lib/examples/Graphics_and_Insets/Instant_Preview.lyx

   1 #LyX 2.4 created this file. For more info see https://www.lyx.org/
   2 \lyxformat 600
   3 \begin_document
   4 \begin_header
   5 \save_transient_properties true
   6 \origin /systemlyxdir/examples/Graphics_and_Insets/
   7 \textclass article
   8 \begin_preamble
   9 \usepackage{etex}
  10 \usepackage[all, knot]{xy}
  11 \xyoption{arc}
  12 \usepackage{qtree}
  13 \usepackage{tipa}
  14 \usepackage{pstricks}
  15 \usepackage{pst-plot}
  16 \usepackage{rotating}
  17 \usepackage{tikz}
  18 \usetikzlibrary{scopes}
  19 \end_preamble
  20 \use_default_options false
  21 \maintain_unincluded_children no
  22 \language english
  23 \language_package default
  24 \inputencoding utf8
  25 \fontencoding auto
  26 \font_roman "lmodern" "default"
  27 \font_sans "default" "default"
  28 \font_typewriter "default" "default"
  29 \font_math "auto" "auto"
  30 \font_default_family default
  31 \use_non_tex_fonts false
  32 \font_sc false
  33 \font_sans_osf false
  34 \font_typewriter_osf false
  35 \font_roman_osf false
  36 \font_sf_scale 100 100
  37 \font_tt_scale 100 100
  38 \use_microtype false
  39 \use_dash_ligatures false
  40 \graphics default
  41 \default_output_format pdf
  42 \output_sync 0
  43 \bibtex_command default
  44 \index_command default
  45 \paperfontsize default
  46 \spacing single
  47 \use_hyperref false
  48 \papersize default
  49 \use_geometry false
  50 \use_package amsmath 1
  51 \use_package amssymb 1
  52 \use_package cancel 1
  53 \use_package esint 1
  54 \use_package mathdots 1
  55 \use_package mathtools 1
  56 \use_package mhchem 1
  57 \use_package stackrel 1
  58 \use_package stmaryrd 1
  59 \use_package undertilde 1
  60 \cite_engine basic
  61 \cite_engine_type default
  62 \biblio_style plain
  63 \use_bibtopic false
  64 \use_indices false
  65 \paperorientation portrait
  66 \suppress_date false
  67 \justification true
  68 \use_refstyle 0
  69 \use_minted 0
  70 \use_lineno 0
  71 \index Index
  72 \shortcut idx
  73 \color #008000
  74 \end_index
  75 \secnumdepth 3
  76 \tocdepth 3
  77 \paragraph_separation indent
  78 \paragraph_indentation default
  79 \is_math_indent 0
  80 \math_numbering_side default
  81 \quotes_style english
  82 \dynamic_quotes 0
  83 \papercolumns 1
  84 \papersides 1
  85 \paperpagestyle default
  86 \tracking_changes false
  87 \postpone_fragile_content false
  88 \output_changes false
  89 \html_math_output 0
  90 \html_css_as_file 0
  91 \html_be_strict true
  92 \end_header
  93
  94 \begin_body
  95
  96 \begin_layout Section
  97 Introduction
  98 \end_layout
  99
 100 \begin_layout Standard
 101 In order to properly typeset the document and have instant preview working,
 102  the following packages have to be installed:
 103 \end_layout
 104
 105 \begin_layout LyX-Code
 106 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf, etex
 107 \end_layout
 108
 109 \begin_layout Standard
 110 Due to the use of postscript specials in Section
 111 \begin_inset CommandInset ref
 112 LatexCommand ref
 113 reference "sec:PSTricks"
 114
 115 \end_inset
 116
 117 , only the Postscript or PDF (ps2pdf) output formats will correctly render
 118  the included images.
 119  However, the PDF (Xe\SpecialChar TeX
 120 ) output seems to also work, while trying to typeset
 121  the document with
 122 \family typewriter
 123 pdflatex
 124 \family default
 125  or
 126 \family typewriter
 127 pdflualatex
 128 \family default
 129  will generate errors.
 130 \end_layout
 131
 132 \begin_layout Section
 133 Diagrams by XY(-pic)
 134 \end_layout
 135
 136 \begin_layout Standard
 137 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
 138  examples, see
 139 \begin_inset Flex URL
 140 status collapsed
 141
 142 \begin_layout Plain Layout
 143
 144 https://www.ctan.org/tex-archive/macros/generic/diagrams/xypic/doc/xyguide.pdf
 145 \end_layout
 146
 147 \end_inset
 148
 149 .
 150 \end_layout
 151
 152 \begin_layout Description
 153 Braid
 154 \end_layout
 155
 156 \begin_layout Standard
 157 \begin_inset Preview
 158
 159 \begin_layout Standard
 160 \begin_inset ERT
 161 status collapsed
 162
 163 \begin_layout Plain Layout
 164
 165
 166 \backslash
 167 xy
 168 \end_layout
 169
 170 \begin_layout Plain Layout
 171
 172 (5,10)*{}; (-10,-10)*{} **
 173 \backslash
 174 crv{(6,-2)&(-12,4)}
 175 \end_layout
 176
 177 \begin_layout Plain Layout
 178
 179
 180 \backslash
 181 POS?(.25)*{
 182 \backslash
 183 hole}="x"
 184 \backslash
 185 POS?(.45)*{
 186 \backslash
 187 hole}="y"
 188 \backslash
 189 POS?(.6)*{
 190 \backslash
 191 hole}="z";
 192 \end_layout
 193
 194 \begin_layout Plain Layout
 195
 196 "y"+(0,-1); (2,-10)*{} **
 197 \backslash
 198 crv{}
 199 \backslash
 200 POS?(.2)*{
 201 \backslash
 202 hole}="M";
 203 \end_layout
 204
 205 \begin_layout Plain Layout
 206
 207 (-10,10)*{}; "z" **
 208 \backslash
 209 crv{(-9,0)};
 210 \end_layout
 211
 212 \begin_layout Plain Layout
 213
 214 "z"; "M" **
 215 \backslash
 216 crv{};
 217 \end_layout
 218
 219 \begin_layout Plain Layout
 220
 221 "M"; "x" **
 222 \backslash
 223 crv{(5,0)};
 224 \end_layout
 225
 226 \begin_layout Plain Layout
 227
 228 "x"; "y" **
 229 \backslash
 230 crv{(0,7) & (-5,6)};
 231 \end_layout
 232
 233 \begin_layout Plain Layout
 234
 235
 236 \backslash
 237 endxy
 238 \end_layout
 239
 240 \end_inset
 241
 242
 243 \end_layout
 244
 245 \end_inset
 246
 247
 248 \end_layout
 249
 250 \begin_layout Description
 251 Knots
 252 \end_layout
 253
 254 \begin_layout Standard
 255 \begin_inset Preview
 256
 257 \begin_layout Standard
 258 \begin_inset ERT
 259 status collapsed
 260
 261 \begin_layout Plain Layout
 262
 263
 264 \backslash
 265 xy
 266 \end_layout
 267
 268 \begin_layout Plain Layout
 269
 270 (6,9)*{}="1";
 271 \end_layout
 272
 273 \begin_layout Plain Layout
 274
 275 (-8.5,-1)*{}="2";
 276 \end_layout
 277
 278 \begin_layout Plain Layout
 279
 280 "1";"2" **
 281 \backslash
 282 crv{~*=<.5pt>{.} (0,30)}?(.75)*
 283 \backslash
 284 dir{>}+(-2,2)*{z};
 285 \end_layout
 286
 287 \begin_layout Plain Layout
 288
 289 (-6.5,8)*{}="1";
 290 \end_layout
 291
 292 \begin_layout Plain Layout
 293
 294 (-.5,-9)*{}="2";
 295 \end_layout
 296
 297 \begin_layout Plain Layout
 298
 299 "1";"2" **
 300 \backslash
 301 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
 302 \backslash
 303 dir{>}+(-2,-2)*{u};
 304 \end_layout
 305
 306 \begin_layout Plain Layout
 307
 308 (-9.5,-3.35)*{}="1";
 309 \end_layout
 310
 311 \begin_layout Plain Layout
 312
 313 (8.5,-3)*{}="2";
 314 \end_layout
 315
 316 \begin_layout Plain Layout
 317
 318 "1";"2" **
 319 \backslash
 320 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
 321 \backslash
 322 dir{>}+(-1,-3)*{x};
 323 \end_layout
 324
 325 \begin_layout Plain Layout
 326
 327 (1,-10)*{}="1";
 328 \end_layout
 329
 330 \begin_layout Plain Layout
 331
 332 (6.5,7.13)*{}="2";
 333 \end_layout
 334
 335 \begin_layout Plain Layout
 336
 337 "1";"2" **
 338 \backslash
 339 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
 340 \backslash
 341 dir{>}+(3,-1)*{y};
 342 \end_layout
 343
 344 \begin_layout Plain Layout
 345
 346 (11,-1)*{}="1";
 347 \end_layout
 348
 349 \begin_layout Plain Layout
 350
 351 (-4,8)*{}="2";
 352 \end_layout
 353
 354 \begin_layout Plain Layout
 355
 356 "1";"2" **
 357 \backslash
 358 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
 359 \backslash
 360 dir{>}+(1,2)*{w};
 361 \end_layout
 362
 363 \begin_layout Plain Layout
 364
 365
 366 \backslash
 367 endxy
 368 \end_layout
 369
 370 \end_inset
 371
 372
 373 \end_layout
 374
 375 \end_inset
 376
 377
 378 \end_layout
 379
 380 \begin_layout Description
 381 Circles
 382 \end_layout
 383
 384 \begin_layout Standard
 385 \begin_inset Preview
 386
 387 \begin_layout Standard
 388 \begin_inset ERT
 389 status collapsed
 390
 391 \begin_layout Plain Layout
 392
 393
 394 \backslash
 395 xy
 396 \end_layout
 397
 398 \begin_layout Plain Layout
 399
 400 (0,0)*
 401 \backslash
 402 xycircle(14,8){++
 403 \backslash
 404 dir{<}};
 405 \end_layout
 406
 407 \begin_layout Plain Layout
 408
 409 (0,0)*
 410 \backslash
 411 xycircle<10pt>{{.}};
 412 \end_layout
 413
 414 \begin_layout Plain Layout
 415
 416 (0,0)*
 417 \backslash
 418 xycircle(5,2){:};
 419 \end_layout
 420
 421 \begin_layout Plain Layout
 422
 423 (0,15)*
 424 \backslash
 425 xycircle(10,4){--};
 426 \end_layout
 427
 428 \begin_layout Plain Layout
 429
 430
 431 \backslash
 432 endxy
 433 \end_layout
 434
 435 \end_inset
 436
 437
 438 \end_layout
 439
 440 \end_inset
 441
 442
 443 \end_layout
 444
 445 \begin_layout Description
 446 Cobordism
 447 \end_layout
 448
 449 \begin_layout Standard
 450 \begin_inset Preview
 451
 452 \begin_layout Standard
 453 \begin_inset ERT
 454 status collapsed
 455
 456 \begin_layout Plain Layout
 457
 458
 459 \backslash
 460 xy
 461 \end_layout
 462
 463 \begin_layout Plain Layout
 464
 465 (0,0)*
 466 \backslash
 467 ellipse(3,1){.};
 468 \end_layout
 469
 470 \begin_layout Plain Layout
 471
 472 (0,0)*
 473 \backslash
 474 ellipse(3,1)__,=:a(-180){-};
 475 \end_layout
 476
 477 \begin_layout Plain Layout
 478
 479 (-6,-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){.};
 489 \end_layout
 490
 491 \begin_layout Plain Layout
 492
 493 (0,-8)*
 494 \backslash
 495 ellipse(3,1){.};
 496 \end_layout
 497
 498 \begin_layout Plain Layout
 499
 500 (-6,-8)*
 501 \backslash
 502 ellipse(3,1)__,=:a(-180){-};
 503 \end_layout
 504
 505 \begin_layout Plain Layout
 506
 507 (6,-8)*
 508 \backslash
 509 ellipse(3,1)__,=:a(-180){-};
 510 \end_layout
 511
 512 \begin_layout Plain Layout
 513
 514 (0,-8)*
 515 \backslash
 516 ellipse(3,1)__,=:a(180){-};
 517 \end_layout
 518
 519 \begin_layout Plain Layout
 520
 521 (-3,6)*
 522 \backslash
 523 ellipse(3,1){-};
 524 \end_layout
 525
 526 \begin_layout Plain Layout
 527
 528 (3,6)*
 529 \backslash
 530 ellipse(3,1){-};
 531 \end_layout
 532
 533 \begin_layout Plain Layout
 534
 535 (-3,12)*{}="1";
 536 \end_layout
 537
 538 \begin_layout Plain Layout
 539
 540 (3,12)*{}="2";
 541 \end_layout
 542
 543 \begin_layout Plain Layout
 544
 545 (-9,12)*{}="A2";
 546 \end_layout
 547
 548 \begin_layout Plain Layout
 549
 550 (9,12)*{}="B2";
 551 \end_layout
 552
 553 \begin_layout Plain Layout
 554
 555 "1";"2" **
 556 \backslash
 557 crv{(-3,7) & (3,7)};
 558 \end_layout
 559
 560 \begin_layout Plain Layout
 561
 562 (-3,0)*{}="A";
 563 \end_layout
 564
 565 \begin_layout Plain Layout
 566
 567 (3,0)*{}="B";
 568 \end_layout
 569
 570 \begin_layout Plain Layout
 571
 572 (-3,1)*{}="A1";
 573 \end_layout
 574
 575 \begin_layout Plain Layout
 576
 577 (3,1)*{}="B1";
 578 \end_layout
 579
 580 \begin_layout Plain Layout
 581
 582 "A";"A1" **
 583 \backslash
 584 dir{-};
 585 \end_layout
 586
 587 \begin_layout Plain Layout
 588
 589 "B";"B1" **
 590 \backslash
 591 dir{-};
 592 \end_layout
 593
 594 \begin_layout Plain Layout
 595
 596 "B2";"B1" **
 597 \backslash
 598 crv{(8,7) & (3,5)};
 599 \end_layout
 600
 601 \begin_layout Plain Layout
 602
 603 "A2";"A1" **
 604 \backslash
 605 crv{(-8,7) & (-3,5)};
 606 \end_layout
 607
 608 \begin_layout Plain Layout
 609
 610 %REFLECT
 611 \end_layout
 612
 613 \begin_layout Plain Layout
 614
 615 (3,-16)*{}="1";
 616 \end_layout
 617
 618 \begin_layout Plain Layout
 619
 620 (9,-16)*{}="2";
 621 \end_layout
 622
 623 \begin_layout Plain Layout
 624
 625 "1";"2" **
 626 \backslash
 627 crv{(3,-10) & (9,-10)};
 628 \end_layout
 629
 630 \begin_layout Plain Layout
 631
 632 (-3,-16)*{}="1";
 633 \end_layout
 634
 635 \begin_layout Plain Layout
 636
 637 (-9,-16)*{}="2";
 638 \end_layout
 639
 640 \begin_layout Plain Layout
 641
 642 "1";"2" **
 643 \backslash
 644 crv{(-3,-10) & (-9,-10)};
 645 \end_layout
 646
 647 \begin_layout Plain Layout
 648
 649 (-15,-16)*{}="A2";
 650 \end_layout
 651
 652 \begin_layout Plain Layout
 653
 654 (15,-16)*{}="B2";
 655 \end_layout
 656
 657 \begin_layout Plain Layout
 658
 659 (-3,0)*{}="A";
 660 \end_layout
 661
 662 \begin_layout Plain Layout
 663
 664 (3,0)*{}="B";
 665 \end_layout
 666
 667 \begin_layout Plain Layout
 668
 669 (-3,-1)*{}="A1";
 670 \end_layout
 671
 672 \begin_layout Plain Layout
 673
 674 (3,-1)*{}="B1";
 675 \end_layout
 676
 677 \begin_layout Plain Layout
 678
 679 "A";"A1" **
 680 \backslash
 681 dir{-};
 682 \end_layout
 683
 684 \begin_layout Plain Layout
 685
 686 "B";"B1" **
 687 \backslash
 688 dir{-};
 689 \end_layout
 690
 691 \begin_layout Plain Layout
 692
 693 "B2";"B1" **
 694 \backslash
 695 crv{(13,-6) & (2,-8)};
 696 \end_layout
 697
 698 \begin_layout Plain Layout
 699
 700 "A2";"A1" **
 701 \backslash
 702 crv{(-13,-6) & (-2,-8)};
 703 \end_layout
 704
 705 \begin_layout Plain Layout
 706
 707
 708 \backslash
 709 endxy
 710 \end_layout
 711
 712 \end_inset
 713
 714
 715 \end_layout
 716
 717 \end_inset
 718
 719
 720 \begin_inset Preview
 721
 722 \begin_layout Standard
 723 \begin_inset ERT
 724 status collapsed
 725
 726 \begin_layout Plain Layout
 727
 728
 729 \backslash
 730 xy 0;/r.18pc/:
 731 \end_layout
 732
 733 \begin_layout Plain Layout
 734
 735 (20,2)*{
 736 \backslash
 737 bullet}="RU"+(1,3)*{x^{
 738 \backslash
 739 ast}};
 740 \end_layout
 741
 742 \begin_layout Plain Layout
 743
 744 (16,-3)*{
 745 \backslash
 746 bullet}="RD"+(2.5,2)*{x^{
 747 \backslash
 748 ast}};
 749 \end_layout
 750
 751 \begin_layout Plain Layout
 752
 753 (-16,2)*{
 754 \backslash
 755 bullet}="LU"+(-1,2)*{x};
 756 \end_layout
 757
 758 \begin_layout Plain Layout
 759
 760 (-20,-3)*{
 761 \backslash
 762 bullet}="LD"+(-1,2)*{x};
 763 \end_layout
 764
 765 \begin_layout Plain Layout
 766
 767 "RU";"RD" **
 768 \backslash
 769 crv{(4,2) & (4,-1)}; ?(.1)*
 770 \backslash
 771 dir{<}; ?(.85)*
 772 \backslash
 773 dir{<};
 774 \end_layout
 775
 776 \begin_layout Plain Layout
 777
 778 "LD";"LU" **
 779 \backslash
 780 crv{(-4,-2) & (-4,1)};
 781 \end_layout
 782
 783 \begin_layout Plain Layout
 784
 785 ?(.08)*
 786 \backslash
 787 dir{<}; ?(.85)*
 788 \backslash
 789 dir{<};
 790 \end_layout
 791
 792 \begin_layout Plain Layout
 793
 794 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
 795 \end_layout
 796
 797 \begin_layout Plain Layout
 798
 799 "x1"; "x2" **
 800 \backslash
 801 crv{(7,-10) & (-7,-10)};
 802 \end_layout
 803
 804 \begin_layout Plain Layout
 805
 806 (16,-20)*{
 807 \backslash
 808 bullet}="RDD"+(2.5,-1)*{x^{
 809 \backslash
 810 ast}};
 811 \end_layout
 812
 813 \begin_layout Plain Layout
 814
 815 (-20,-20)*{
 816 \backslash
 817 bullet}="LDD"+(-1,-3)*{x};
 818 \end_layout
 819
 820 \begin_layout Plain Layout
 821
 822 (20,-12.5)*{
 823 \backslash
 824 bullet}="RUD"+(3.5,1)*{x^{
 825 \backslash
 826 ast}};
 827 \end_layout
 828
 829 \begin_layout Plain Layout
 830
 831 (-16,-15)*{
 832 \backslash
 833 bullet}="LUD";
 834 \end_layout
 835
 836 \begin_layout Plain Layout
 837
 838 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
 839 \end_layout
 840
 841 \begin_layout Plain Layout
 842
 843 "RD"; "RDD" **
 844 \backslash
 845 dir{-};
 846 \end_layout
 847
 848 \begin_layout Plain Layout
 849
 850 "LD"; "LDD" **
 851 \backslash
 852 dir{-};
 853 \end_layout
 854
 855 \begin_layout Plain Layout
 856
 857 "A"; "LUD" **
 858 \backslash
 859 dir{.};
 860 \end_layout
 861
 862 \begin_layout Plain Layout
 863
 864 "RDD"; "LDD" **
 865 \backslash
 866 crv{(0,-17)}; ?(.57)*
 867 \backslash
 868 dir{>};
 869 \end_layout
 870
 871 \begin_layout Plain Layout
 872
 873 "RU"; "RUD" **
 874 \backslash
 875 dir{-};
 876 \end_layout
 877
 878 \begin_layout Plain Layout
 879
 880 "LU"; "A" **
 881 \backslash
 882 dir{-};
 883 \end_layout
 884
 885 \begin_layout Plain Layout
 886
 887 "B"; "RUD" **
 888 \backslash
 889 crv{(18,-14.15)};
 890 \end_layout
 891
 892 \begin_layout Plain Layout
 893
 894 "B"; "LUD" **
 895 \backslash
 896 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
 897 \backslash
 898 dir{<};
 899 \end_layout
 900
 901 \begin_layout Plain Layout
 902
 903
 904 \backslash
 905 endxy
 906 \end_layout
 907
 908 \end_inset
 909
 910
 911 \end_layout
 912
 913 \end_inset
 914
 915
 916 \end_layout
 917
 918 \begin_layout Description
 919 Strings
 920 \end_layout
 921
 922 \begin_layout Standard
 923 \begin_inset Preview
 924
 925 \begin_layout Standard
 926 \begin_inset ERT
 927 status open
 928
 929 \begin_layout Plain Layout
 930
 931
 932 \backslash
 933 xy (-15,0)*{};(15,0)*{};
 934 \end_layout
 935
 936 \begin_layout Plain Layout
 937
 938
 939 \backslash
 940 endxy
 941 \end_layout
 942
 943 \begin_layout Plain Layout
 944
 945
 946 \backslash
 947 qquad =
 948 \backslash
 949 qquad
 950 \backslash
 951 xy
 952 \end_layout
 953
 954 \begin_layout Plain Layout
 955
 956 (-10,12)*{}; (-10,-12)*{}; **
 957 \backslash
 958 dir{-}?(.5)*
 959 \backslash
 960 dir{<}+(-4,0)*{F(x)};
 961 \end_layout
 962
 963 \begin_layout Plain Layout
 964
 965 (-2,12)*{}="1";
 966 \end_layout
 967
 968 \begin_layout Plain Layout
 969
 970 (6,-7) *{}="2";
 971 \end_layout
 972
 973 \begin_layout Plain Layout
 974
 975 (14,-7) *{}="3";
 976 \end_layout
 977
 978 \begin_layout Plain Layout
 979
 980 (14,-13)*{}="3'";
 981 \end_layout
 982
 983 \begin_layout Plain Layout
 984
 985 (18,0) *={}="";
 986 \end_layout
 987
 988 \begin_layout Plain Layout
 989
 990 "1";"2" **
 991 \backslash
 992 crv{(-4,-21)&(5,-15)};
 993 \end_layout
 994
 995 \begin_layout Plain Layout
 996
 997 ?(.15)*
 998 \backslash
 999 dir{<}+(5,10)*{
1000 \backslash
1001 overline{F(x)}};
1002 \end_layout
1003
1004 \begin_layout Plain Layout
1005
1006 "2";"3" **
1007 \backslash
1008 crv{(6,1)&(14,1)};
1009 \end_layout
1010
1011 \begin_layout Plain Layout
1012
1013 ?(0)*
1014 \backslash
1015 dir{<}+(4,8)*{
1016 \backslash
1017 widetilde{F(i_x)}} ;
1018 \end_layout
1019
1020 \begin_layout Plain Layout
1021
1022 ?(.95)*
1023 \backslash
1024 dir{<}+(5,-2)*{F(
1025 \backslash
1026 overline x)};
1027 \end_layout
1028
1029 \begin_layout Plain Layout
1030
1031 "3";"3'" **
1032 \backslash
1033 dir{-};
1034 \end_layout
1035
1036 \begin_layout Plain Layout
1037
1038 (-2,6)*{}="X1";
1039 \end_layout
1040
1041 \begin_layout Plain Layout
1042
1043 (-10,6)*{}="X2";
1044 \end_layout
1045
1046 \begin_layout Plain Layout
1047
1048 "X1";"X2" **
1049 \backslash
1050 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1051 \end_layout
1052
1053 \begin_layout Plain Layout
1054
1055 (-2,-6)*{}="XA";
1056 \end_layout
1057
1058 \begin_layout Plain Layout
1059
1060 (-10,-6)*{}="XB";
1061 \end_layout
1062
1063 \begin_layout Plain Layout
1064
1065 "XA";"XB" **
1066 \backslash
1067 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1068 \end_layout
1069
1070 \begin_layout Plain Layout
1071
1072
1073 \backslash
1074 endxy
1075 \end_layout
1076
1077 \end_inset
1078
1079
1080 \end_layout
1081
1082 \end_inset
1083
1084
1085 \end_layout
1086
1087 \begin_layout Description
1088 Categories
1089 \end_layout
1090
1091 \begin_layout Standard
1092 \begin_inset Preview
1093
1094 \begin_layout Standard
1095 \begin_inset ERT
1096 status collapsed
1097
1098 \begin_layout Plain Layout
1099
1100
1101 \backslash
1102 xymatrix{
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[rr]^{a_{x,1,y}}
1119 \end_layout
1120
1121 \begin_layout Plain Layout
1122
1123
1124 \backslash
1125 ar[dr]_{r_x
1126 \backslash
1127 otimes 1_y}
1128 \end_layout
1129
1130 \begin_layout Plain Layout
1131
1132 && x
1133 \backslash
1134 otimes(1
1135 \backslash
1136 otimes y)
1137 \end_layout
1138
1139 \begin_layout Plain Layout
1140
1141
1142 \backslash
1143 ar[dl]^{1_x
1144 \backslash
1145 otimes
1146 \backslash
1147 ell_y }
1148 \backslash
1149
1150 \backslash
1151
1152 \end_layout
1153
1154 \begin_layout Plain Layout
1155
1156 & x
1157 \backslash
1158 otimes y }
1159 \end_layout
1160
1161 \end_inset
1162
1163
1164 \end_layout
1165
1166 \end_inset
1167
1168
1169 \begin_inset Preview
1170
1171 \begin_layout Standard
1172 \begin_inset ERT
1173 status collapsed
1174
1175 \begin_layout Plain Layout
1176
1177
1178 \backslash
1179 xy
1180 \end_layout
1181
1182 \begin_layout Plain Layout
1183
1184 (-9,0)*+{
1185 \backslash
1186 bullet}="1";
1187 \end_layout
1188
1189 \begin_layout Plain Layout
1190
1191 (0,0)*+{
1192 \backslash
1193 bullet}="2";
1194 \end_layout
1195
1196 \begin_layout Plain Layout
1197
1198 {
1199 \backslash
1200 ar@/^.9pc/ "1";"2"};
1201 \end_layout
1202
1203 \begin_layout Plain Layout
1204
1205 {
1206 \backslash
1207 ar@/_.9pc/ "1";"2"};
1208 \end_layout
1209
1210 \begin_layout Plain Layout
1211
1212 {
1213 \backslash
1214 ar@/^2pc/ "1";"2"};
1215 \end_layout
1216
1217 \begin_layout Plain Layout
1218
1219 {
1220 \backslash
1221 ar@/_2pc/ "1";"2"};
1222 \end_layout
1223
1224 \begin_layout Plain Layout
1225
1226 {
1227 \backslash
1228 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1229 \end_layout
1230
1231 \begin_layout Plain Layout
1232
1233 {
1234 \backslash
1235 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1236 \end_layout
1237
1238 \begin_layout Plain Layout
1239
1240 {
1241 \backslash
1242 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1243 \end_layout
1244
1245 \begin_layout Plain Layout
1246
1247 (0,0)*+{
1248 \backslash
1249 bullet}="1";
1250 \end_layout
1251
1252 \begin_layout Plain Layout
1253
1254 (9,0)*+{
1255 \backslash
1256 bullet}="2";
1257 \end_layout
1258
1259 \begin_layout Plain Layout
1260
1261 (18,0)*+{
1262 \backslash
1263 bullet}="3";
1264 \end_layout
1265
1266 \begin_layout Plain Layout
1267
1268 {
1269 \backslash
1270 ar "1";"2"};
1271 \end_layout
1272
1273 \begin_layout Plain Layout
1274
1275 {
1276 \backslash
1277 ar "2";"3"};
1278 \end_layout
1279
1280 \begin_layout Plain Layout
1281
1282 {
1283 \backslash
1284 ar@/^1pc/ "1";"2"};
1285 \end_layout
1286
1287 \begin_layout Plain Layout
1288
1289 {
1290 \backslash
1291 ar@/_1pc/ "1";"2"};
1292 \end_layout
1293
1294 \begin_layout Plain Layout
1295
1296 {
1297 \backslash
1298 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1299 \end_layout
1300
1301 \begin_layout Plain Layout
1302
1303 {
1304 \backslash
1305 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1306 \end_layout
1307
1308 \begin_layout Plain Layout
1309
1310
1311 \backslash
1312 endxy
1313 \end_layout
1314
1315 \end_inset
1316
1317
1318 \end_layout
1319
1320 \end_inset
1321
1322
1323 \end_layout
1324
1325 \begin_layout Description
1326 Transformations
1327 \end_layout
1328
1329 \begin_layout Standard
1330 \begin_inset Preview
1331
1332 \begin_layout Standard
1333 \begin_inset ERT
1334 status collapsed
1335
1336 \begin_layout Plain Layout
1337
1338
1339 \backslash
1340 xy %FIG.19.
1341  Natural transformation between functors.
1342 \end_layout
1343
1344 \begin_layout Plain Layout
1345
1346 (-26,-2)*+{
1347 \backslash
1348 bullet}="a";
1349 \end_layout
1350
1351 \begin_layout Plain Layout
1352
1353 (-12,3)*+{
1354 \backslash
1355 bullet}="b";
1356 \end_layout
1357
1358 \begin_layout Plain Layout
1359
1360 (-16,-5)*+{
1361 \backslash
1362 bullet}="c";
1363 \end_layout
1364
1365 \begin_layout Plain Layout
1366
1367 {
1368 \backslash
1369 ar@/^.25pc/ "a";"b"};
1370 \end_layout
1371
1372 \begin_layout Plain Layout
1373
1374 {
1375 \backslash
1376 ar@/_.25pc/"a";"c"};
1377 \end_layout
1378
1379 \begin_layout Plain Layout
1380
1381 {
1382 \backslash
1383 ar@/_.15pc/ "b";"c"};
1384 \end_layout
1385
1386 \begin_layout Plain Layout
1387
1388 %START TOP
1389 \end_layout
1390
1391 \begin_layout Plain Layout
1392
1393 (12,10)*+{
1394 \backslash
1395 bullet}="ta";
1396 \end_layout
1397
1398 \begin_layout Plain Layout
1399
1400 (26,15)*+{
1401 \backslash
1402 bullet}="tb";
1403 \end_layout
1404
1405 \begin_layout Plain Layout
1406
1407 (22,8)*+{
1408 \backslash
1409 bullet}="tc";
1410 \end_layout
1411
1412 \begin_layout Plain Layout
1413
1414 {
1415 \backslash
1416 ar@/^.25pc/ "ta";"tb"};
1417 \end_layout
1418
1419 \begin_layout Plain Layout
1420
1421 {
1422 \backslash
1423 ar@/_.25pc/ "ta";"tc"};
1424 \end_layout
1425
1426 \begin_layout Plain Layout
1427
1428 {
1429 \backslash
1430 ar@/_.15pc/ "tb";"tc"};
1431 \end_layout
1432
1433 \begin_layout Plain Layout
1434
1435 %START bottom
1436 \end_layout
1437
1438 \begin_layout Plain Layout
1439
1440 (12,-10)*+{
1441 \backslash
1442 bullet}="ba";
1443 \end_layout
1444
1445 \begin_layout Plain Layout
1446
1447 (26,-5)*+{
1448 \backslash
1449 bullet}="bb";
1450 \end_layout
1451
1452 \begin_layout Plain Layout
1453
1454 (22,-12)*+{
1455 \backslash
1456 bullet}="bc";
1457 \end_layout
1458
1459 \begin_layout Plain Layout
1460
1461 {
1462 \backslash
1463 ar@/^.25pc/@{.>} "ba";"bb"};
1464 \end_layout
1465
1466 \begin_layout Plain Layout
1467
1468 {
1469 \backslash
1470 ar@/_.25pc/ "ba";"bc"};
1471 \end_layout
1472
1473 \begin_layout Plain Layout
1474
1475 {
1476 \backslash
1477 ar@/_.15pc/ "bb";"bc"};
1478 \end_layout
1479
1480 \begin_layout Plain Layout
1481
1482 %START CONNECT
1483 \end_layout
1484
1485 \begin_layout Plain Layout
1486
1487 {
1488 \backslash
1489 ar@/_.15pc/ "ta";"ba"};
1490 \end_layout
1491
1492 \begin_layout Plain Layout
1493
1494 {
1495 \backslash
1496 ar@/_.15pc/ "tb";"bb"};
1497 \end_layout
1498
1499 \begin_layout Plain Layout
1500
1501 {
1502 \backslash
1503 ar@/_.15pc/ "tc";"bc"};
1504 \end_layout
1505
1506 \begin_layout Plain Layout
1507
1508 %START ARROWS AND LABELS
1509 \end_layout
1510
1511 \begin_layout Plain Layout
1512
1513 (-12,6)*{}="DF";
1514 \end_layout
1515
1516 \begin_layout Plain Layout
1517
1518 (6,10)*{}="CF";
1519 \end_layout
1520
1521 \begin_layout Plain Layout
1522
1523 {
1524 \backslash
1525 ar@/^.35pc/^F "DF";"CF"};
1526 \end_layout
1527
1528 \begin_layout Plain Layout
1529
1530 (-12,-6)*{}="DF";
1531 \end_layout
1532
1533 \begin_layout Plain Layout
1534
1535 (6,-10)*{}="CF";
1536 \end_layout
1537
1538 \begin_layout Plain Layout
1539
1540 {
1541 \backslash
1542 ar@/_.35pc/_G "DF";"CF"};
1543 \end_layout
1544
1545 \begin_layout Plain Layout
1546
1547 (-2,5)*{}="DF";
1548 \end_layout
1549
1550 \begin_layout Plain Layout
1551
1552 (-2,-5)*{}="CF";
1553 \end_layout
1554
1555 \begin_layout Plain Layout
1556
1557 {
1558 \backslash
1559 ar@{=>}^{
1560 \backslash
1561 alpha} "DF";"CF"};
1562 \end_layout
1563
1564 \begin_layout Plain Layout
1565
1566 (29,3)*{D};
1567 \end_layout
1568
1569 \begin_layout Plain Layout
1570
1571 (-23,3)*{C};
1572 \end_layout
1573
1574 \begin_layout Plain Layout
1575
1576
1577 \backslash
1578 endxy
1579 \end_layout
1580
1581 \end_inset
1582
1583
1584 \end_layout
1585
1586 \end_inset
1587
1588
1589 \end_layout
1590
1591 \begin_layout Section
1592 IPA
1593 \end_layout
1594
1595 \begin_layout Standard
1596 \begin_inset Preview
1597
1598 \begin_layout Standard
1599 \begin_inset ERT
1600 status collapsed
1601
1602 \begin_layout Plain Layout
1603
1604
1605 \backslash
1606 textipa{Ekspl@"neIS@n}
1607 \end_layout
1608
1609 \end_inset
1610
1611
1612 \end_layout
1613
1614 \end_inset
1615
1616
1617 \end_layout
1618
1619 \begin_layout Section
1620 QTree
1621 \end_layout
1622
1623 \begin_layout Standard
1624 \begin_inset Preview
1625
1626 \begin_layout Standard
1627 \begin_inset ERT
1628 status collapsed
1629
1630 \begin_layout Plain Layout
1631
1632
1633 \backslash
1634 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1635 \end_layout
1636
1637 \end_inset
1638
1639
1640 \end_layout
1641
1642 \end_inset
1643
1644
1645 \begin_inset Preview
1646
1647 \begin_layout Standard
1648 \begin_inset ERT
1649 status collapsed
1650
1651 \begin_layout Plain Layout
1652
1653
1654 \backslash
1655 Tree [.$
1656 \backslash
1657 sigma$ $
1658 \backslash
1659 mu$ $
1660 \backslash
1661 mu$ ]
1662 \end_layout
1663
1664 \end_inset
1665
1666
1667 \end_layout
1668
1669 \end_inset
1670
1671
1672 \end_layout
1673
1674 \begin_layout Section
1675 PSTricks
1676 \begin_inset CommandInset label
1677 LatexCommand label
1678 name "sec:PSTricks"
1679
1680 \end_inset
1681
1682
1683 \end_layout
1684
1685 \begin_layout Standard
1686 Some simple graphing examples.
1687 \end_layout
1688
1689 \begin_layout Subsection
1690 Function plotting
1691 \end_layout
1692
1693 \begin_layout Standard
1694 \begin_inset Preview
1695
1696 \begin_layout Standard
1697 \begin_inset ERT
1698 status open
1699
1700 \begin_layout Plain Layout
1701
1702
1703 \backslash
1704 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1705 \end_layout
1706
1707 \begin_layout Plain Layout
1708
1709
1710 \backslash
1711 psaxes{->}(0,0)(0,-3)(10,3)
1712 \end_layout
1713
1714 \begin_layout Plain Layout
1715
1716
1717 \backslash
1718 uput[-90](10,0){$x$}
1719 \backslash
1720 uput[0](0,3){$f(x)$}
1721 \end_layout
1722
1723 \begin_layout Plain Layout
1724
1725
1726 \backslash
1727 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1728 \end_layout
1729
1730 \begin_layout Plain Layout
1731
1732
1733 \backslash
1734 end{pspicture*}
1735 \end_layout
1736
1737 \end_inset
1738
1739
1740 \end_layout
1741
1742 \end_inset
1743
1744
1745 \end_layout
1746
1747 \begin_layout Subsection
1748 Inline data plotting
1749 \end_layout
1750
1751 \begin_layout Standard
1752 \align center
1753 \begin_inset Preview
1754
1755 \begin_layout Standard
1756 \align center
1757 \begin_inset ERT
1758 status open
1759
1760 \begin_layout Plain Layout
1761
1762
1763 \backslash
1764 begin{pspicture*}(-1.5,-1.5)(11,5)
1765 \end_layout
1766
1767 \begin_layout Plain Layout
1768
1769
1770 \backslash
1771 psaxes{->}(0,0)(0,0)(10,5)
1772 \end_layout
1773
1774 \begin_layout Plain Layout
1775
1776
1777 \backslash
1778 psset{linewidth=2.5pt}
1779 \end_layout
1780
1781 \begin_layout Plain Layout
1782
1783
1784 \backslash
1785 rput(5.0,-1.0){Speed [MPH]}
1786 \end_layout
1787
1788 \begin_layout Plain Layout
1789
1790
1791 \backslash
1792 rput(-1.0,1.0){
1793 \backslash
1794 begin{rotate}{90}Cost [Dollars]
1795 \backslash
1796 end{rotate}}
1797 \end_layout
1798
1799 \begin_layout Plain Layout
1800
1801
1802 \backslash
1803 savedata{
1804 \backslash
1805 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1806 \end_layout
1807
1808 \begin_layout Plain Layout
1809
1810
1811 \backslash
1812 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1813 \backslash
1814 mydata}
1815 \end_layout
1816
1817 \begin_layout Plain Layout
1818
1819
1820 \backslash
1821 end{pspicture*}
1822 \end_layout
1823
1824 \end_inset
1825
1826
1827 \end_layout
1828
1829 \end_inset
1830
1831
1832 \end_layout
1833
1834 \begin_layout Subsection
1835 Lissajous curves
1836 \end_layout
1837
1838 \begin_layout Standard
1839 \begin_inset Preview
1840
1841 \begin_layout Standard
1842 \begin_inset ERT
1843 status open
1844
1845 \begin_layout Plain Layout
1846
1847
1848 \backslash
1849 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1850 \end_layout
1851
1852 \begin_layout Plain Layout
1853
1854
1855 \backslash
1856 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1857  cos 100 t mul sin}
1858 \end_layout
1859
1860 \begin_layout Plain Layout
1861
1862
1863 \backslash
1864 end{pspicture*}
1865 \end_layout
1866
1867 \end_inset
1868
1869
1870 \end_layout
1871
1872 \end_inset
1873
1874
1875 \begin_inset space \hfill{}
1876 \end_inset
1877
1878
1879 \begin_inset Preview
1880
1881 \begin_layout Standard
1882 \begin_inset ERT
1883 status open
1884
1885 \begin_layout Plain Layout
1886
1887
1888 \backslash
1889 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1890 \end_layout
1891
1892 \begin_layout Plain Layout
1893
1894
1895 \backslash
1896 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1897  mul cos 100 t mul sin}
1898 \end_layout
1899
1900 \begin_layout Plain Layout
1901
1902
1903 \backslash
1904 end{pspicture*}
1905 \end_layout
1906
1907 \end_inset
1908
1909
1910 \end_layout
1911
1912 \end_inset
1913
1914
1915 \begin_inset space \hfill{}
1916 \end_inset
1917
1918
1919 \begin_inset Preview
1920
1921 \begin_layout Standard
1922 \begin_inset ERT
1923 status open
1924
1925 \begin_layout Plain Layout
1926
1927
1928 \backslash
1929 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1930 \end_layout
1931
1932 \begin_layout Plain Layout
1933
1934
1935 \backslash
1936 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1937  mul cos 200 t mul sin}
1938 \end_layout
1939
1940 \begin_layout Plain Layout
1941
1942
1943 \backslash
1944 end{pspicture*}
1945 \end_layout
1946
1947 \end_inset
1948
1949
1950 \end_layout
1951
1952 \end_inset
1953
1954
1955 \begin_inset space \hfill{}
1956 \end_inset
1957
1958
1959 \begin_inset Preview
1960
1961 \begin_layout Standard
1962 \begin_inset ERT
1963 status open
1964
1965 \begin_layout Plain Layout
1966
1967
1968 \backslash
1969 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1970 \end_layout
1971
1972 \begin_layout Plain Layout
1973
1974
1975 \backslash
1976 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1977  mul cos 200 t mul sin}
1978 \end_layout
1979
1980 \begin_layout Plain Layout
1981
1982
1983 \backslash
1984 end{pspicture*}
1985 \end_layout
1986
1987 \end_inset
1988
1989
1990 \end_layout
1991
1992 \end_inset
1993
1994
1995 \end_layout
1996
1997 \begin_layout Section
1998 TikZ
1999 \end_layout
2000
2001 \begin_layout Standard
2002 \begin_inset Flex URL
2003 status collapsed
2004
2005 \begin_layout Plain Layout
2006
2007 http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
2008 \end_layout
2009
2010 \end_inset
2011
2012
2013 \end_layout
2014
2015 \begin_layout Standard
2016 \begin_inset Preview
2017
2018 \begin_layout Standard
2019 \begin_inset ERT
2020 status collapsed
2021
2022 \begin_layout Plain Layout
2023
2024
2025 \backslash
2026 def
2027 \backslash
2028 iangle{35} % Angle of the inclined plane
2029 \end_layout
2030
2031 \begin_layout Plain Layout
2032
2033
2034 \backslash
2035 def
2036 \backslash
2037 down{-90}
2038 \end_layout
2039
2040 \begin_layout Plain Layout
2041
2042
2043 \backslash
2044 def
2045 \backslash
2046 arcr{0.5cm} % Radius of the arc used to indicate angles
2047 \end_layout
2048
2049 \begin_layout Plain Layout
2050
2051 \end_layout
2052
2053 \begin_layout Plain Layout
2054
2055
2056 \backslash
2057 begin{tikzpicture}[
2058 \end_layout
2059
2060 \begin_layout Plain Layout
2061
2062     force/.style={>=latex,draw=blue,fill=blue},
2063 \end_layout
2064
2065 \begin_layout Plain Layout
2066
2067     axis/.style={densely dashed,gray,font=
2068 \backslash
2069 small},
2070 \end_layout
2071
2072 \begin_layout Plain Layout
2073
2074     M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2075 \end_layout
2076
2077 \begin_layout Plain Layout
2078
2079     m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2080 \end_layout
2081
2082 \begin_layout Plain Layout
2083
2084     plane/.style={draw=black,fill=blue!10},
2085 \end_layout
2086
2087 \begin_layout Plain Layout
2088
2089     string/.style={draw=red, thick},
2090 \end_layout
2091
2092 \begin_layout Plain Layout
2093
2094     pulley/.style={thick},
2095 \end_layout
2096
2097 \begin_layout Plain Layout
2098
2099 ]
2100 \end_layout
2101
2102 \begin_layout Plain Layout
2103
2104 \end_layout
2105
2106 \begin_layout Plain Layout
2107
2108
2109 \backslash
2110 matrix[column sep=1cm] {
2111 \end_layout
2112
2113 \begin_layout Plain Layout
2114
2115     %% Sketch
2116 \end_layout
2117
2118 \begin_layout Plain Layout
2119
2120
2121 \backslash
2122 draw[plane] (0,-1) coordinate (base)
2123 \end_layout
2124
2125 \begin_layout Plain Layout
2126
2127                      -- coordinate[pos=0.5] (mid) ++(
2128 \backslash
2129 iangle:3) coordinate (top)
2130 \end_layout
2131
2132 \begin_layout Plain Layout
2133
2134                      |- (base) -- cycle;
2135 \end_layout
2136
2137 \begin_layout Plain Layout
2138
2139
2140 \backslash
2141 path (mid) node[M,rotate=
2142 \backslash
2143 iangle,yshift=0.25cm] (M) {};
2144 \end_layout
2145
2146 \begin_layout Plain Layout
2147
2148
2149 \backslash
2150 draw[pulley] (top) -- ++(
2151 \backslash
2152 iangle:0.25) circle (0.25cm)
2153 \end_layout
2154
2155 \begin_layout Plain Layout
2156
2157                    ++ (90-
2158 \backslash
2159 iangle:0.5) coordinate (pulley);
2160 \end_layout
2161
2162 \begin_layout Plain Layout
2163
2164
2165 \backslash
2166 draw[string] (M.east) -- ++(
2167 \backslash
2168 iangle:1.5cm) arc (90+
2169 \backslash
2170 iangle:0:0.25)
2171 \end_layout
2172
2173 \begin_layout Plain Layout
2174
2175                   -- ++(0,-1) node[m] {};
2176 \end_layout
2177
2178 \begin_layout Plain Layout
2179
2180 \end_layout
2181
2182 \begin_layout Plain Layout
2183
2184
2185 \backslash
2186 draw[->] (base)++(
2187 \backslash
2188 arcr,0) arc (0:
2189 \backslash
2190 iangle:
2191 \backslash
2192 arcr);
2193 \end_layout
2194
2195 \begin_layout Plain Layout
2196
2197
2198 \backslash
2199 path (base)++(
2200 \backslash
2201 iangle*0.5:
2202 \backslash
2203 arcr+5pt) node {$
2204 \backslash
2205 alpha$};
2206 \end_layout
2207
2208 \begin_layout Plain Layout
2209
2210     %%
2211 \end_layout
2212
2213 \begin_layout Plain Layout
2214
2215 \end_layout
2216
2217 \begin_layout Plain Layout
2218
2219 &
2220 \end_layout
2221
2222 \begin_layout Plain Layout
2223
2224     %% Free body diagram of M
2225 \end_layout
2226
2227 \begin_layout Plain Layout
2228
2229
2230 \backslash
2231 begin{scope}[rotate=
2232 \backslash
2233 iangle]
2234 \end_layout
2235
2236 \begin_layout Plain Layout
2237
2238
2239 \backslash
2240 node[M,transform shape] (M) {};
2241 \end_layout
2242
2243 \begin_layout Plain Layout
2244
2245         % Draw axes and help lines
2246 \end_layout
2247
2248 \begin_layout Plain Layout
2249
2250 \end_layout
2251
2252 \begin_layout Plain Layout
2253
2254         {[axis,->]
2255 \end_layout
2256
2257 \begin_layout Plain Layout
2258
2259
2260 \backslash
2261 draw (0,-1) -- (0,2) node[right] {$+y$};
2262 \end_layout
2263
2264 \begin_layout Plain Layout
2265
2266
2267 \backslash
2268 draw (M) -- ++(2,0) node[right] {$+x$};
2269 \end_layout
2270
2271 \begin_layout Plain Layout
2272
2273             % Indicate angle.
2274  The code is a bit awkward.
2275 \end_layout
2276
2277 \begin_layout Plain Layout
2278
2279 \end_layout
2280
2281 \begin_layout Plain Layout
2282
2283
2284 \backslash
2285 draw[solid,shorten >=0.5pt] (
2286 \backslash
2287 down-
2288 \backslash
2289 iangle:
2290 \backslash
2291 arcr)
2292 \end_layout
2293
2294 \begin_layout Plain Layout
2295
2296                 arc(
2297 \backslash
2298 down-
2299 \backslash
2300 iangle:
2301 \backslash
2302 down:
2303 \backslash
2304 arcr);
2305 \end_layout
2306
2307 \begin_layout Plain Layout
2308
2309
2310 \backslash
2311 node at (
2312 \backslash
2313 down-0.5*
2314 \backslash
2315 iangle:1.3*
2316 \backslash
2317 arcr) {$
2318 \backslash
2319 alpha$};
2320 \end_layout
2321
2322 \begin_layout Plain Layout
2323
2324         }
2325 \end_layout
2326
2327 \begin_layout Plain Layout
2328
2329 \end_layout
2330
2331 \begin_layout Plain Layout
2332
2333         % Forces
2334 \end_layout
2335
2336 \begin_layout Plain Layout
2337
2338         {[force,->]
2339 \end_layout
2340
2341 \begin_layout Plain Layout
2342
2343             % Assuming that Mg = 1.
2344  The normal force will therefore be cos(alpha)
2345 \end_layout
2346
2347 \begin_layout Plain Layout
2348
2349
2350 \backslash
2351 draw (M.center) -- ++(0,{cos(
2352 \backslash
2353 iangle)}) node[above right] {$N$};
2354 \end_layout
2355
2356 \begin_layout Plain Layout
2357
2358
2359 \backslash
2360 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2361 \end_layout
2362
2363 \begin_layout Plain Layout
2364
2365
2366 \backslash
2367 draw (M.east) -- ++(1,0) node[above] {$T$};
2368 \end_layout
2369
2370 \begin_layout Plain Layout
2371
2372         }
2373 \end_layout
2374
2375 \begin_layout Plain Layout
2376
2377 \end_layout
2378
2379 \begin_layout Plain Layout
2380
2381
2382 \backslash
2383 end{scope}
2384 \end_layout
2385
2386 \begin_layout Plain Layout
2387
2388     % Draw gravity force.
2389  The code is put outside the rotated
2390 \end_layout
2391
2392 \begin_layout Plain Layout
2393
2394     % scope for simplicity.
2395  No need to do any angle calculations.
2396
2397 \end_layout
2398
2399 \begin_layout Plain Layout
2400
2401
2402 \backslash
2403 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2404 \end_layout
2405
2406 \begin_layout Plain Layout
2407
2408     %%
2409 \end_layout
2410
2411 \begin_layout Plain Layout
2412
2413 \end_layout
2414
2415 \begin_layout Plain Layout
2416
2417 &
2418 \end_layout
2419
2420 \begin_layout Plain Layout
2421
2422     %%%
2423 \end_layout
2424
2425 \begin_layout Plain Layout
2426
2427     % Free body diagram of m
2428 \end_layout
2429
2430 \begin_layout Plain Layout
2431
2432
2433 \backslash
2434 node[m] (m) {};
2435 \end_layout
2436
2437 \begin_layout Plain Layout
2438
2439
2440 \backslash
2441 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2442 \end_layout
2443
2444 \begin_layout Plain Layout
2445
2446     {[force,->]
2447 \end_layout
2448
2449 \begin_layout Plain Layout
2450
2451
2452 \backslash
2453 draw (m.north) -- ++(0,1) node[above] {$T'$};
2454 \end_layout
2455
2456 \begin_layout Plain Layout
2457
2458
2459 \backslash
2460 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2461 \end_layout
2462
2463 \begin_layout Plain Layout
2464
2465     }
2466 \end_layout
2467
2468 \begin_layout Plain Layout
2469
2470 \end_layout
2471
2472 \begin_layout Plain Layout
2473
2474
2475 \backslash
2476
2477 \backslash
2478
2479 \end_layout
2480
2481 \begin_layout Plain Layout
2482
2483 };
2484 \end_layout
2485
2486 \begin_layout Plain Layout
2487
2488
2489 \backslash
2490 end{tikzpicture}
2491 \end_layout
2492
2493 \begin_layout Plain Layout
2494
2495 \end_layout
2496
2497 \end_inset
2498
2499
2500 \end_layout
2501
2502 \end_inset
2503
2504
2505 \end_layout
2506
2507 \end_body
2508 \end_document