1 #LyX 2.3 created this file. For more info see http://www.lyx.org/
5 \save_transient_properties true
6 \origin /systemlyxdir/examples/
10 \usepackage[all, knot]{xy}
18 \usetikzlibrary{scopes}
20 \use_default_options false
21 \maintain_unincluded_children false
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_sf_scale 100 100
35 \font_tt_scale 100 100
37 \use_dash_ligatures false
39 \default_output_format pdf
41 \bibtex_command default
42 \index_command default
43 \paperfontsize default
48 \use_package amsmath 1
49 \use_package amssymb 1
52 \use_package mathdots 1
53 \use_package mathtools 0
55 \use_package stackrel 0
56 \use_package stmaryrd 0
57 \use_package undertilde 0
59 \cite_engine_type default
63 \paperorientation portrait
73 \paragraph_separation indent
74 \paragraph_indentation default
76 \math_numbering_side default
80 \paperpagestyle default
81 \tracking_changes false
95 \begin_layout Standard
96 In order to properly typeset the document and have instant preview working,
97 the following packages have to be installed:
100 \begin_layout LyX-Code
101 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf, etex
104 \begin_layout Standard
105 Due to the use of postscript specials in Section
106 \begin_inset CommandInset ref
108 reference "sec:PSTricks"
112 , only the Postscript or PDF (ps2pdf) output formats will correctly render
114 However, the PDF (Xe\SpecialChar TeX
115 ) output seems to also work, while trying to typeset
124 will generate errors.
127 \begin_layout Section
131 \begin_layout Standard
132 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
134 \begin_inset Flex URL
137 \begin_layout Plain Layout
139 https://www.ctan.org/tex-archive/macros/generic/diagrams/xypic/doc/xyguide.pdf
147 \begin_layout Description
151 \begin_layout Standard
154 \begin_layout Standard
158 \begin_layout Plain Layout
165 \begin_layout Plain Layout
167 (5,10)*{}; (-10,-10)*{} **
172 \begin_layout Plain Layout
189 \begin_layout Plain Layout
191 "y"+(0,-1); (2,-10)*{} **
200 \begin_layout Plain Layout
207 \begin_layout Plain Layout
214 \begin_layout Plain Layout
221 \begin_layout Plain Layout
228 \begin_layout Plain Layout
245 \begin_layout Description
249 \begin_layout Standard
252 \begin_layout Standard
256 \begin_layout Plain Layout
263 \begin_layout Plain Layout
268 \begin_layout Plain Layout
273 \begin_layout Plain Layout
277 crv{~*=<.5pt>{.} (0,30)}?(.75)*
282 \begin_layout Plain Layout
287 \begin_layout Plain Layout
292 \begin_layout Plain Layout
296 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
301 \begin_layout Plain Layout
306 \begin_layout Plain Layout
311 \begin_layout Plain Layout
315 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
320 \begin_layout Plain Layout
325 \begin_layout Plain Layout
330 \begin_layout Plain Layout
334 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
339 \begin_layout Plain Layout
344 \begin_layout Plain Layout
349 \begin_layout Plain Layout
353 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
358 \begin_layout Plain Layout
375 \begin_layout Description
379 \begin_layout Standard
382 \begin_layout Standard
386 \begin_layout Plain Layout
393 \begin_layout Plain Layout
402 \begin_layout Plain Layout
409 \begin_layout Plain Layout
416 \begin_layout Plain Layout
423 \begin_layout Plain Layout
440 \begin_layout Description
444 \begin_layout Standard
447 \begin_layout Standard
451 \begin_layout Plain Layout
458 \begin_layout Plain Layout
465 \begin_layout Plain Layout
469 ellipse(3,1)__,=:a(-180){-};
472 \begin_layout Plain Layout
479 \begin_layout Plain Layout
486 \begin_layout Plain Layout
493 \begin_layout Plain Layout
497 ellipse(3,1)__,=:a(-180){-};
500 \begin_layout Plain Layout
504 ellipse(3,1)__,=:a(-180){-};
507 \begin_layout Plain Layout
511 ellipse(3,1)__,=:a(180){-};
514 \begin_layout Plain Layout
521 \begin_layout Plain Layout
528 \begin_layout Plain Layout
533 \begin_layout Plain Layout
538 \begin_layout Plain Layout
543 \begin_layout Plain Layout
548 \begin_layout Plain Layout
555 \begin_layout Plain Layout
560 \begin_layout Plain Layout
565 \begin_layout Plain Layout
570 \begin_layout Plain Layout
575 \begin_layout Plain Layout
582 \begin_layout Plain Layout
589 \begin_layout Plain Layout
596 \begin_layout Plain Layout
600 crv{(-8,7) & (-3,5)};
603 \begin_layout Plain Layout
608 \begin_layout Plain Layout
613 \begin_layout Plain Layout
618 \begin_layout Plain Layout
622 crv{(3,-10) & (9,-10)};
625 \begin_layout Plain Layout
630 \begin_layout Plain Layout
635 \begin_layout Plain Layout
639 crv{(-3,-10) & (-9,-10)};
642 \begin_layout Plain Layout
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
679 \begin_layout Plain Layout
686 \begin_layout Plain Layout
690 crv{(13,-6) & (2,-8)};
693 \begin_layout Plain Layout
697 crv{(-13,-6) & (-2,-8)};
700 \begin_layout Plain Layout
717 \begin_layout Standard
721 \begin_layout Plain Layout
728 \begin_layout Plain Layout
732 bullet}="RU"+(1,3)*{x^{
737 \begin_layout Plain Layout
741 bullet}="RD"+(2.5,2)*{x^{
746 \begin_layout Plain Layout
750 bullet}="LU"+(-1,2)*{x};
753 \begin_layout Plain Layout
757 bullet}="LD"+(-1,2)*{x};
760 \begin_layout Plain Layout
764 crv{(4,2) & (4,-1)}; ?(.1)*
771 \begin_layout Plain Layout
775 crv{(-4,-2) & (-4,1)};
778 \begin_layout Plain Layout
787 \begin_layout Plain Layout
789 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
792 \begin_layout Plain Layout
796 crv{(7,-10) & (-7,-10)};
799 \begin_layout Plain Layout
803 bullet}="RDD"+(2.5,-1)*{x^{
808 \begin_layout Plain Layout
812 bullet}="LDD"+(-1,-3)*{x};
815 \begin_layout Plain Layout
819 bullet}="RUD"+(3.5,1)*{x^{
824 \begin_layout Plain Layout
831 \begin_layout Plain Layout
833 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
836 \begin_layout Plain Layout
843 \begin_layout Plain Layout
850 \begin_layout Plain Layout
857 \begin_layout Plain Layout
861 crv{(0,-17)}; ?(.57)*
866 \begin_layout Plain Layout
873 \begin_layout Plain Layout
880 \begin_layout Plain Layout
887 \begin_layout Plain Layout
891 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
896 \begin_layout Plain Layout
913 \begin_layout Description
917 \begin_layout Standard
920 \begin_layout Standard
924 \begin_layout Plain Layout
928 xy (-15,0)*{};(15,0)*{};
931 \begin_layout Plain Layout
938 \begin_layout Plain Layout
949 \begin_layout Plain Layout
951 (-10,12)*{}; (-10,-12)*{}; **
955 dir{<}+(-4,0)*{F(x)};
958 \begin_layout Plain Layout
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
987 crv{(-4,-21)&(5,-15)};
990 \begin_layout Plain Layout
999 \begin_layout Plain Layout
1006 \begin_layout Plain Layout
1012 widetilde{F(i_x)}} ;
1015 \begin_layout Plain Layout
1024 \begin_layout Plain Layout
1031 \begin_layout Plain Layout
1036 \begin_layout Plain Layout
1041 \begin_layout Plain Layout
1045 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1048 \begin_layout Plain Layout
1053 \begin_layout Plain Layout
1058 \begin_layout Plain Layout
1062 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1065 \begin_layout Plain Layout
1082 \begin_layout Description
1086 \begin_layout Standard
1087 \begin_inset Preview
1089 \begin_layout Standard
1093 \begin_layout Plain Layout
1100 \begin_layout Plain Layout
1109 \begin_layout Plain Layout
1116 \begin_layout Plain Layout
1125 \begin_layout Plain Layout
1134 \begin_layout Plain Layout
1149 \begin_layout Plain Layout
1164 \begin_inset Preview
1166 \begin_layout Standard
1170 \begin_layout Plain Layout
1177 \begin_layout Plain Layout
1184 \begin_layout Plain Layout
1191 \begin_layout Plain Layout
1195 ar@/^.9pc/ "1";"2"};
1198 \begin_layout Plain Layout
1202 ar@/_.9pc/ "1";"2"};
1205 \begin_layout Plain Layout
1212 \begin_layout Plain Layout
1219 \begin_layout Plain Layout
1223 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1226 \begin_layout Plain Layout
1230 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1233 \begin_layout Plain Layout
1237 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1240 \begin_layout Plain Layout
1247 \begin_layout Plain Layout
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
1293 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1296 \begin_layout Plain Layout
1300 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1303 \begin_layout Plain Layout
1320 \begin_layout Description
1324 \begin_layout Standard
1325 \begin_inset Preview
1327 \begin_layout Standard
1331 \begin_layout Plain Layout
1336 Natural transformation between functors.
1339 \begin_layout Plain Layout
1346 \begin_layout Plain Layout
1353 \begin_layout Plain Layout
1360 \begin_layout Plain Layout
1364 ar@/^.25pc/ "a";"b"};
1367 \begin_layout Plain Layout
1371 ar@/_.25pc/"a";"c"};
1374 \begin_layout Plain Layout
1378 ar@/_.15pc/ "b";"c"};
1381 \begin_layout Plain Layout
1386 \begin_layout Plain Layout
1393 \begin_layout Plain Layout
1400 \begin_layout Plain Layout
1407 \begin_layout Plain Layout
1411 ar@/^.25pc/ "ta";"tb"};
1414 \begin_layout Plain Layout
1418 ar@/_.25pc/ "ta";"tc"};
1421 \begin_layout Plain Layout
1425 ar@/_.15pc/ "tb";"tc"};
1428 \begin_layout Plain Layout
1433 \begin_layout Plain Layout
1440 \begin_layout Plain Layout
1447 \begin_layout Plain Layout
1454 \begin_layout Plain Layout
1458 ar@/^.25pc/@{.>} "ba";"bb"};
1461 \begin_layout Plain Layout
1465 ar@/_.25pc/ "ba";"bc"};
1468 \begin_layout Plain Layout
1472 ar@/_.15pc/ "bb";"bc"};
1475 \begin_layout Plain Layout
1480 \begin_layout Plain Layout
1484 ar@/_.15pc/ "ta";"ba"};
1487 \begin_layout Plain Layout
1491 ar@/_.15pc/ "tb";"bb"};
1494 \begin_layout Plain Layout
1498 ar@/_.15pc/ "tc";"bc"};
1501 \begin_layout Plain Layout
1503 %START ARROWS AND LABELS
1506 \begin_layout Plain Layout
1511 \begin_layout Plain Layout
1516 \begin_layout Plain Layout
1520 ar@/^.35pc/^F "DF";"CF"};
1523 \begin_layout Plain Layout
1528 \begin_layout Plain Layout
1533 \begin_layout Plain Layout
1537 ar@/_.35pc/_G "DF";"CF"};
1540 \begin_layout Plain Layout
1545 \begin_layout Plain Layout
1550 \begin_layout Plain Layout
1559 \begin_layout Plain Layout
1564 \begin_layout Plain Layout
1569 \begin_layout Plain Layout
1586 \begin_layout Section
1590 \begin_layout Standard
1591 \begin_inset Preview
1593 \begin_layout Standard
1597 \begin_layout Plain Layout
1601 textipa{Ekspl@"neIS@n}
1614 \begin_layout Section
1618 \begin_layout Standard
1619 \begin_inset Preview
1621 \begin_layout Standard
1625 \begin_layout Plain Layout
1629 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1640 \begin_inset Preview
1642 \begin_layout Standard
1646 \begin_layout Plain Layout
1669 \begin_layout Section
1671 \begin_inset CommandInset label
1680 \begin_layout Standard
1681 Some simple graphing examples.
1684 \begin_layout Subsection
1688 \begin_layout Standard
1689 \begin_inset Preview
1691 \begin_layout Standard
1695 \begin_layout Plain Layout
1699 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1702 \begin_layout Plain Layout
1706 psaxes{->}(0,0)(0,-3)(10,3)
1709 \begin_layout Plain Layout
1713 uput[-90](10,0){$x$}
1715 uput[0](0,3){$f(x)$}
1718 \begin_layout Plain Layout
1722 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1725 \begin_layout Plain Layout
1742 \begin_layout Subsection
1743 Inline data plotting
1746 \begin_layout Standard
1748 \begin_inset Preview
1750 \begin_layout Standard
1755 \begin_layout Plain Layout
1759 begin{pspicture*}(-1.5,-1.5)(11,5)
1762 \begin_layout Plain Layout
1766 psaxes{->}(0,0)(0,0)(10,5)
1769 \begin_layout Plain Layout
1773 psset{linewidth=2.5pt}
1776 \begin_layout Plain Layout
1780 rput(5.0,-1.0){Speed [MPH]}
1783 \begin_layout Plain Layout
1789 begin{rotate}{90}Cost [Dollars]
1794 \begin_layout Plain Layout
1800 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1803 \begin_layout Plain Layout
1807 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1812 \begin_layout Plain Layout
1829 \begin_layout Subsection
1833 \begin_layout Standard
1834 \begin_inset Preview
1836 \begin_layout Standard
1840 \begin_layout Plain Layout
1844 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1847 \begin_layout Plain Layout
1851 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1855 \begin_layout Plain Layout
1870 \begin_inset space \hfill{}
1874 \begin_inset Preview
1876 \begin_layout Standard
1880 \begin_layout Plain Layout
1884 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1887 \begin_layout Plain Layout
1891 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1892 mul cos 100 t mul sin}
1895 \begin_layout Plain Layout
1910 \begin_inset space \hfill{}
1914 \begin_inset Preview
1916 \begin_layout Standard
1920 \begin_layout Plain Layout
1924 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1927 \begin_layout Plain Layout
1931 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1932 mul cos 200 t mul sin}
1935 \begin_layout Plain Layout
1950 \begin_inset space \hfill{}
1954 \begin_inset Preview
1956 \begin_layout Standard
1960 \begin_layout Plain Layout
1964 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1967 \begin_layout Plain Layout
1971 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1972 mul cos 200 t mul sin}
1975 \begin_layout Plain Layout
1992 \begin_layout Section
1996 \begin_layout Standard
1997 \begin_inset Flex URL
2000 \begin_layout Plain Layout
2002 http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
2010 \begin_layout Standard
2011 \begin_inset Preview
2013 \begin_layout Standard
2017 \begin_layout Plain Layout
2023 iangle{35} % Angle of the inclined plane
2026 \begin_layout Plain Layout
2035 \begin_layout Plain Layout
2041 arcr{0.5cm} % Radius of the arc used to indicate angles
2044 \begin_layout Plain Layout
2048 \begin_layout Plain Layout
2055 \begin_layout Plain Layout
2057 force/.style={>=latex,draw=blue,fill=blue},
2060 \begin_layout Plain Layout
2062 axis/.style={densely dashed,gray,font=
2067 \begin_layout Plain Layout
2069 M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2072 \begin_layout Plain Layout
2074 m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2077 \begin_layout Plain Layout
2079 plane/.style={draw=black,fill=blue!10},
2082 \begin_layout Plain Layout
2084 string/.style={draw=red, thick},
2087 \begin_layout Plain Layout
2089 pulley/.style={thick},
2092 \begin_layout Plain Layout
2097 \begin_layout Plain Layout
2101 \begin_layout Plain Layout
2105 matrix[column sep=1cm] {
2108 \begin_layout Plain Layout
2113 \begin_layout Plain Layout
2117 draw[plane] (0,-1) coordinate (base)
2120 \begin_layout Plain Layout
2122 -- coordinate[pos=0.5] (mid) ++(
2124 iangle:3) coordinate (top)
2127 \begin_layout Plain Layout
2132 \begin_layout Plain Layout
2136 path (mid) node[M,rotate=
2138 iangle,yshift=0.25cm] (M) {};
2141 \begin_layout Plain Layout
2145 draw[pulley] (top) -- ++(
2147 iangle:0.25) circle (0.25cm)
2150 \begin_layout Plain Layout
2154 iangle:0.5) coordinate (pulley);
2157 \begin_layout Plain Layout
2161 draw[string] (M.east) -- ++(
2163 iangle:1.5cm) arc (90+
2168 \begin_layout Plain Layout
2170 -- ++(0,-1) node[m] {};
2173 \begin_layout Plain Layout
2177 \begin_layout Plain Layout
2190 \begin_layout Plain Layout
2203 \begin_layout Plain Layout
2208 \begin_layout Plain Layout
2212 \begin_layout Plain Layout
2217 \begin_layout Plain Layout
2219 %% Free body diagram of M
2222 \begin_layout Plain Layout
2226 begin{scope}[rotate=
2231 \begin_layout Plain Layout
2235 node[M,transform shape] (M) {};
2238 \begin_layout Plain Layout
2240 % Draw axes and help lines
2243 \begin_layout Plain Layout
2247 \begin_layout Plain Layout
2252 \begin_layout Plain Layout
2256 draw (0,-1) -- (0,2) node[right] {$+y$};
2259 \begin_layout Plain Layout
2263 draw (M) -- ++(2,0) node[right] {$+x$};
2266 \begin_layout Plain Layout
2269 The code is a bit awkward.
2272 \begin_layout Plain Layout
2276 \begin_layout Plain Layout
2280 draw[solid,shorten >=0.5pt] (
2289 \begin_layout Plain Layout
2302 \begin_layout Plain Layout
2317 \begin_layout Plain Layout
2322 \begin_layout Plain Layout
2326 \begin_layout Plain Layout
2331 \begin_layout Plain Layout
2336 \begin_layout Plain Layout
2338 % Assuming that Mg = 1.
2339 The normal force will therefore be cos(alpha)
2342 \begin_layout Plain Layout
2346 draw (M.center) -- ++(0,{cos(
2348 iangle)}) node[above right] {$N$};
2351 \begin_layout Plain Layout
2355 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2358 \begin_layout Plain Layout
2362 draw (M.east) -- ++(1,0) node[above] {$T$};
2365 \begin_layout Plain Layout
2370 \begin_layout Plain Layout
2374 \begin_layout Plain Layout
2381 \begin_layout Plain Layout
2383 % Draw gravity force.
2384 The code is put outside the rotated
2387 \begin_layout Plain Layout
2389 % scope for simplicity.
2390 No need to do any angle calculations.
2394 \begin_layout Plain Layout
2398 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2401 \begin_layout Plain Layout
2406 \begin_layout Plain Layout
2410 \begin_layout Plain Layout
2415 \begin_layout Plain Layout
2420 \begin_layout Plain Layout
2422 % Free body diagram of m
2425 \begin_layout Plain Layout
2432 \begin_layout Plain Layout
2436 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2439 \begin_layout Plain Layout
2444 \begin_layout Plain Layout
2448 draw (m.north) -- ++(0,1) node[above] {$T'$};
2451 \begin_layout Plain Layout
2455 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2458 \begin_layout Plain Layout
2463 \begin_layout Plain Layout
2467 \begin_layout Plain Layout
2476 \begin_layout Plain Layout
2481 \begin_layout Plain Layout
2488 \begin_layout Plain Layout