1 #LyX 2.4 created this file. For more info see https://www.lyx.org/
5 \save_transient_properties true
6 \origin /systemlyxdir/examples/Graphics_and_Insets/
10 \usepackage[all, knot]{xy}
18 \usetikzlibrary{scopes}
20 \use_default_options false
21 \maintain_unincluded_children no
23 \language_package default
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
34 \font_typewriter_osf false
36 \font_sf_scale 100 100
37 \font_tt_scale 100 100
39 \use_dash_ligatures false
41 \default_output_format pdf
43 \bibtex_command default
44 \index_command default
45 \paperfontsize default
50 \use_package amsmath 1
51 \use_package amssymb 1
54 \use_package mathdots 1
55 \use_package mathtools 1
57 \use_package stackrel 1
58 \use_package stmaryrd 1
59 \use_package undertilde 1
61 \cite_engine_type default
65 \paperorientation portrait
77 \paragraph_separation indent
78 \paragraph_indentation default
80 \math_numbering_side default
85 \paperpagestyle default
86 \tracking_changes false
87 \postpone_fragile_content false
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:
105 \begin_layout LyX-Code
106 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf, etex
109 \begin_layout Standard
110 Due to the use of postscript specials in Section
111 \begin_inset CommandInset ref
113 reference "sec:PSTricks"
117 , only the Postscript or PDF (ps2pdf) output formats will correctly render
119 Starting with TeX Live 2021, you may need to add the flag
121 -dALLOWPSTRANSPARENCY
128 The PDF (Xe\SpecialChar TeX
129 ) output seems to also work, while trying to typeset the document
138 will generate errors.
141 \begin_layout Section
145 \begin_layout Standard
146 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
148 \begin_inset Flex URL
151 \begin_layout Plain Layout
153 https://www.ctan.org/tex-archive/macros/generic/diagrams/xypic/doc/xyguide.pdf
161 \begin_layout Description
165 \begin_layout Standard
168 \begin_layout Standard
172 \begin_layout Plain Layout
179 \begin_layout Plain Layout
181 (5,10)*{}; (-10,-10)*{} **
186 \begin_layout Plain Layout
203 \begin_layout Plain Layout
205 "y"+(0,-1); (2,-10)*{} **
214 \begin_layout Plain Layout
221 \begin_layout Plain Layout
228 \begin_layout Plain Layout
235 \begin_layout Plain Layout
242 \begin_layout Plain Layout
259 \begin_layout Description
263 \begin_layout Standard
266 \begin_layout Standard
270 \begin_layout Plain Layout
277 \begin_layout Plain Layout
282 \begin_layout Plain Layout
287 \begin_layout Plain Layout
291 crv{~*=<.5pt>{.} (0,30)}?(.75)*
296 \begin_layout Plain Layout
301 \begin_layout Plain Layout
306 \begin_layout Plain Layout
310 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
315 \begin_layout Plain Layout
320 \begin_layout Plain Layout
325 \begin_layout Plain Layout
329 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
334 \begin_layout Plain Layout
339 \begin_layout Plain Layout
344 \begin_layout Plain Layout
348 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
353 \begin_layout Plain Layout
358 \begin_layout Plain Layout
363 \begin_layout Plain Layout
367 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
372 \begin_layout Plain Layout
389 \begin_layout Description
393 \begin_layout Standard
396 \begin_layout Standard
400 \begin_layout Plain Layout
407 \begin_layout Plain Layout
416 \begin_layout Plain Layout
423 \begin_layout Plain Layout
430 \begin_layout Plain Layout
437 \begin_layout Plain Layout
454 \begin_layout Description
458 \begin_layout Standard
461 \begin_layout Standard
465 \begin_layout Plain Layout
472 \begin_layout Plain Layout
479 \begin_layout Plain Layout
483 ellipse(3,1)__,=:a(-180){-};
486 \begin_layout Plain Layout
493 \begin_layout Plain Layout
500 \begin_layout Plain Layout
507 \begin_layout Plain Layout
511 ellipse(3,1)__,=:a(-180){-};
514 \begin_layout Plain Layout
518 ellipse(3,1)__,=:a(-180){-};
521 \begin_layout Plain Layout
525 ellipse(3,1)__,=:a(180){-};
528 \begin_layout Plain Layout
535 \begin_layout Plain Layout
542 \begin_layout Plain Layout
547 \begin_layout Plain Layout
552 \begin_layout Plain Layout
557 \begin_layout Plain Layout
562 \begin_layout Plain Layout
569 \begin_layout Plain Layout
574 \begin_layout Plain Layout
579 \begin_layout Plain Layout
584 \begin_layout Plain Layout
589 \begin_layout Plain Layout
596 \begin_layout Plain Layout
603 \begin_layout Plain Layout
610 \begin_layout Plain Layout
614 crv{(-8,7) & (-3,5)};
617 \begin_layout Plain Layout
622 \begin_layout Plain Layout
627 \begin_layout Plain Layout
632 \begin_layout Plain Layout
636 crv{(3,-10) & (9,-10)};
639 \begin_layout Plain Layout
644 \begin_layout Plain Layout
649 \begin_layout Plain Layout
653 crv{(-3,-10) & (-9,-10)};
656 \begin_layout Plain Layout
661 \begin_layout Plain Layout
666 \begin_layout Plain Layout
671 \begin_layout Plain Layout
676 \begin_layout Plain Layout
681 \begin_layout Plain Layout
686 \begin_layout Plain Layout
693 \begin_layout Plain Layout
700 \begin_layout Plain Layout
704 crv{(13,-6) & (2,-8)};
707 \begin_layout Plain Layout
711 crv{(-13,-6) & (-2,-8)};
714 \begin_layout Plain Layout
731 \begin_layout Standard
735 \begin_layout Plain Layout
742 \begin_layout Plain Layout
746 bullet}="RU"+(1,3)*{x^{
751 \begin_layout Plain Layout
755 bullet}="RD"+(2.5,2)*{x^{
760 \begin_layout Plain Layout
764 bullet}="LU"+(-1,2)*{x};
767 \begin_layout Plain Layout
771 bullet}="LD"+(-1,2)*{x};
774 \begin_layout Plain Layout
778 crv{(4,2) & (4,-1)}; ?(.1)*
785 \begin_layout Plain Layout
789 crv{(-4,-2) & (-4,1)};
792 \begin_layout Plain Layout
801 \begin_layout Plain Layout
803 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
806 \begin_layout Plain Layout
810 crv{(7,-10) & (-7,-10)};
813 \begin_layout Plain Layout
817 bullet}="RDD"+(2.5,-1)*{x^{
822 \begin_layout Plain Layout
826 bullet}="LDD"+(-1,-3)*{x};
829 \begin_layout Plain Layout
833 bullet}="RUD"+(3.5,1)*{x^{
838 \begin_layout Plain Layout
845 \begin_layout Plain Layout
847 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
850 \begin_layout Plain Layout
857 \begin_layout Plain Layout
864 \begin_layout Plain Layout
871 \begin_layout Plain Layout
875 crv{(0,-17)}; ?(.57)*
880 \begin_layout Plain Layout
887 \begin_layout Plain Layout
894 \begin_layout Plain Layout
901 \begin_layout Plain Layout
905 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
910 \begin_layout Plain Layout
927 \begin_layout Description
931 \begin_layout Standard
934 \begin_layout Standard
938 \begin_layout Plain Layout
942 xy (-15,0)*{};(15,0)*{};
945 \begin_layout Plain Layout
952 \begin_layout Plain Layout
963 \begin_layout Plain Layout
965 (-10,12)*{}; (-10,-12)*{}; **
969 dir{<}+(-4,0)*{F(x)};
972 \begin_layout Plain Layout
977 \begin_layout Plain Layout
982 \begin_layout Plain Layout
987 \begin_layout Plain Layout
992 \begin_layout Plain Layout
997 \begin_layout Plain Layout
1001 crv{(-4,-21)&(5,-15)};
1004 \begin_layout Plain Layout
1013 \begin_layout Plain Layout
1020 \begin_layout Plain Layout
1026 widetilde{F(i_x)}} ;
1029 \begin_layout Plain Layout
1038 \begin_layout Plain Layout
1045 \begin_layout Plain Layout
1050 \begin_layout Plain Layout
1055 \begin_layout Plain Layout
1059 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1062 \begin_layout Plain Layout
1067 \begin_layout Plain Layout
1072 \begin_layout Plain Layout
1076 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1079 \begin_layout Plain Layout
1096 \begin_layout Description
1100 \begin_layout Standard
1101 \begin_inset Preview
1103 \begin_layout Standard
1107 \begin_layout Plain Layout
1114 \begin_layout Plain Layout
1123 \begin_layout Plain Layout
1130 \begin_layout Plain Layout
1139 \begin_layout Plain Layout
1148 \begin_layout Plain Layout
1163 \begin_layout Plain Layout
1178 \begin_inset Preview
1180 \begin_layout Standard
1184 \begin_layout Plain Layout
1191 \begin_layout Plain Layout
1198 \begin_layout Plain Layout
1205 \begin_layout Plain Layout
1209 ar@/^.9pc/ "1";"2"};
1212 \begin_layout Plain Layout
1216 ar@/_.9pc/ "1";"2"};
1219 \begin_layout Plain Layout
1226 \begin_layout Plain Layout
1233 \begin_layout Plain Layout
1237 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1240 \begin_layout Plain Layout
1244 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1247 \begin_layout Plain Layout
1251 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1254 \begin_layout Plain Layout
1261 \begin_layout Plain Layout
1268 \begin_layout Plain Layout
1275 \begin_layout Plain Layout
1282 \begin_layout Plain Layout
1289 \begin_layout Plain Layout
1296 \begin_layout Plain Layout
1303 \begin_layout Plain Layout
1307 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1310 \begin_layout Plain Layout
1314 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1317 \begin_layout Plain Layout
1334 \begin_layout Description
1338 \begin_layout Standard
1339 \begin_inset Preview
1341 \begin_layout Standard
1345 \begin_layout Plain Layout
1350 Natural transformation between functors.
1353 \begin_layout Plain Layout
1360 \begin_layout Plain Layout
1367 \begin_layout Plain Layout
1374 \begin_layout Plain Layout
1378 ar@/^.25pc/ "a";"b"};
1381 \begin_layout Plain Layout
1385 ar@/_.25pc/"a";"c"};
1388 \begin_layout Plain Layout
1392 ar@/_.15pc/ "b";"c"};
1395 \begin_layout Plain Layout
1400 \begin_layout Plain Layout
1407 \begin_layout Plain Layout
1414 \begin_layout Plain Layout
1421 \begin_layout Plain Layout
1425 ar@/^.25pc/ "ta";"tb"};
1428 \begin_layout Plain Layout
1432 ar@/_.25pc/ "ta";"tc"};
1435 \begin_layout Plain Layout
1439 ar@/_.15pc/ "tb";"tc"};
1442 \begin_layout Plain Layout
1447 \begin_layout Plain Layout
1454 \begin_layout Plain Layout
1461 \begin_layout Plain Layout
1468 \begin_layout Plain Layout
1472 ar@/^.25pc/@{.>} "ba";"bb"};
1475 \begin_layout Plain Layout
1479 ar@/_.25pc/ "ba";"bc"};
1482 \begin_layout Plain Layout
1486 ar@/_.15pc/ "bb";"bc"};
1489 \begin_layout Plain Layout
1494 \begin_layout Plain Layout
1498 ar@/_.15pc/ "ta";"ba"};
1501 \begin_layout Plain Layout
1505 ar@/_.15pc/ "tb";"bb"};
1508 \begin_layout Plain Layout
1512 ar@/_.15pc/ "tc";"bc"};
1515 \begin_layout Plain Layout
1517 %START ARROWS AND LABELS
1520 \begin_layout Plain Layout
1525 \begin_layout Plain Layout
1530 \begin_layout Plain Layout
1534 ar@/^.35pc/^F "DF";"CF"};
1537 \begin_layout Plain Layout
1542 \begin_layout Plain Layout
1547 \begin_layout Plain Layout
1551 ar@/_.35pc/_G "DF";"CF"};
1554 \begin_layout Plain Layout
1559 \begin_layout Plain Layout
1564 \begin_layout Plain Layout
1573 \begin_layout Plain Layout
1578 \begin_layout Plain Layout
1583 \begin_layout Plain Layout
1600 \begin_layout Section
1604 \begin_layout Standard
1605 \begin_inset Preview
1607 \begin_layout Standard
1611 \begin_layout Plain Layout
1615 textipa{Ekspl@"neIS@n}
1628 \begin_layout Section
1632 \begin_layout Standard
1633 \begin_inset Preview
1635 \begin_layout Standard
1639 \begin_layout Plain Layout
1643 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1654 \begin_inset Preview
1656 \begin_layout Standard
1660 \begin_layout Plain Layout
1683 \begin_layout Section
1685 \begin_inset CommandInset label
1694 \begin_layout Standard
1695 Some simple graphing examples.
1698 \begin_layout Subsection
1702 \begin_layout Standard
1703 \begin_inset Preview
1705 \begin_layout Standard
1709 \begin_layout Plain Layout
1713 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1716 \begin_layout Plain Layout
1720 psaxes{->}(0,0)(0,-3)(10,3)
1723 \begin_layout Plain Layout
1727 uput[-90](10,0){$x$}
1729 uput[0](0,3){$f(x)$}
1732 \begin_layout Plain Layout
1736 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1739 \begin_layout Plain Layout
1756 \begin_layout Subsection
1757 Inline data plotting
1760 \begin_layout Standard
1762 \begin_inset Preview
1764 \begin_layout Standard
1769 \begin_layout Plain Layout
1773 begin{pspicture*}(-1.5,-1.5)(11,5)
1776 \begin_layout Plain Layout
1780 psaxes{->}(0,0)(0,0)(10,5)
1783 \begin_layout Plain Layout
1787 psset{linewidth=2.5pt}
1790 \begin_layout Plain Layout
1794 rput(5.0,-1.0){Speed [MPH]}
1797 \begin_layout Plain Layout
1803 begin{rotate}{90}Cost [Dollars]
1808 \begin_layout Plain Layout
1814 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1817 \begin_layout Plain Layout
1821 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1826 \begin_layout Plain Layout
1843 \begin_layout Subsection
1847 \begin_layout Standard
1848 \begin_inset Preview
1850 \begin_layout Standard
1854 \begin_layout Plain Layout
1858 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1861 \begin_layout Plain Layout
1865 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1869 \begin_layout Plain Layout
1884 \begin_inset space \hfill{}
1888 \begin_inset Preview
1890 \begin_layout Standard
1894 \begin_layout Plain Layout
1898 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1901 \begin_layout Plain Layout
1905 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1906 mul cos 100 t mul sin}
1909 \begin_layout Plain Layout
1924 \begin_inset space \hfill{}
1928 \begin_inset Preview
1930 \begin_layout Standard
1934 \begin_layout Plain Layout
1938 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1941 \begin_layout Plain Layout
1945 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1946 mul cos 200 t mul sin}
1949 \begin_layout Plain Layout
1964 \begin_inset space \hfill{}
1968 \begin_inset Preview
1970 \begin_layout Standard
1974 \begin_layout Plain Layout
1978 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1981 \begin_layout Plain Layout
1985 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1986 mul cos 200 t mul sin}
1989 \begin_layout Plain Layout
2006 \begin_layout Section
2010 \begin_layout Standard
2011 \begin_inset Flex URL
2014 \begin_layout Plain Layout
2016 http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
2024 \begin_layout Standard
2025 \begin_inset Preview
2027 \begin_layout Standard
2031 \begin_layout Plain Layout
2037 iangle{35} % Angle of the inclined plane
2040 \begin_layout Plain Layout
2049 \begin_layout Plain Layout
2055 arcr{0.5cm} % Radius of the arc used to indicate angles
2058 \begin_layout Plain Layout
2062 \begin_layout Plain Layout
2069 \begin_layout Plain Layout
2071 force/.style={>=latex,draw=blue,fill=blue},
2074 \begin_layout Plain Layout
2076 axis/.style={densely dashed,gray,font=
2081 \begin_layout Plain Layout
2083 M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2086 \begin_layout Plain Layout
2088 m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2091 \begin_layout Plain Layout
2093 plane/.style={draw=black,fill=blue!10},
2096 \begin_layout Plain Layout
2098 string/.style={draw=red, thick},
2101 \begin_layout Plain Layout
2103 pulley/.style={thick},
2106 \begin_layout Plain Layout
2111 \begin_layout Plain Layout
2115 \begin_layout Plain Layout
2119 matrix[column sep=1cm] {
2122 \begin_layout Plain Layout
2127 \begin_layout Plain Layout
2131 draw[plane] (0,-1) coordinate (base)
2134 \begin_layout Plain Layout
2136 -- coordinate[pos=0.5] (mid) ++(
2138 iangle:3) coordinate (top)
2141 \begin_layout Plain Layout
2146 \begin_layout Plain Layout
2150 path (mid) node[M,rotate=
2152 iangle,yshift=0.25cm] (M) {};
2155 \begin_layout Plain Layout
2159 draw[pulley] (top) -- ++(
2161 iangle:0.25) circle (0.25cm)
2164 \begin_layout Plain Layout
2168 iangle:0.5) coordinate (pulley);
2171 \begin_layout Plain Layout
2175 draw[string] (M.east) -- ++(
2177 iangle:1.5cm) arc (90+
2182 \begin_layout Plain Layout
2184 -- ++(0,-1) node[m] {};
2187 \begin_layout Plain Layout
2191 \begin_layout Plain Layout
2204 \begin_layout Plain Layout
2217 \begin_layout Plain Layout
2222 \begin_layout Plain Layout
2226 \begin_layout Plain Layout
2231 \begin_layout Plain Layout
2233 %% Free body diagram of M
2236 \begin_layout Plain Layout
2240 begin{scope}[rotate=
2245 \begin_layout Plain Layout
2249 node[M,transform shape] (M) {};
2252 \begin_layout Plain Layout
2254 % Draw axes and help lines
2257 \begin_layout Plain Layout
2261 \begin_layout Plain Layout
2266 \begin_layout Plain Layout
2270 draw (0,-1) -- (0,2) node[right] {$+y$};
2273 \begin_layout Plain Layout
2277 draw (M) -- ++(2,0) node[right] {$+x$};
2280 \begin_layout Plain Layout
2283 The code is a bit awkward.
2286 \begin_layout Plain Layout
2290 \begin_layout Plain Layout
2294 draw[solid,shorten >=0.5pt] (
2303 \begin_layout Plain Layout
2316 \begin_layout Plain Layout
2331 \begin_layout Plain Layout
2336 \begin_layout Plain Layout
2340 \begin_layout Plain Layout
2345 \begin_layout Plain Layout
2350 \begin_layout Plain Layout
2352 % Assuming that Mg = 1.
2353 The normal force will therefore be cos(alpha)
2356 \begin_layout Plain Layout
2360 draw (M.center) -- ++(0,{cos(
2362 iangle)}) node[above right] {$N$};
2365 \begin_layout Plain Layout
2369 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2372 \begin_layout Plain Layout
2376 draw (M.east) -- ++(1,0) node[above] {$T$};
2379 \begin_layout Plain Layout
2384 \begin_layout Plain Layout
2388 \begin_layout Plain Layout
2395 \begin_layout Plain Layout
2397 % Draw gravity force.
2398 The code is put outside the rotated
2401 \begin_layout Plain Layout
2403 % scope for simplicity.
2404 No need to do any angle calculations.
2408 \begin_layout Plain Layout
2412 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2415 \begin_layout Plain Layout
2420 \begin_layout Plain Layout
2424 \begin_layout Plain Layout
2429 \begin_layout Plain Layout
2434 \begin_layout Plain Layout
2436 % Free body diagram of m
2439 \begin_layout Plain Layout
2446 \begin_layout Plain Layout
2450 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2453 \begin_layout Plain Layout
2458 \begin_layout Plain Layout
2462 draw (m.north) -- ++(0,1) node[above] {$T'$};
2465 \begin_layout Plain Layout
2469 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2472 \begin_layout Plain Layout
2477 \begin_layout Plain Layout
2481 \begin_layout Plain Layout
2490 \begin_layout Plain Layout
2495 \begin_layout Plain Layout
2502 \begin_layout Plain Layout