
2467 \begin_layout Plain Layout
2468
2469 };
2470 \end_layout
2471
2472 \begin_layout Plain Layout
2473
2474
2475 \backslash
2476 end{tikzpicture}
2477 \end_layout
2478
2479 \begin_layout Plain Layout
2480
2481 \end_layout
2482
2483 \end_inset
2484
2485
2486 \end_layout
2487
2488 \end_inset
2489
2490
2491 \end_layout
2492
2493 \end_body
2494 \end_document