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 However, the PDF (Xe\SpecialChar TeX
120 ) output seems to also work, while trying to typeset
129 will generate errors.
132 \begin_layout Section
136 \begin_layout Standard
137 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
139 \begin_inset Flex URL
142 \begin_layout Plain Layout
144 https://www.ctan.org/tex-archive/macros/generic/diagrams/xypic/doc/xyguide.pdf
152 \begin_layout Description
156 \begin_layout Standard
159 \begin_layout Standard
163 \begin_layout Plain Layout
170 \begin_layout Plain Layout
172 (5,10)*{}; (-10,-10)*{} **
177 \begin_layout Plain Layout
194 \begin_layout Plain Layout
196 "y"+(0,-1); (2,-10)*{} **
205 \begin_layout Plain Layout
212 \begin_layout Plain Layout
219 \begin_layout Plain Layout
226 \begin_layout Plain Layout
233 \begin_layout Plain Layout
250 \begin_layout Description
254 \begin_layout Standard
257 \begin_layout Standard
261 \begin_layout Plain Layout
268 \begin_layout Plain Layout
273 \begin_layout Plain Layout
278 \begin_layout Plain Layout
282 crv{~*=<.5pt>{.} (0,30)}?(.75)*
287 \begin_layout Plain Layout
292 \begin_layout Plain Layout
297 \begin_layout Plain Layout
301 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
306 \begin_layout Plain Layout
311 \begin_layout Plain Layout
316 \begin_layout Plain Layout
320 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
325 \begin_layout Plain Layout
330 \begin_layout Plain Layout
335 \begin_layout Plain Layout
339 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
344 \begin_layout Plain Layout
349 \begin_layout Plain Layout
354 \begin_layout Plain Layout
358 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
363 \begin_layout Plain Layout
380 \begin_layout Description
384 \begin_layout Standard
387 \begin_layout Standard
391 \begin_layout Plain Layout
398 \begin_layout Plain Layout
407 \begin_layout Plain Layout
414 \begin_layout Plain Layout
421 \begin_layout Plain Layout
428 \begin_layout Plain Layout
445 \begin_layout Description
449 \begin_layout Standard
452 \begin_layout Standard
456 \begin_layout Plain Layout
463 \begin_layout Plain Layout
470 \begin_layout Plain Layout
474 ellipse(3,1)__,=:a(-180){-};
477 \begin_layout Plain Layout
484 \begin_layout Plain Layout
491 \begin_layout Plain Layout
498 \begin_layout Plain Layout
502 ellipse(3,1)__,=:a(-180){-};
505 \begin_layout Plain Layout
509 ellipse(3,1)__,=:a(-180){-};
512 \begin_layout Plain Layout
516 ellipse(3,1)__,=:a(180){-};
519 \begin_layout Plain Layout
526 \begin_layout Plain Layout
533 \begin_layout Plain Layout
538 \begin_layout Plain Layout
543 \begin_layout Plain Layout
548 \begin_layout Plain Layout
553 \begin_layout Plain Layout
560 \begin_layout Plain Layout
565 \begin_layout Plain Layout
570 \begin_layout Plain Layout
575 \begin_layout Plain Layout
580 \begin_layout Plain Layout
587 \begin_layout Plain Layout
594 \begin_layout Plain Layout
601 \begin_layout Plain Layout
605 crv{(-8,7) & (-3,5)};
608 \begin_layout Plain Layout
613 \begin_layout Plain Layout
618 \begin_layout Plain Layout
623 \begin_layout Plain Layout
627 crv{(3,-10) & (9,-10)};
630 \begin_layout Plain Layout
635 \begin_layout Plain Layout
640 \begin_layout Plain Layout
644 crv{(-3,-10) & (-9,-10)};
647 \begin_layout Plain Layout
652 \begin_layout Plain Layout
657 \begin_layout Plain Layout
662 \begin_layout Plain Layout
667 \begin_layout Plain Layout
672 \begin_layout Plain Layout
677 \begin_layout Plain Layout
684 \begin_layout Plain Layout
691 \begin_layout Plain Layout
695 crv{(13,-6) & (2,-8)};
698 \begin_layout Plain Layout
702 crv{(-13,-6) & (-2,-8)};
705 \begin_layout Plain Layout
722 \begin_layout Standard
726 \begin_layout Plain Layout
733 \begin_layout Plain Layout
737 bullet}="RU"+(1,3)*{x^{
742 \begin_layout Plain Layout
746 bullet}="RD"+(2.5,2)*{x^{
751 \begin_layout Plain Layout
755 bullet}="LU"+(-1,2)*{x};
758 \begin_layout Plain Layout
762 bullet}="LD"+(-1,2)*{x};
765 \begin_layout Plain Layout
769 crv{(4,2) & (4,-1)}; ?(.1)*
776 \begin_layout Plain Layout
780 crv{(-4,-2) & (-4,1)};
783 \begin_layout Plain Layout
792 \begin_layout Plain Layout
794 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
797 \begin_layout Plain Layout
801 crv{(7,-10) & (-7,-10)};
804 \begin_layout Plain Layout
808 bullet}="RDD"+(2.5,-1)*{x^{
813 \begin_layout Plain Layout
817 bullet}="LDD"+(-1,-3)*{x};
820 \begin_layout Plain Layout
824 bullet}="RUD"+(3.5,1)*{x^{
829 \begin_layout Plain Layout
836 \begin_layout Plain Layout
838 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
841 \begin_layout Plain Layout
848 \begin_layout Plain Layout
855 \begin_layout Plain Layout
862 \begin_layout Plain Layout
866 crv{(0,-17)}; ?(.57)*
871 \begin_layout Plain Layout
878 \begin_layout Plain Layout
885 \begin_layout Plain Layout
892 \begin_layout Plain Layout
896 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
901 \begin_layout Plain Layout
918 \begin_layout Description
922 \begin_layout Standard
925 \begin_layout Standard
929 \begin_layout Plain Layout
933 xy (-15,0)*{};(15,0)*{};
936 \begin_layout Plain Layout
943 \begin_layout Plain Layout
954 \begin_layout Plain Layout
956 (-10,12)*{}; (-10,-12)*{}; **
960 dir{<}+(-4,0)*{F(x)};
963 \begin_layout Plain Layout
968 \begin_layout Plain Layout
973 \begin_layout Plain Layout
978 \begin_layout Plain Layout
983 \begin_layout Plain Layout
988 \begin_layout Plain Layout
992 crv{(-4,-21)&(5,-15)};
995 \begin_layout Plain Layout
1004 \begin_layout Plain Layout
1011 \begin_layout Plain Layout
1017 widetilde{F(i_x)}} ;
1020 \begin_layout Plain Layout
1029 \begin_layout Plain Layout
1036 \begin_layout Plain Layout
1041 \begin_layout Plain Layout
1046 \begin_layout Plain Layout
1050 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1053 \begin_layout Plain Layout
1058 \begin_layout Plain Layout
1063 \begin_layout Plain Layout
1067 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1070 \begin_layout Plain Layout
1087 \begin_layout Description
1091 \begin_layout Standard
1092 \begin_inset Preview
1094 \begin_layout Standard
1098 \begin_layout Plain Layout
1105 \begin_layout Plain Layout
1114 \begin_layout Plain Layout
1121 \begin_layout Plain Layout
1130 \begin_layout Plain Layout
1139 \begin_layout Plain Layout
1154 \begin_layout Plain Layout
1169 \begin_inset Preview
1171 \begin_layout Standard
1175 \begin_layout Plain Layout
1182 \begin_layout Plain Layout
1189 \begin_layout Plain Layout
1196 \begin_layout Plain Layout
1200 ar@/^.9pc/ "1";"2"};
1203 \begin_layout Plain Layout
1207 ar@/_.9pc/ "1";"2"};
1210 \begin_layout Plain Layout
1217 \begin_layout Plain Layout
1224 \begin_layout Plain Layout
1228 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1231 \begin_layout Plain Layout
1235 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1238 \begin_layout Plain Layout
1242 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1245 \begin_layout Plain Layout
1252 \begin_layout Plain Layout
1259 \begin_layout Plain Layout
1266 \begin_layout Plain Layout
1273 \begin_layout Plain Layout
1280 \begin_layout Plain Layout
1287 \begin_layout Plain Layout
1294 \begin_layout Plain Layout
1298 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1301 \begin_layout Plain Layout
1305 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1308 \begin_layout Plain Layout
1325 \begin_layout Description
1329 \begin_layout Standard
1330 \begin_inset Preview
1332 \begin_layout Standard
1336 \begin_layout Plain Layout
1341 Natural transformation between functors.
1344 \begin_layout Plain Layout
1351 \begin_layout Plain Layout
1358 \begin_layout Plain Layout
1365 \begin_layout Plain Layout
1369 ar@/^.25pc/ "a";"b"};
1372 \begin_layout Plain Layout
1376 ar@/_.25pc/"a";"c"};
1379 \begin_layout Plain Layout
1383 ar@/_.15pc/ "b";"c"};
1386 \begin_layout Plain Layout
1391 \begin_layout Plain Layout
1398 \begin_layout Plain Layout
1405 \begin_layout Plain Layout
1412 \begin_layout Plain Layout
1416 ar@/^.25pc/ "ta";"tb"};
1419 \begin_layout Plain Layout
1423 ar@/_.25pc/ "ta";"tc"};
1426 \begin_layout Plain Layout
1430 ar@/_.15pc/ "tb";"tc"};
1433 \begin_layout Plain Layout
1438 \begin_layout Plain Layout
1445 \begin_layout Plain Layout
1452 \begin_layout Plain Layout
1459 \begin_layout Plain Layout
1463 ar@/^.25pc/@{.>} "ba";"bb"};
1466 \begin_layout Plain Layout
1470 ar@/_.25pc/ "ba";"bc"};
1473 \begin_layout Plain Layout
1477 ar@/_.15pc/ "bb";"bc"};
1480 \begin_layout Plain Layout
1485 \begin_layout Plain Layout
1489 ar@/_.15pc/ "ta";"ba"};
1492 \begin_layout Plain Layout
1496 ar@/_.15pc/ "tb";"bb"};
1499 \begin_layout Plain Layout
1503 ar@/_.15pc/ "tc";"bc"};
1506 \begin_layout Plain Layout
1508 %START ARROWS AND LABELS
1511 \begin_layout Plain Layout
1516 \begin_layout Plain Layout
1521 \begin_layout Plain Layout
1525 ar@/^.35pc/^F "DF";"CF"};
1528 \begin_layout Plain Layout
1533 \begin_layout Plain Layout
1538 \begin_layout Plain Layout
1542 ar@/_.35pc/_G "DF";"CF"};
1545 \begin_layout Plain Layout
1550 \begin_layout Plain Layout
1555 \begin_layout Plain Layout
1564 \begin_layout Plain Layout
1569 \begin_layout Plain Layout
1574 \begin_layout Plain Layout
1591 \begin_layout Section
1595 \begin_layout Standard
1596 \begin_inset Preview
1598 \begin_layout Standard
1602 \begin_layout Plain Layout
1606 textipa{Ekspl@"neIS@n}
1619 \begin_layout Section
1623 \begin_layout Standard
1624 \begin_inset Preview
1626 \begin_layout Standard
1630 \begin_layout Plain Layout
1634 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1645 \begin_inset Preview
1647 \begin_layout Standard
1651 \begin_layout Plain Layout
1674 \begin_layout Section
1676 \begin_inset CommandInset label
1685 \begin_layout Standard
1686 Some simple graphing examples.
1689 \begin_layout Subsection
1693 \begin_layout Standard
1694 \begin_inset Preview
1696 \begin_layout Standard
1700 \begin_layout Plain Layout
1704 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1707 \begin_layout Plain Layout
1711 psaxes{->}(0,0)(0,-3)(10,3)
1714 \begin_layout Plain Layout
1718 uput[-90](10,0){$x$}
1720 uput[0](0,3){$f(x)$}
1723 \begin_layout Plain Layout
1727 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1730 \begin_layout Plain Layout
1747 \begin_layout Subsection
1748 Inline data plotting
1751 \begin_layout Standard
1753 \begin_inset Preview
1755 \begin_layout Standard
1760 \begin_layout Plain Layout
1764 begin{pspicture*}(-1.5,-1.5)(11,5)
1767 \begin_layout Plain Layout
1771 psaxes{->}(0,0)(0,0)(10,5)
1774 \begin_layout Plain Layout
1778 psset{linewidth=2.5pt}
1781 \begin_layout Plain Layout
1785 rput(5.0,-1.0){Speed [MPH]}
1788 \begin_layout Plain Layout
1794 begin{rotate}{90}Cost [Dollars]
1799 \begin_layout Plain Layout
1805 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1808 \begin_layout Plain Layout
1812 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1817 \begin_layout Plain Layout
1834 \begin_layout Subsection
1838 \begin_layout Standard
1839 \begin_inset Preview
1841 \begin_layout Standard
1845 \begin_layout Plain Layout
1849 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1852 \begin_layout Plain Layout
1856 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1860 \begin_layout Plain Layout
1875 \begin_inset space \hfill{}
1879 \begin_inset Preview
1881 \begin_layout Standard
1885 \begin_layout Plain Layout
1889 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1892 \begin_layout Plain Layout
1896 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1897 mul cos 100 t mul sin}
1900 \begin_layout Plain Layout
1915 \begin_inset space \hfill{}
1919 \begin_inset Preview
1921 \begin_layout Standard
1925 \begin_layout Plain Layout
1929 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1932 \begin_layout Plain Layout
1936 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1937 mul cos 200 t mul sin}
1940 \begin_layout Plain Layout
1955 \begin_inset space \hfill{}
1959 \begin_inset Preview
1961 \begin_layout Standard
1965 \begin_layout Plain Layout
1969 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1972 \begin_layout Plain Layout
1976 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1977 mul cos 200 t mul sin}
1980 \begin_layout Plain Layout
1997 \begin_layout Section
2001 \begin_layout Standard
2002 \begin_inset Flex URL
2005 \begin_layout Plain Layout
2007 http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
2015 \begin_layout Standard
2016 \begin_inset Preview
2018 \begin_layout Standard
2022 \begin_layout Plain Layout
2028 iangle{35} % Angle of the inclined plane
2031 \begin_layout Plain Layout
2040 \begin_layout Plain Layout
2046 arcr{0.5cm} % Radius of the arc used to indicate angles
2049 \begin_layout Plain Layout
2053 \begin_layout Plain Layout
2060 \begin_layout Plain Layout
2062 force/.style={>=latex,draw=blue,fill=blue},
2065 \begin_layout Plain Layout
2067 axis/.style={densely dashed,gray,font=
2072 \begin_layout Plain Layout
2074 M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2077 \begin_layout Plain Layout
2079 m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2082 \begin_layout Plain Layout
2084 plane/.style={draw=black,fill=blue!10},
2087 \begin_layout Plain Layout
2089 string/.style={draw=red, thick},
2092 \begin_layout Plain Layout
2094 pulley/.style={thick},
2097 \begin_layout Plain Layout
2102 \begin_layout Plain Layout
2106 \begin_layout Plain Layout
2110 matrix[column sep=1cm] {
2113 \begin_layout Plain Layout
2118 \begin_layout Plain Layout
2122 draw[plane] (0,-1) coordinate (base)
2125 \begin_layout Plain Layout
2127 -- coordinate[pos=0.5] (mid) ++(
2129 iangle:3) coordinate (top)
2132 \begin_layout Plain Layout
2137 \begin_layout Plain Layout
2141 path (mid) node[M,rotate=
2143 iangle,yshift=0.25cm] (M) {};
2146 \begin_layout Plain Layout
2150 draw[pulley] (top) -- ++(
2152 iangle:0.25) circle (0.25cm)
2155 \begin_layout Plain Layout
2159 iangle:0.5) coordinate (pulley);
2162 \begin_layout Plain Layout
2166 draw[string] (M.east) -- ++(
2168 iangle:1.5cm) arc (90+
2173 \begin_layout Plain Layout
2175 -- ++(0,-1) node[m] {};
2178 \begin_layout Plain Layout
2182 \begin_layout Plain Layout
2195 \begin_layout Plain Layout
2208 \begin_layout Plain Layout
2213 \begin_layout Plain Layout
2217 \begin_layout Plain Layout
2222 \begin_layout Plain Layout
2224 %% Free body diagram of M
2227 \begin_layout Plain Layout
2231 begin{scope}[rotate=
2236 \begin_layout Plain Layout
2240 node[M,transform shape] (M) {};
2243 \begin_layout Plain Layout
2245 % Draw axes and help lines
2248 \begin_layout Plain Layout
2252 \begin_layout Plain Layout
2257 \begin_layout Plain Layout
2261 draw (0,-1) -- (0,2) node[right] {$+y$};
2264 \begin_layout Plain Layout
2268 draw (M) -- ++(2,0) node[right] {$+x$};
2271 \begin_layout Plain Layout
2274 The code is a bit awkward.
2277 \begin_layout Plain Layout
2281 \begin_layout Plain Layout
2285 draw[solid,shorten >=0.5pt] (
2294 \begin_layout Plain Layout
2307 \begin_layout Plain Layout
2322 \begin_layout Plain Layout
2327 \begin_layout Plain Layout
2331 \begin_layout Plain Layout
2336 \begin_layout Plain Layout
2341 \begin_layout Plain Layout
2343 % Assuming that Mg = 1.
2344 The normal force will therefore be cos(alpha)
2347 \begin_layout Plain Layout
2351 draw (M.center) -- ++(0,{cos(
2353 iangle)}) node[above right] {$N$};
2356 \begin_layout Plain Layout
2360 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2363 \begin_layout Plain Layout
2367 draw (M.east) -- ++(1,0) node[above] {$T$};
2370 \begin_layout Plain Layout
2375 \begin_layout Plain Layout
2379 \begin_layout Plain Layout
2386 \begin_layout Plain Layout
2388 % Draw gravity force.
2389 The code is put outside the rotated
2392 \begin_layout Plain Layout
2394 % scope for simplicity.
2395 No need to do any angle calculations.
2399 \begin_layout Plain Layout
2403 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2406 \begin_layout Plain Layout
2411 \begin_layout Plain Layout
2415 \begin_layout Plain Layout
2420 \begin_layout Plain Layout
2425 \begin_layout Plain Layout
2427 % Free body diagram of m
2430 \begin_layout Plain Layout
2437 \begin_layout Plain Layout
2441 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2444 \begin_layout Plain Layout
2449 \begin_layout Plain Layout
2453 draw (m.north) -- ++(0,1) node[above] {$T'$};
2456 \begin_layout Plain Layout
2460 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2463 \begin_layout Plain Layout
2468 \begin_layout Plain Layout
2472 \begin_layout Plain Layout
2481 \begin_layout Plain Layout
2486 \begin_layout Plain Layout
2493 \begin_layout Plain Layout