1 #LyX 2.2 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 \default_output_format pdf
39 \bibtex_command default
40 \index_command default
41 \paperfontsize default
46 \use_package amsmath 1
47 \use_package amssymb 1
50 \use_package mathdots 1
51 \use_package mathtools 0
53 \use_package stackrel 0
54 \use_package stmaryrd 0
55 \use_package undertilde 0
57 \cite_engine_type default
61 \paperorientation portrait
71 \paragraph_separation indent
72 \paragraph_indentation default
73 \quotes_language english
76 \paperpagestyle default
77 \tracking_changes false
90 \begin_layout Standard
91 In order to properly typeset the document and have instant preview working,
92 the following packages have to be installed:
95 \begin_layout LyX-Code
96 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf, etex
99 \begin_layout Standard
100 Due to the use of postscript specials in Section
101 \begin_inset CommandInset ref
103 reference "sec:PSTricks"
107 , only the Postscript or PDF (ps2pdf) output formats will correctly render
109 However, the PDF (Xe\SpecialChar TeX
110 ) output seems to also work, while trying to typeset
119 will generate errors.
122 \begin_layout Section
126 \begin_layout Standard
127 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
129 \begin_inset Flex URL
132 \begin_layout Plain Layout
134 https://www.ctan.org/tex-archive/macros/generic/diagrams/xypic/doc/xyguide.pdf
142 \begin_layout Description
146 \begin_layout Standard
149 \begin_layout Standard
153 \begin_layout Plain Layout
160 \begin_layout Plain Layout
162 (5,10)*{}; (-10,-10)*{} **
167 \begin_layout Plain Layout
184 \begin_layout Plain Layout
186 "y"+(0,-1); (2,-10)*{} **
195 \begin_layout Plain Layout
202 \begin_layout Plain Layout
209 \begin_layout Plain Layout
216 \begin_layout Plain Layout
223 \begin_layout Plain Layout
240 \begin_layout Description
244 \begin_layout Standard
247 \begin_layout Standard
251 \begin_layout Plain Layout
258 \begin_layout Plain Layout
263 \begin_layout Plain Layout
268 \begin_layout Plain Layout
272 crv{~*=<.5pt>{.} (0,30)}?(.75)*
277 \begin_layout Plain Layout
282 \begin_layout Plain Layout
287 \begin_layout Plain Layout
291 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
296 \begin_layout Plain Layout
301 \begin_layout Plain Layout
306 \begin_layout Plain Layout
310 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.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>{.} (28.5,9.3)}?(.93)*
353 \begin_layout Plain Layout
370 \begin_layout Description
374 \begin_layout Standard
377 \begin_layout Standard
381 \begin_layout Plain Layout
388 \begin_layout Plain Layout
397 \begin_layout Plain Layout
404 \begin_layout Plain Layout
411 \begin_layout Plain Layout
418 \begin_layout Plain Layout
435 \begin_layout Description
439 \begin_layout Standard
442 \begin_layout Standard
446 \begin_layout Plain Layout
453 \begin_layout Plain Layout
460 \begin_layout Plain Layout
464 ellipse(3,1)__,=:a(-180){-};
467 \begin_layout Plain Layout
474 \begin_layout Plain Layout
481 \begin_layout Plain Layout
488 \begin_layout Plain Layout
492 ellipse(3,1)__,=:a(-180){-};
495 \begin_layout Plain Layout
499 ellipse(3,1)__,=:a(-180){-};
502 \begin_layout Plain Layout
506 ellipse(3,1)__,=:a(180){-};
509 \begin_layout Plain Layout
516 \begin_layout Plain Layout
523 \begin_layout Plain Layout
528 \begin_layout Plain Layout
533 \begin_layout Plain Layout
538 \begin_layout Plain Layout
543 \begin_layout Plain Layout
550 \begin_layout Plain Layout
555 \begin_layout Plain Layout
560 \begin_layout Plain Layout
565 \begin_layout Plain Layout
570 \begin_layout Plain Layout
577 \begin_layout Plain Layout
584 \begin_layout Plain Layout
591 \begin_layout Plain Layout
595 crv{(-8,7) & (-3,5)};
598 \begin_layout Plain Layout
603 \begin_layout Plain Layout
608 \begin_layout Plain Layout
613 \begin_layout Plain Layout
617 crv{(3,-10) & (9,-10)};
620 \begin_layout Plain Layout
625 \begin_layout Plain Layout
630 \begin_layout Plain Layout
634 crv{(-3,-10) & (-9,-10)};
637 \begin_layout Plain Layout
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
674 \begin_layout Plain Layout
681 \begin_layout Plain Layout
685 crv{(13,-6) & (2,-8)};
688 \begin_layout Plain Layout
692 crv{(-13,-6) & (-2,-8)};
695 \begin_layout Plain Layout
712 \begin_layout Standard
716 \begin_layout Plain Layout
723 \begin_layout Plain Layout
727 bullet}="RU"+(1,3)*{x^{
732 \begin_layout Plain Layout
736 bullet}="RD"+(2.5,2)*{x^{
741 \begin_layout Plain Layout
745 bullet}="LU"+(-1,2)*{x};
748 \begin_layout Plain Layout
752 bullet}="LD"+(-1,2)*{x};
755 \begin_layout Plain Layout
759 crv{(4,2) & (4,-1)}; ?(.1)*
766 \begin_layout Plain Layout
770 crv{(-4,-2) & (-4,1)};
773 \begin_layout Plain Layout
782 \begin_layout Plain Layout
784 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
787 \begin_layout Plain Layout
791 crv{(7,-10) & (-7,-10)};
794 \begin_layout Plain Layout
798 bullet}="RDD"+(2.5,-1)*{x^{
803 \begin_layout Plain Layout
807 bullet}="LDD"+(-1,-3)*{x};
810 \begin_layout Plain Layout
814 bullet}="RUD"+(3.5,1)*{x^{
819 \begin_layout Plain Layout
826 \begin_layout Plain Layout
828 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
831 \begin_layout Plain Layout
838 \begin_layout Plain Layout
845 \begin_layout Plain Layout
852 \begin_layout Plain Layout
856 crv{(0,-17)}; ?(.57)*
861 \begin_layout Plain Layout
868 \begin_layout Plain Layout
875 \begin_layout Plain Layout
882 \begin_layout Plain Layout
886 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
891 \begin_layout Plain Layout
908 \begin_layout Description
912 \begin_layout Standard
915 \begin_layout Standard
919 \begin_layout Plain Layout
923 xy (-15,0)*{};(15,0)*{};
926 \begin_layout Plain Layout
933 \begin_layout Plain Layout
944 \begin_layout Plain Layout
946 (-10,12)*{}; (-10,-12)*{}; **
950 dir{<}+(-4,0)*{F(x)};
953 \begin_layout Plain Layout
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
982 crv{(-4,-21)&(5,-15)};
985 \begin_layout Plain Layout
994 \begin_layout Plain Layout
1001 \begin_layout Plain Layout
1007 widetilde{F(i_x)}} ;
1010 \begin_layout Plain Layout
1019 \begin_layout Plain Layout
1026 \begin_layout Plain Layout
1031 \begin_layout Plain Layout
1036 \begin_layout Plain Layout
1040 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1043 \begin_layout Plain Layout
1048 \begin_layout Plain Layout
1053 \begin_layout Plain Layout
1057 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1060 \begin_layout Plain Layout
1077 \begin_layout Description
1081 \begin_layout Standard
1082 \begin_inset Preview
1084 \begin_layout Standard
1088 \begin_layout Plain Layout
1095 \begin_layout Plain Layout
1104 \begin_layout Plain Layout
1111 \begin_layout Plain Layout
1120 \begin_layout Plain Layout
1129 \begin_layout Plain Layout
1144 \begin_layout Plain Layout
1159 \begin_inset Preview
1161 \begin_layout Standard
1165 \begin_layout Plain Layout
1172 \begin_layout Plain Layout
1179 \begin_layout Plain Layout
1186 \begin_layout Plain Layout
1190 ar@/^.9pc/ "1";"2"};
1193 \begin_layout Plain Layout
1197 ar@/_.9pc/ "1";"2"};
1200 \begin_layout Plain Layout
1207 \begin_layout Plain Layout
1214 \begin_layout Plain Layout
1218 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1221 \begin_layout Plain Layout
1225 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1228 \begin_layout Plain Layout
1232 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1235 \begin_layout Plain Layout
1242 \begin_layout Plain Layout
1249 \begin_layout Plain Layout
1256 \begin_layout Plain Layout
1263 \begin_layout Plain Layout
1270 \begin_layout Plain Layout
1277 \begin_layout Plain Layout
1284 \begin_layout Plain Layout
1288 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1291 \begin_layout Plain Layout
1295 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1298 \begin_layout Plain Layout
1315 \begin_layout Description
1319 \begin_layout Standard
1320 \begin_inset Preview
1322 \begin_layout Standard
1326 \begin_layout Plain Layout
1331 Natural transformation between functors.
1334 \begin_layout Plain Layout
1341 \begin_layout Plain Layout
1348 \begin_layout Plain Layout
1355 \begin_layout Plain Layout
1359 ar@/^.25pc/ "a";"b"};
1362 \begin_layout Plain Layout
1366 ar@/_.25pc/"a";"c"};
1369 \begin_layout Plain Layout
1373 ar@/_.15pc/ "b";"c"};
1376 \begin_layout Plain Layout
1381 \begin_layout Plain Layout
1388 \begin_layout Plain Layout
1395 \begin_layout Plain Layout
1402 \begin_layout Plain Layout
1406 ar@/^.25pc/ "ta";"tb"};
1409 \begin_layout Plain Layout
1413 ar@/_.25pc/ "ta";"tc"};
1416 \begin_layout Plain Layout
1420 ar@/_.15pc/ "tb";"tc"};
1423 \begin_layout Plain Layout
1428 \begin_layout Plain Layout
1435 \begin_layout Plain Layout
1442 \begin_layout Plain Layout
1449 \begin_layout Plain Layout
1453 ar@/^.25pc/@{.>} "ba";"bb"};
1456 \begin_layout Plain Layout
1460 ar@/_.25pc/ "ba";"bc"};
1463 \begin_layout Plain Layout
1467 ar@/_.15pc/ "bb";"bc"};
1470 \begin_layout Plain Layout
1475 \begin_layout Plain Layout
1479 ar@/_.15pc/ "ta";"ba"};
1482 \begin_layout Plain Layout
1486 ar@/_.15pc/ "tb";"bb"};
1489 \begin_layout Plain Layout
1493 ar@/_.15pc/ "tc";"bc"};
1496 \begin_layout Plain Layout
1498 %START ARROWS AND LABELS
1501 \begin_layout Plain Layout
1506 \begin_layout Plain Layout
1511 \begin_layout Plain Layout
1515 ar@/^.35pc/^F "DF";"CF"};
1518 \begin_layout Plain Layout
1523 \begin_layout Plain Layout
1528 \begin_layout Plain Layout
1532 ar@/_.35pc/_G "DF";"CF"};
1535 \begin_layout Plain Layout
1540 \begin_layout Plain Layout
1545 \begin_layout Plain Layout
1554 \begin_layout Plain Layout
1559 \begin_layout Plain Layout
1564 \begin_layout Plain Layout
1581 \begin_layout Section
1585 \begin_layout Standard
1586 \begin_inset Preview
1588 \begin_layout Standard
1592 \begin_layout Plain Layout
1596 textipa{Ekspl@"neIS@n}
1609 \begin_layout Section
1613 \begin_layout Standard
1614 \begin_inset Preview
1616 \begin_layout Standard
1620 \begin_layout Plain Layout
1624 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1635 \begin_inset Preview
1637 \begin_layout Standard
1641 \begin_layout Plain Layout
1664 \begin_layout Section
1666 \begin_inset CommandInset label
1675 \begin_layout Standard
1676 Some simple graphing examples.
1679 \begin_layout Subsection
1683 \begin_layout Standard
1684 \begin_inset Preview
1686 \begin_layout Standard
1690 \begin_layout Plain Layout
1694 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1697 \begin_layout Plain Layout
1701 psaxes{->}(0,0)(0,-3)(10,3)
1704 \begin_layout Plain Layout
1708 uput[-90](10,0){$x$}
1710 uput[0](0,3){$f(x)$}
1713 \begin_layout Plain Layout
1717 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1720 \begin_layout Plain Layout
1737 \begin_layout Subsection
1738 Inline data plotting
1741 \begin_layout Standard
1743 \begin_inset Preview
1745 \begin_layout Standard
1750 \begin_layout Plain Layout
1754 begin{pspicture*}(-1.5,-1.5)(11,5)
1757 \begin_layout Plain Layout
1761 psaxes{->}(0,0)(0,0)(10,5)
1764 \begin_layout Plain Layout
1768 psset{linewidth=2.5pt}
1771 \begin_layout Plain Layout
1775 rput(5.0,-1.0){Speed [MPH]}
1778 \begin_layout Plain Layout
1784 begin{rotate}{90}Cost [Dollars]
1789 \begin_layout Plain Layout
1795 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1798 \begin_layout Plain Layout
1802 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1807 \begin_layout Plain Layout
1824 \begin_layout Subsection
1828 \begin_layout Standard
1829 \begin_inset Preview
1831 \begin_layout Standard
1835 \begin_layout Plain Layout
1839 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1842 \begin_layout Plain Layout
1846 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1850 \begin_layout Plain Layout
1865 \begin_inset space \hfill{}
1869 \begin_inset Preview
1871 \begin_layout Standard
1875 \begin_layout Plain Layout
1879 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1882 \begin_layout Plain Layout
1886 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1887 mul cos 100 t mul sin}
1890 \begin_layout Plain Layout
1905 \begin_inset space \hfill{}
1909 \begin_inset Preview
1911 \begin_layout Standard
1915 \begin_layout Plain Layout
1919 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1922 \begin_layout Plain Layout
1926 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1927 mul cos 200 t mul sin}
1930 \begin_layout Plain Layout
1945 \begin_inset space \hfill{}
1949 \begin_inset Preview
1951 \begin_layout Standard
1955 \begin_layout Plain Layout
1959 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1962 \begin_layout Plain Layout
1966 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1967 mul cos 200 t mul sin}
1970 \begin_layout Plain Layout
1987 \begin_layout Section
1991 \begin_layout Standard
1992 \begin_inset Flex URL
1995 \begin_layout Plain Layout
1997 http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
2005 \begin_layout Standard
2006 \begin_inset Preview
2008 \begin_layout Standard
2012 \begin_layout Plain Layout
2018 iangle{35} % Angle of the inclined plane
2021 \begin_layout Plain Layout
2030 \begin_layout Plain Layout
2036 arcr{0.5cm} % Radius of the arc used to indicate angles
2039 \begin_layout Plain Layout
2043 \begin_layout Plain Layout
2050 \begin_layout Plain Layout
2052 force/.style={>=latex,draw=blue,fill=blue},
2055 \begin_layout Plain Layout
2057 axis/.style={densely dashed,gray,font=
2062 \begin_layout Plain Layout
2064 M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2067 \begin_layout Plain Layout
2069 m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2072 \begin_layout Plain Layout
2074 plane/.style={draw=black,fill=blue!10},
2077 \begin_layout Plain Layout
2079 string/.style={draw=red, thick},
2082 \begin_layout Plain Layout
2084 pulley/.style={thick},
2087 \begin_layout Plain Layout
2092 \begin_layout Plain Layout
2096 \begin_layout Plain Layout
2100 matrix[column sep=1cm] {
2103 \begin_layout Plain Layout
2108 \begin_layout Plain Layout
2112 draw[plane] (0,-1) coordinate (base)
2115 \begin_layout Plain Layout
2117 -- coordinate[pos=0.5] (mid) ++(
2119 iangle:3) coordinate (top)
2122 \begin_layout Plain Layout
2127 \begin_layout Plain Layout
2131 path (mid) node[M,rotate=
2133 iangle,yshift=0.25cm] (M) {};
2136 \begin_layout Plain Layout
2140 draw[pulley] (top) -- ++(
2142 iangle:0.25) circle (0.25cm)
2145 \begin_layout Plain Layout
2149 iangle:0.5) coordinate (pulley);
2152 \begin_layout Plain Layout
2156 draw[string] (M.east) -- ++(
2158 iangle:1.5cm) arc (90+
2163 \begin_layout Plain Layout
2165 -- ++(0,-1) node[m] {};
2168 \begin_layout Plain Layout
2172 \begin_layout Plain Layout
2185 \begin_layout Plain Layout
2198 \begin_layout Plain Layout
2203 \begin_layout Plain Layout
2207 \begin_layout Plain Layout
2212 \begin_layout Plain Layout
2214 %% Free body diagram of M
2217 \begin_layout Plain Layout
2221 begin{scope}[rotate=
2226 \begin_layout Plain Layout
2230 node[M,transform shape] (M) {};
2233 \begin_layout Plain Layout
2235 % Draw axes and help lines
2238 \begin_layout Plain Layout
2242 \begin_layout Plain Layout
2247 \begin_layout Plain Layout
2251 draw (0,-1) -- (0,2) node[right] {$+y$};
2254 \begin_layout Plain Layout
2258 draw (M) -- ++(2,0) node[right] {$+x$};
2261 \begin_layout Plain Layout
2264 The code is a bit awkward.
2267 \begin_layout Plain Layout
2271 \begin_layout Plain Layout
2275 draw[solid,shorten >=0.5pt] (
2284 \begin_layout Plain Layout
2297 \begin_layout Plain Layout
2312 \begin_layout Plain Layout
2317 \begin_layout Plain Layout
2321 \begin_layout Plain Layout
2326 \begin_layout Plain Layout
2331 \begin_layout Plain Layout
2333 % Assuming that Mg = 1.
2334 The normal force will therefore be cos(alpha)
2337 \begin_layout Plain Layout
2341 draw (M.center) -- ++(0,{cos(
2343 iangle)}) node[above right] {$N$};
2346 \begin_layout Plain Layout
2350 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2353 \begin_layout Plain Layout
2357 draw (M.east) -- ++(1,0) node[above] {$T$};
2360 \begin_layout Plain Layout
2365 \begin_layout Plain Layout
2369 \begin_layout Plain Layout
2376 \begin_layout Plain Layout
2378 % Draw gravity force.
2379 The code is put outside the rotated
2382 \begin_layout Plain Layout
2384 % scope for simplicity.
2385 No need to do any angle calculations.
2389 \begin_layout Plain Layout
2393 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2396 \begin_layout Plain Layout
2401 \begin_layout Plain Layout
2405 \begin_layout Plain Layout
2410 \begin_layout Plain Layout
2415 \begin_layout Plain Layout
2417 % Free body diagram of m
2420 \begin_layout Plain Layout
2427 \begin_layout Plain Layout
2431 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2434 \begin_layout Plain Layout
2439 \begin_layout Plain Layout
2443 draw (m.north) -- ++(0,1) node[above] {$T'$};
2446 \begin_layout Plain Layout
2450 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2453 \begin_layout Plain Layout
2458 \begin_layout Plain Layout
2462 \begin_layout Plain Layout
2471 \begin_layout Plain Layout
2476 \begin_layout Plain Layout
2483 \begin_layout Plain Layout