1 #LyX 2.0 created this file. For more info see http://www.lyx.org/
7 \usepackage[all, knot]{xy}
15 \usetikzlibrary{scopes}
17 \use_default_options false
18 \maintain_unincluded_children false
20 \language_package default
25 \font_typewriter default
26 \font_default_family default
27 \use_non_tex_fonts false
34 \default_output_format default
36 \bibtex_command default
37 \index_command default
38 \paperfontsize default
50 \paperorientation portrait
59 \paragraph_separation indent
60 \paragraph_indentation default
61 \quotes_language english
64 \paperpagestyle default
65 \tracking_changes false
78 \begin_layout Standard
79 In order to properly typeset the document and have instant preview working,
80 the following packages have to be installed:
83 \begin_layout LyX-Code
84 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf
87 \begin_layout Standard
88 Due to the use of postscript specials in Section
89 \begin_inset CommandInset ref
91 reference "sec:PSTricks"
95 , only the Postscript or PDF (ps2pdf) output formats will correctly render
97 However, the PDF (XeTeX) output seems to also work, while trying to typeset
106 will generate errors.
109 \begin_layout Section
113 \begin_layout Standard
114 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
116 \begin_inset Flex URL
119 \begin_layout Plain Layout
121 http://www.math.columbia.edu/~lauda/xy/
129 \begin_layout Description
133 \begin_layout Standard
136 \begin_layout Standard
140 \begin_layout Plain Layout
147 \begin_layout Plain Layout
149 (5,10)*{}; (-10,-10)*{} **
154 \begin_layout Plain Layout
171 \begin_layout Plain Layout
173 "y"+(0,-1); (2,-10)*{} **
182 \begin_layout Plain Layout
189 \begin_layout Plain Layout
196 \begin_layout Plain Layout
203 \begin_layout Plain Layout
210 \begin_layout Plain Layout
227 \begin_layout Description
231 \begin_layout Standard
234 \begin_layout Standard
238 \begin_layout Plain Layout
245 \begin_layout Plain Layout
250 \begin_layout Plain Layout
255 \begin_layout Plain Layout
259 crv{~*=<.5pt>{.} (0,30)}?(.75)*
264 \begin_layout Plain Layout
269 \begin_layout Plain Layout
274 \begin_layout Plain Layout
278 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
283 \begin_layout Plain Layout
288 \begin_layout Plain Layout
293 \begin_layout Plain Layout
297 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
302 \begin_layout Plain Layout
307 \begin_layout Plain Layout
312 \begin_layout Plain Layout
316 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
321 \begin_layout Plain Layout
326 \begin_layout Plain Layout
331 \begin_layout Plain Layout
335 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
340 \begin_layout Plain Layout
357 \begin_layout Description
361 \begin_layout Standard
364 \begin_layout Standard
368 \begin_layout Plain Layout
375 \begin_layout Plain Layout
384 \begin_layout Plain Layout
391 \begin_layout Plain Layout
398 \begin_layout Plain Layout
405 \begin_layout Plain Layout
422 \begin_layout Description
426 \begin_layout Standard
429 \begin_layout Standard
433 \begin_layout Plain Layout
440 \begin_layout Plain Layout
447 \begin_layout Plain Layout
451 ellipse(3,1)__,=:a(-180){-};
454 \begin_layout Plain Layout
461 \begin_layout Plain Layout
468 \begin_layout Plain Layout
475 \begin_layout Plain Layout
479 ellipse(3,1)__,=:a(-180){-};
482 \begin_layout Plain Layout
486 ellipse(3,1)__,=:a(-180){-};
489 \begin_layout Plain Layout
493 ellipse(3,1)__,=:a(180){-};
496 \begin_layout Plain Layout
503 \begin_layout Plain Layout
510 \begin_layout Plain Layout
515 \begin_layout Plain Layout
520 \begin_layout Plain Layout
525 \begin_layout Plain Layout
530 \begin_layout Plain Layout
537 \begin_layout Plain Layout
542 \begin_layout Plain Layout
547 \begin_layout Plain Layout
552 \begin_layout Plain Layout
557 \begin_layout Plain Layout
564 \begin_layout Plain Layout
571 \begin_layout Plain Layout
578 \begin_layout Plain Layout
582 crv{(-8,7) & (-3,5)};
585 \begin_layout Plain Layout
590 \begin_layout Plain Layout
595 \begin_layout Plain Layout
600 \begin_layout Plain Layout
604 crv{(3,-10) & (9,-10)};
607 \begin_layout Plain Layout
612 \begin_layout Plain Layout
617 \begin_layout Plain Layout
621 crv{(-3,-10) & (-9,-10)};
624 \begin_layout Plain Layout
629 \begin_layout Plain Layout
634 \begin_layout Plain Layout
639 \begin_layout Plain Layout
644 \begin_layout Plain Layout
649 \begin_layout Plain Layout
654 \begin_layout Plain Layout
661 \begin_layout Plain Layout
668 \begin_layout Plain Layout
672 crv{(13,-6) & (2,-8)};
675 \begin_layout Plain Layout
679 crv{(-13,-6) & (-2,-8)};
682 \begin_layout Plain Layout
699 \begin_layout Standard
703 \begin_layout Plain Layout
710 \begin_layout Plain Layout
714 bullet}="RU"+(1,3)*{x^{
719 \begin_layout Plain Layout
723 bullet}="RD"+(2.5,2)*{x^{
728 \begin_layout Plain Layout
732 bullet}="LU"+(-1,2)*{x};
735 \begin_layout Plain Layout
739 bullet}="LD"+(-1,2)*{x};
742 \begin_layout Plain Layout
746 crv{(4,2) & (4,-1)}; ?(.1)*
753 \begin_layout Plain Layout
757 crv{(-4,-2) & (-4,1)};
760 \begin_layout Plain Layout
769 \begin_layout Plain Layout
771 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
774 \begin_layout Plain Layout
778 crv{(7,-10) & (-7,-10)};
781 \begin_layout Plain Layout
785 bullet}="RDD"+(2.5,-1)*{x^{
790 \begin_layout Plain Layout
794 bullet}="LDD"+(-1,-3)*{x};
797 \begin_layout Plain Layout
801 bullet}="RUD"+(3.5,1)*{x^{
806 \begin_layout Plain Layout
813 \begin_layout Plain Layout
815 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
818 \begin_layout Plain Layout
825 \begin_layout Plain Layout
832 \begin_layout Plain Layout
839 \begin_layout Plain Layout
843 crv{(0,-17)}; ?(.57)*
848 \begin_layout Plain Layout
855 \begin_layout Plain Layout
862 \begin_layout Plain Layout
869 \begin_layout Plain Layout
873 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
878 \begin_layout Plain Layout
895 \begin_layout Description
899 \begin_layout Standard
902 \begin_layout Standard
906 \begin_layout Plain Layout
910 xy (-15,0)*{};(15,0)*{};
913 \begin_layout Plain Layout
920 \begin_layout Plain Layout
931 \begin_layout Plain Layout
933 (-10,12)*{}; (-10,-12)*{}; **
937 dir{<}+(-4,0)*{F(x)};
940 \begin_layout Plain Layout
945 \begin_layout Plain Layout
950 \begin_layout Plain Layout
955 \begin_layout Plain Layout
960 \begin_layout Plain Layout
965 \begin_layout Plain Layout
969 crv{(-4,-21)&(5,-15)};
972 \begin_layout Plain Layout
981 \begin_layout Plain Layout
988 \begin_layout Plain Layout
997 \begin_layout Plain Layout
1006 \begin_layout Plain Layout
1013 \begin_layout Plain Layout
1018 \begin_layout Plain Layout
1023 \begin_layout Plain Layout
1027 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1030 \begin_layout Plain Layout
1035 \begin_layout Plain Layout
1040 \begin_layout Plain Layout
1044 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1047 \begin_layout Plain Layout
1064 \begin_layout Description
1068 \begin_layout Standard
1069 \begin_inset Preview
1071 \begin_layout Standard
1075 \begin_layout Plain Layout
1082 \begin_layout Plain Layout
1091 \begin_layout Plain Layout
1098 \begin_layout Plain Layout
1107 \begin_layout Plain Layout
1116 \begin_layout Plain Layout
1131 \begin_layout Plain Layout
1146 \begin_inset Preview
1148 \begin_layout Standard
1152 \begin_layout Plain Layout
1159 \begin_layout Plain Layout
1166 \begin_layout Plain Layout
1173 \begin_layout Plain Layout
1177 ar@/^.9pc/ "1";"2"};
1180 \begin_layout Plain Layout
1184 ar@/_.9pc/ "1";"2"};
1187 \begin_layout Plain Layout
1194 \begin_layout Plain Layout
1201 \begin_layout Plain Layout
1205 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1208 \begin_layout Plain Layout
1212 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1215 \begin_layout Plain Layout
1219 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1222 \begin_layout Plain Layout
1229 \begin_layout Plain Layout
1236 \begin_layout Plain Layout
1243 \begin_layout Plain Layout
1250 \begin_layout Plain Layout
1257 \begin_layout Plain Layout
1264 \begin_layout Plain Layout
1271 \begin_layout Plain Layout
1275 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1278 \begin_layout Plain Layout
1282 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1285 \begin_layout Plain Layout
1302 \begin_layout Description
1306 \begin_layout Standard
1307 \begin_inset Preview
1309 \begin_layout Standard
1313 \begin_layout Plain Layout
1318 Natural transformation between functors.
1321 \begin_layout Plain Layout
1328 \begin_layout Plain Layout
1335 \begin_layout Plain Layout
1342 \begin_layout Plain Layout
1346 ar@/^.25pc/ "a";"b"};
1349 \begin_layout Plain Layout
1353 ar@/_.25pc/"a";"c"};
1356 \begin_layout Plain Layout
1360 ar@/_.15pc/ "b";"c"};
1363 \begin_layout Plain Layout
1368 \begin_layout Plain Layout
1375 \begin_layout Plain Layout
1382 \begin_layout Plain Layout
1389 \begin_layout Plain Layout
1393 ar@/^.25pc/ "ta";"tb"};
1396 \begin_layout Plain Layout
1400 ar@/_.25pc/ "ta";"tc"};
1403 \begin_layout Plain Layout
1407 ar@/_.15pc/ "tb";"tc"};
1410 \begin_layout Plain Layout
1415 \begin_layout Plain Layout
1422 \begin_layout Plain Layout
1429 \begin_layout Plain Layout
1436 \begin_layout Plain Layout
1440 ar@/^.25pc/@{.>} "ba";"bb"};
1443 \begin_layout Plain Layout
1447 ar@/_.25pc/ "ba";"bc"};
1450 \begin_layout Plain Layout
1454 ar@/_.15pc/ "bb";"bc"};
1457 \begin_layout Plain Layout
1462 \begin_layout Plain Layout
1466 ar@/_.15pc/ "ta";"ba"};
1469 \begin_layout Plain Layout
1473 ar@/_.15pc/ "tb";"bb"};
1476 \begin_layout Plain Layout
1480 ar@/_.15pc/ "tc";"bc"};
1483 \begin_layout Plain Layout
1485 %START ARROWS AND LABELS
1488 \begin_layout Plain Layout
1493 \begin_layout Plain Layout
1498 \begin_layout Plain Layout
1502 ar@/^.35pc/^F "DF";"CF"};
1505 \begin_layout Plain Layout
1510 \begin_layout Plain Layout
1515 \begin_layout Plain Layout
1519 ar@/_.35pc/_G "DF";"CF"};
1522 \begin_layout Plain Layout
1527 \begin_layout Plain Layout
1532 \begin_layout Plain Layout
1541 \begin_layout Plain Layout
1546 \begin_layout Plain Layout
1551 \begin_layout Plain Layout
1568 \begin_layout Section
1572 \begin_layout Standard
1573 \begin_inset Preview
1575 \begin_layout Standard
1579 \begin_layout Plain Layout
1583 textipa{Ekspl@"neIS@n}
1596 \begin_layout Section
1600 \begin_layout Standard
1601 \begin_inset Preview
1603 \begin_layout Standard
1607 \begin_layout Plain Layout
1611 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1622 \begin_inset Preview
1624 \begin_layout Standard
1628 \begin_layout Plain Layout
1651 \begin_layout Section
1653 \begin_inset CommandInset label
1662 \begin_layout Standard
1663 Some simple graphing examples.
1666 \begin_layout Subsection
1670 \begin_layout Standard
1671 \begin_inset Preview
1673 \begin_layout Standard
1677 \begin_layout Plain Layout
1681 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1684 \begin_layout Plain Layout
1688 psaxes{->}(0,0)(0,-3)(10,3)
1691 \begin_layout Plain Layout
1695 uput[-90](10,0){$x$}
1697 uput[0](0,3){$f(x)$}
1700 \begin_layout Plain Layout
1704 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1707 \begin_layout Plain Layout
1724 \begin_layout Subsection
1725 Inline data plotting
1728 \begin_layout Standard
1730 \begin_inset Preview
1732 \begin_layout Standard
1737 \begin_layout Plain Layout
1741 begin{pspicture*}(-1.5,-1.5)(11,5)
1744 \begin_layout Plain Layout
1748 psaxes{->}(0,0)(0,0)(10,5)
1751 \begin_layout Plain Layout
1755 psset{linewidth=2.5pt}
1758 \begin_layout Plain Layout
1762 rput(5.0,-1.0){Speed [MPH]}
1765 \begin_layout Plain Layout
1771 begin{rotate}{90}Cost [Dollars]
1776 \begin_layout Plain Layout
1782 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1785 \begin_layout Plain Layout
1789 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1794 \begin_layout Plain Layout
1811 \begin_layout Subsection
1815 \begin_layout Standard
1816 \begin_inset Preview
1818 \begin_layout Standard
1822 \begin_layout Plain Layout
1826 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1829 \begin_layout Plain Layout
1833 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1837 \begin_layout Plain Layout
1852 \begin_inset space \hfill{}
1856 \begin_inset Preview
1858 \begin_layout Standard
1862 \begin_layout Plain Layout
1866 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1869 \begin_layout Plain Layout
1873 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1874 mul cos 100 t mul sin}
1877 \begin_layout Plain Layout
1892 \begin_inset space \hfill{}
1896 \begin_inset Preview
1898 \begin_layout Standard
1902 \begin_layout Plain Layout
1906 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1909 \begin_layout Plain Layout
1913 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1914 mul cos 200 t mul sin}
1917 \begin_layout Plain Layout
1932 \begin_inset space \hfill{}
1936 \begin_inset Preview
1938 \begin_layout Standard
1942 \begin_layout Plain Layout
1946 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1949 \begin_layout Plain Layout
1953 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1954 mul cos 200 t mul sin}
1957 \begin_layout Plain Layout
1974 \begin_layout Section
1978 \begin_layout Standard
1979 \begin_inset Flex URL
1982 \begin_layout Plain Layout
1984 http://media.texample.net/tikz/examples/TEX/free-body-diagrams.tex
1992 \begin_layout Standard
1993 \begin_inset Preview
1995 \begin_layout Standard
1999 \begin_layout Plain Layout
2005 iangle{35} % Angle of the inclined plane
2008 \begin_layout Plain Layout
2017 \begin_layout Plain Layout
2023 arcr{0.5cm} % Radius of the arc used to indicate angles
2026 \begin_layout Plain Layout
2030 \begin_layout Plain Layout
2037 \begin_layout Plain Layout
2039 force/.style={>=latex,draw=blue,fill=blue},
2042 \begin_layout Plain Layout
2044 axis/.style={densely dashed,gray,font=
2049 \begin_layout Plain Layout
2051 M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2054 \begin_layout Plain Layout
2056 m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2059 \begin_layout Plain Layout
2061 plane/.style={draw=black,fill=blue!10},
2064 \begin_layout Plain Layout
2066 string/.style={draw=red, thick},
2069 \begin_layout Plain Layout
2071 pulley/.style={thick},
2074 \begin_layout Plain Layout
2079 \begin_layout Plain Layout
2083 \begin_layout Plain Layout
2087 matrix[column sep=1cm] {
2090 \begin_layout Plain Layout
2095 \begin_layout Plain Layout
2099 draw[plane] (0,-1) coordinate (base)
2102 \begin_layout Plain Layout
2104 -- coordinate[pos=0.5] (mid) ++(
2106 iangle:3) coordinate (top)
2109 \begin_layout Plain Layout
2114 \begin_layout Plain Layout
2118 path (mid) node[M,rotate=
2120 iangle,yshift=0.25cm] (M) {};
2123 \begin_layout Plain Layout
2127 draw[pulley] (top) -- ++(
2129 iangle:0.25) circle (0.25cm)
2132 \begin_layout Plain Layout
2136 iangle:0.5) coordinate (pulley);
2139 \begin_layout Plain Layout
2143 draw[string] (M.east) -- ++(
2145 iangle:1.5cm) arc (90+
2150 \begin_layout Plain Layout
2152 -- ++(0,-1) node[m] {};
2155 \begin_layout Plain Layout
2159 \begin_layout Plain Layout
2172 \begin_layout Plain Layout
2185 \begin_layout Plain Layout
2190 \begin_layout Plain Layout
2194 \begin_layout Plain Layout
2199 \begin_layout Plain Layout
2201 %% Free body diagram of M
2204 \begin_layout Plain Layout
2208 begin{scope}[rotate=
2213 \begin_layout Plain Layout
2217 node[M,transform shape] (M) {};
2220 \begin_layout Plain Layout
2222 % Draw axes and help lines
2225 \begin_layout Plain Layout
2229 \begin_layout Plain Layout
2234 \begin_layout Plain Layout
2238 draw (0,-1) -- (0,2) node[right] {$+y$};
2241 \begin_layout Plain Layout
2245 draw (M) -- ++(2,0) node[right] {$+x$};
2248 \begin_layout Plain Layout
2251 The code is a bit awkward.
2254 \begin_layout Plain Layout
2258 \begin_layout Plain Layout
2262 draw[solid,shorten >=0.5pt] (
2271 \begin_layout Plain Layout
2284 \begin_layout Plain Layout
2299 \begin_layout Plain Layout
2304 \begin_layout Plain Layout
2308 \begin_layout Plain Layout
2313 \begin_layout Plain Layout
2318 \begin_layout Plain Layout
2320 % Assuming that Mg = 1.
2321 The normal force will therefore be cos(alpha)
2324 \begin_layout Plain Layout
2328 draw (M.center) -- ++(0,{cos(
2330 iangle)}) node[above right] {$N$};
2333 \begin_layout Plain Layout
2337 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2340 \begin_layout Plain Layout
2344 draw (M.east) -- ++(1,0) node[above] {$T$};
2347 \begin_layout Plain Layout
2352 \begin_layout Plain Layout
2356 \begin_layout Plain Layout
2363 \begin_layout Plain Layout
2365 % Draw gravity force.
2366 The code is put outside the rotated
2369 \begin_layout Plain Layout
2371 % scope for simplicity.
2372 No need to do any angle calculations.
2376 \begin_layout Plain Layout
2380 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2383 \begin_layout Plain Layout
2388 \begin_layout Plain Layout
2392 \begin_layout Plain Layout
2397 \begin_layout Plain Layout
2402 \begin_layout Plain Layout
2404 % Free body diagram of m
2407 \begin_layout Plain Layout
2414 \begin_layout Plain Layout
2418 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2421 \begin_layout Plain Layout
2426 \begin_layout Plain Layout
2430 draw (m.north) -- ++(0,1) node[above] {$T'$};
2433 \begin_layout Plain Layout
2437 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2440 \begin_layout Plain Layout
2445 \begin_layout Plain Layout
2449 \begin_layout Plain Layout
2458 \begin_layout Plain Layout
2463 \begin_layout Plain Layout
2470 \begin_layout Plain Layout