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
79 \paperpagestyle default
80 \tracking_changes false
93 \begin_layout Standard
94 In order to properly typeset the document and have instant preview working,
95 the following packages have to be installed:
98 \begin_layout LyX-Code
99 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf, etex
102 \begin_layout Standard
103 Due to the use of postscript specials in Section
104 \begin_inset CommandInset ref
106 reference "sec:PSTricks"
110 , only the Postscript or PDF (ps2pdf) output formats will correctly render
112 However, the PDF (Xe\SpecialChar TeX
113 ) output seems to also work, while trying to typeset
122 will generate errors.
125 \begin_layout Section
129 \begin_layout Standard
130 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
132 \begin_inset Flex URL
135 \begin_layout Plain Layout
137 https://www.ctan.org/tex-archive/macros/generic/diagrams/xypic/doc/xyguide.pdf
145 \begin_layout Description
149 \begin_layout Standard
152 \begin_layout Standard
156 \begin_layout Plain Layout
163 \begin_layout Plain Layout
165 (5,10)*{}; (-10,-10)*{} **
170 \begin_layout Plain Layout
187 \begin_layout Plain Layout
189 "y"+(0,-1); (2,-10)*{} **
198 \begin_layout Plain Layout
205 \begin_layout Plain Layout
212 \begin_layout Plain Layout
219 \begin_layout Plain Layout
226 \begin_layout Plain Layout
243 \begin_layout Description
247 \begin_layout Standard
250 \begin_layout Standard
254 \begin_layout Plain Layout
261 \begin_layout Plain Layout
266 \begin_layout Plain Layout
271 \begin_layout Plain Layout
275 crv{~*=<.5pt>{.} (0,30)}?(.75)*
280 \begin_layout Plain Layout
285 \begin_layout Plain Layout
290 \begin_layout Plain Layout
294 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
299 \begin_layout Plain Layout
304 \begin_layout Plain Layout
309 \begin_layout Plain Layout
313 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
318 \begin_layout Plain Layout
323 \begin_layout Plain Layout
328 \begin_layout Plain Layout
332 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
337 \begin_layout Plain Layout
342 \begin_layout Plain Layout
347 \begin_layout Plain Layout
351 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
356 \begin_layout Plain Layout
373 \begin_layout Description
377 \begin_layout Standard
380 \begin_layout Standard
384 \begin_layout Plain Layout
391 \begin_layout Plain Layout
400 \begin_layout Plain Layout
407 \begin_layout Plain Layout
414 \begin_layout Plain Layout
421 \begin_layout Plain Layout
438 \begin_layout Description
442 \begin_layout Standard
445 \begin_layout Standard
449 \begin_layout Plain Layout
456 \begin_layout Plain Layout
463 \begin_layout Plain Layout
467 ellipse(3,1)__,=:a(-180){-};
470 \begin_layout Plain Layout
477 \begin_layout Plain Layout
484 \begin_layout Plain Layout
491 \begin_layout Plain Layout
495 ellipse(3,1)__,=:a(-180){-};
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
519 \begin_layout Plain Layout
526 \begin_layout Plain Layout
531 \begin_layout Plain Layout
536 \begin_layout Plain Layout
541 \begin_layout Plain Layout
546 \begin_layout Plain Layout
553 \begin_layout Plain Layout
558 \begin_layout Plain Layout
563 \begin_layout Plain Layout
568 \begin_layout Plain Layout
573 \begin_layout Plain Layout
580 \begin_layout Plain Layout
587 \begin_layout Plain Layout
594 \begin_layout Plain Layout
598 crv{(-8,7) & (-3,5)};
601 \begin_layout Plain Layout
606 \begin_layout Plain Layout
611 \begin_layout Plain Layout
616 \begin_layout Plain Layout
620 crv{(3,-10) & (9,-10)};
623 \begin_layout Plain Layout
628 \begin_layout Plain Layout
633 \begin_layout Plain Layout
637 crv{(-3,-10) & (-9,-10)};
640 \begin_layout Plain Layout
645 \begin_layout Plain Layout
650 \begin_layout Plain Layout
655 \begin_layout Plain Layout
660 \begin_layout Plain Layout
665 \begin_layout Plain Layout
670 \begin_layout Plain Layout
677 \begin_layout Plain Layout
684 \begin_layout Plain Layout
688 crv{(13,-6) & (2,-8)};
691 \begin_layout Plain Layout
695 crv{(-13,-6) & (-2,-8)};
698 \begin_layout Plain Layout
715 \begin_layout Standard
719 \begin_layout Plain Layout
726 \begin_layout Plain Layout
730 bullet}="RU"+(1,3)*{x^{
735 \begin_layout Plain Layout
739 bullet}="RD"+(2.5,2)*{x^{
744 \begin_layout Plain Layout
748 bullet}="LU"+(-1,2)*{x};
751 \begin_layout Plain Layout
755 bullet}="LD"+(-1,2)*{x};
758 \begin_layout Plain Layout
762 crv{(4,2) & (4,-1)}; ?(.1)*
769 \begin_layout Plain Layout
773 crv{(-4,-2) & (-4,1)};
776 \begin_layout Plain Layout
785 \begin_layout Plain Layout
787 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
790 \begin_layout Plain Layout
794 crv{(7,-10) & (-7,-10)};
797 \begin_layout Plain Layout
801 bullet}="RDD"+(2.5,-1)*{x^{
806 \begin_layout Plain Layout
810 bullet}="LDD"+(-1,-3)*{x};
813 \begin_layout Plain Layout
817 bullet}="RUD"+(3.5,1)*{x^{
822 \begin_layout Plain Layout
829 \begin_layout Plain Layout
831 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
834 \begin_layout Plain Layout
841 \begin_layout Plain Layout
848 \begin_layout Plain Layout
855 \begin_layout Plain Layout
859 crv{(0,-17)}; ?(.57)*
864 \begin_layout Plain Layout
871 \begin_layout Plain Layout
878 \begin_layout Plain Layout
885 \begin_layout Plain Layout
889 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
894 \begin_layout Plain Layout
911 \begin_layout Description
915 \begin_layout Standard
918 \begin_layout Standard
922 \begin_layout Plain Layout
926 xy (-15,0)*{};(15,0)*{};
929 \begin_layout Plain Layout
936 \begin_layout Plain Layout
947 \begin_layout Plain Layout
949 (-10,12)*{}; (-10,-12)*{}; **
953 dir{<}+(-4,0)*{F(x)};
956 \begin_layout Plain Layout
961 \begin_layout Plain Layout
966 \begin_layout Plain Layout
971 \begin_layout Plain Layout
976 \begin_layout Plain Layout
981 \begin_layout Plain Layout
985 crv{(-4,-21)&(5,-15)};
988 \begin_layout Plain Layout
997 \begin_layout Plain Layout
1004 \begin_layout Plain Layout
1010 widetilde{F(i_x)}} ;
1013 \begin_layout Plain Layout
1022 \begin_layout Plain Layout
1029 \begin_layout Plain Layout
1034 \begin_layout Plain Layout
1039 \begin_layout Plain Layout
1043 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1046 \begin_layout Plain Layout
1051 \begin_layout Plain Layout
1056 \begin_layout Plain Layout
1060 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1063 \begin_layout Plain Layout
1080 \begin_layout Description
1084 \begin_layout Standard
1085 \begin_inset Preview
1087 \begin_layout Standard
1091 \begin_layout Plain Layout
1098 \begin_layout Plain Layout
1107 \begin_layout Plain Layout
1114 \begin_layout Plain Layout
1123 \begin_layout Plain Layout
1132 \begin_layout Plain Layout
1147 \begin_layout Plain Layout
1162 \begin_inset Preview
1164 \begin_layout Standard
1168 \begin_layout Plain Layout
1175 \begin_layout Plain Layout
1182 \begin_layout Plain Layout
1189 \begin_layout Plain Layout
1193 ar@/^.9pc/ "1";"2"};
1196 \begin_layout Plain Layout
1200 ar@/_.9pc/ "1";"2"};
1203 \begin_layout Plain Layout
1210 \begin_layout Plain Layout
1217 \begin_layout Plain Layout
1221 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1224 \begin_layout Plain Layout
1228 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1231 \begin_layout Plain Layout
1235 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1238 \begin_layout Plain Layout
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
1291 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1294 \begin_layout Plain Layout
1298 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1301 \begin_layout Plain Layout
1318 \begin_layout Description
1322 \begin_layout Standard
1323 \begin_inset Preview
1325 \begin_layout Standard
1329 \begin_layout Plain Layout
1334 Natural transformation between functors.
1337 \begin_layout Plain Layout
1344 \begin_layout Plain Layout
1351 \begin_layout Plain Layout
1358 \begin_layout Plain Layout
1362 ar@/^.25pc/ "a";"b"};
1365 \begin_layout Plain Layout
1369 ar@/_.25pc/"a";"c"};
1372 \begin_layout Plain Layout
1376 ar@/_.15pc/ "b";"c"};
1379 \begin_layout Plain Layout
1384 \begin_layout Plain Layout
1391 \begin_layout Plain Layout
1398 \begin_layout Plain Layout
1405 \begin_layout Plain Layout
1409 ar@/^.25pc/ "ta";"tb"};
1412 \begin_layout Plain Layout
1416 ar@/_.25pc/ "ta";"tc"};
1419 \begin_layout Plain Layout
1423 ar@/_.15pc/ "tb";"tc"};
1426 \begin_layout Plain Layout
1431 \begin_layout Plain Layout
1438 \begin_layout Plain Layout
1445 \begin_layout Plain Layout
1452 \begin_layout Plain Layout
1456 ar@/^.25pc/@{.>} "ba";"bb"};
1459 \begin_layout Plain Layout
1463 ar@/_.25pc/ "ba";"bc"};
1466 \begin_layout Plain Layout
1470 ar@/_.15pc/ "bb";"bc"};
1473 \begin_layout Plain Layout
1478 \begin_layout Plain Layout
1482 ar@/_.15pc/ "ta";"ba"};
1485 \begin_layout Plain Layout
1489 ar@/_.15pc/ "tb";"bb"};
1492 \begin_layout Plain Layout
1496 ar@/_.15pc/ "tc";"bc"};
1499 \begin_layout Plain Layout
1501 %START ARROWS AND LABELS
1504 \begin_layout Plain Layout
1509 \begin_layout Plain Layout
1514 \begin_layout Plain Layout
1518 ar@/^.35pc/^F "DF";"CF"};
1521 \begin_layout Plain Layout
1526 \begin_layout Plain Layout
1531 \begin_layout Plain Layout
1535 ar@/_.35pc/_G "DF";"CF"};
1538 \begin_layout Plain Layout
1543 \begin_layout Plain Layout
1548 \begin_layout Plain Layout
1557 \begin_layout Plain Layout
1562 \begin_layout Plain Layout
1567 \begin_layout Plain Layout
1584 \begin_layout Section
1588 \begin_layout Standard
1589 \begin_inset Preview
1591 \begin_layout Standard
1595 \begin_layout Plain Layout
1599 textipa{Ekspl@"neIS@n}
1612 \begin_layout Section
1616 \begin_layout Standard
1617 \begin_inset Preview
1619 \begin_layout Standard
1623 \begin_layout Plain Layout
1627 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1638 \begin_inset Preview
1640 \begin_layout Standard
1644 \begin_layout Plain Layout
1667 \begin_layout Section
1669 \begin_inset CommandInset label
1678 \begin_layout Standard
1679 Some simple graphing examples.
1682 \begin_layout Subsection
1686 \begin_layout Standard
1687 \begin_inset Preview
1689 \begin_layout Standard
1693 \begin_layout Plain Layout
1697 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1700 \begin_layout Plain Layout
1704 psaxes{->}(0,0)(0,-3)(10,3)
1707 \begin_layout Plain Layout
1711 uput[-90](10,0){$x$}
1713 uput[0](0,3){$f(x)$}
1716 \begin_layout Plain Layout
1720 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1723 \begin_layout Plain Layout
1740 \begin_layout Subsection
1741 Inline data plotting
1744 \begin_layout Standard
1746 \begin_inset Preview
1748 \begin_layout Standard
1753 \begin_layout Plain Layout
1757 begin{pspicture*}(-1.5,-1.5)(11,5)
1760 \begin_layout Plain Layout
1764 psaxes{->}(0,0)(0,0)(10,5)
1767 \begin_layout Plain Layout
1771 psset{linewidth=2.5pt}
1774 \begin_layout Plain Layout
1778 rput(5.0,-1.0){Speed [MPH]}
1781 \begin_layout Plain Layout
1787 begin{rotate}{90}Cost [Dollars]
1792 \begin_layout Plain Layout
1798 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1801 \begin_layout Plain Layout
1805 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1810 \begin_layout Plain Layout
1827 \begin_layout Subsection
1831 \begin_layout Standard
1832 \begin_inset Preview
1834 \begin_layout Standard
1838 \begin_layout Plain Layout
1842 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1845 \begin_layout Plain Layout
1849 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1853 \begin_layout Plain Layout
1868 \begin_inset space \hfill{}
1872 \begin_inset Preview
1874 \begin_layout Standard
1878 \begin_layout Plain Layout
1882 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1885 \begin_layout Plain Layout
1889 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1890 mul cos 100 t mul sin}
1893 \begin_layout Plain Layout
1908 \begin_inset space \hfill{}
1912 \begin_inset Preview
1914 \begin_layout Standard
1918 \begin_layout Plain Layout
1922 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1925 \begin_layout Plain Layout
1929 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1930 mul cos 200 t mul sin}
1933 \begin_layout Plain Layout
1948 \begin_inset space \hfill{}
1952 \begin_inset Preview
1954 \begin_layout Standard
1958 \begin_layout Plain Layout
1962 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1965 \begin_layout Plain Layout
1969 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1970 mul cos 200 t mul sin}
1973 \begin_layout Plain Layout
1990 \begin_layout Section
1994 \begin_layout Standard
1995 \begin_inset Flex URL
1998 \begin_layout Plain Layout
2000 http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
2008 \begin_layout Standard
2009 \begin_inset Preview
2011 \begin_layout Standard
2015 \begin_layout Plain Layout
2021 iangle{35} % Angle of the inclined plane
2024 \begin_layout Plain Layout
2033 \begin_layout Plain Layout
2039 arcr{0.5cm} % Radius of the arc used to indicate angles
2042 \begin_layout Plain Layout
2046 \begin_layout Plain Layout
2053 \begin_layout Plain Layout
2055 force/.style={>=latex,draw=blue,fill=blue},
2058 \begin_layout Plain Layout
2060 axis/.style={densely dashed,gray,font=
2065 \begin_layout Plain Layout
2067 M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2070 \begin_layout Plain Layout
2072 m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2075 \begin_layout Plain Layout
2077 plane/.style={draw=black,fill=blue!10},
2080 \begin_layout Plain Layout
2082 string/.style={draw=red, thick},
2085 \begin_layout Plain Layout
2087 pulley/.style={thick},
2090 \begin_layout Plain Layout
2095 \begin_layout Plain Layout
2099 \begin_layout Plain Layout
2103 matrix[column sep=1cm] {
2106 \begin_layout Plain Layout
2111 \begin_layout Plain Layout
2115 draw[plane] (0,-1) coordinate (base)
2118 \begin_layout Plain Layout
2120 -- coordinate[pos=0.5] (mid) ++(
2122 iangle:3) coordinate (top)
2125 \begin_layout Plain Layout
2130 \begin_layout Plain Layout
2134 path (mid) node[M,rotate=
2136 iangle,yshift=0.25cm] (M) {};
2139 \begin_layout Plain Layout
2143 draw[pulley] (top) -- ++(
2145 iangle:0.25) circle (0.25cm)
2148 \begin_layout Plain Layout
2152 iangle:0.5) coordinate (pulley);
2155 \begin_layout Plain Layout
2159 draw[string] (M.east) -- ++(
2161 iangle:1.5cm) arc (90+
2166 \begin_layout Plain Layout
2168 -- ++(0,-1) node[m] {};
2171 \begin_layout Plain Layout
2175 \begin_layout Plain Layout
2188 \begin_layout Plain Layout
2201 \begin_layout Plain Layout
2206 \begin_layout Plain Layout
2210 \begin_layout Plain Layout
2215 \begin_layout Plain Layout
2217 %% Free body diagram of M
2220 \begin_layout Plain Layout
2224 begin{scope}[rotate=
2229 \begin_layout Plain Layout
2233 node[M,transform shape] (M) {};
2236 \begin_layout Plain Layout
2238 % Draw axes and help lines
2241 \begin_layout Plain Layout
2245 \begin_layout Plain Layout
2250 \begin_layout Plain Layout
2254 draw (0,-1) -- (0,2) node[right] {$+y$};
2257 \begin_layout Plain Layout
2261 draw (M) -- ++(2,0) node[right] {$+x$};
2264 \begin_layout Plain Layout
2267 The code is a bit awkward.
2270 \begin_layout Plain Layout
2274 \begin_layout Plain Layout
2278 draw[solid,shorten >=0.5pt] (
2287 \begin_layout Plain Layout
2300 \begin_layout Plain Layout
2315 \begin_layout Plain Layout
2320 \begin_layout Plain Layout
2324 \begin_layout Plain Layout
2329 \begin_layout Plain Layout
2334 \begin_layout Plain Layout
2336 % Assuming that Mg = 1.
2337 The normal force will therefore be cos(alpha)
2340 \begin_layout Plain Layout
2344 draw (M.center) -- ++(0,{cos(
2346 iangle)}) node[above right] {$N$};
2349 \begin_layout Plain Layout
2353 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2356 \begin_layout Plain Layout
2360 draw (M.east) -- ++(1,0) node[above] {$T$};
2363 \begin_layout Plain Layout
2368 \begin_layout Plain Layout
2372 \begin_layout Plain Layout
2379 \begin_layout Plain Layout
2381 % Draw gravity force.
2382 The code is put outside the rotated
2385 \begin_layout Plain Layout
2387 % scope for simplicity.
2388 No need to do any angle calculations.
2392 \begin_layout Plain Layout
2396 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2399 \begin_layout Plain Layout
2404 \begin_layout Plain Layout
2408 \begin_layout Plain Layout
2413 \begin_layout Plain Layout
2418 \begin_layout Plain Layout
2420 % Free body diagram of m
2423 \begin_layout Plain Layout
2430 \begin_layout Plain Layout
2434 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2437 \begin_layout Plain Layout
2442 \begin_layout Plain Layout
2446 draw (m.north) -- ++(0,1) node[above] {$T'$};
2449 \begin_layout Plain Layout
2453 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2456 \begin_layout Plain Layout
2461 \begin_layout Plain Layout
2465 \begin_layout Plain Layout
2474 \begin_layout Plain Layout
2479 \begin_layout Plain Layout
2486 \begin_layout Plain Layout