1 #LyX 2.0.0svn 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
24 \font_typewriter default
25 \font_default_family default
26 \use_non_tex_fonts false
33 \default_output_format default
35 \bibtex_command default
36 \index_command default
37 \paperfontsize default
49 \paperorientation portrait
58 \paragraph_separation indent
59 \paragraph_indentation default
60 \quotes_language english
63 \paperpagestyle default
64 \tracking_changes false
76 \begin_layout Standard
77 In order to properly typeset the document and have instant preview working,
78 the following packages have to be installed:
81 \begin_layout LyX-Code
82 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf
85 \begin_layout Standard
86 Due to the use of postscript specials in Section
87 \begin_inset CommandInset ref
89 reference "sec:PSTricks"
93 , only the Postscript or PDF (ps2pdf) output formats will correctly render
95 However, the PDF (XeTeX) output seems to also work, while trying to typeset
104 will generate errors.
107 \begin_layout Section
111 \begin_layout Standard
112 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
114 \begin_inset Flex URL
117 \begin_layout Plain Layout
119 http://www.math.columbia.edu/~lauda/xy/
127 \begin_layout Description
131 \begin_layout Standard
134 \begin_layout Standard
138 \begin_layout Plain Layout
145 \begin_layout Plain Layout
147 (5,10)*{}; (-10,-10)*{} **
152 \begin_layout Plain Layout
169 \begin_layout Plain Layout
171 "y"+(0,-1); (2,-10)*{} **
180 \begin_layout Plain Layout
187 \begin_layout Plain Layout
194 \begin_layout Plain Layout
201 \begin_layout Plain Layout
208 \begin_layout Plain Layout
225 \begin_layout Description
229 \begin_layout Standard
232 \begin_layout Standard
236 \begin_layout Plain Layout
243 \begin_layout Plain Layout
248 \begin_layout Plain Layout
253 \begin_layout Plain Layout
257 crv{~*=<.5pt>{.} (0,30)}?(.75)*
262 \begin_layout Plain Layout
267 \begin_layout Plain Layout
272 \begin_layout Plain Layout
276 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
281 \begin_layout Plain Layout
286 \begin_layout Plain Layout
291 \begin_layout Plain Layout
295 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
300 \begin_layout Plain Layout
305 \begin_layout Plain Layout
310 \begin_layout Plain Layout
314 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
319 \begin_layout Plain Layout
324 \begin_layout Plain Layout
329 \begin_layout Plain Layout
333 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
338 \begin_layout Plain Layout
355 \begin_layout Description
359 \begin_layout Standard
362 \begin_layout Standard
366 \begin_layout Plain Layout
373 \begin_layout Plain Layout
382 \begin_layout Plain Layout
389 \begin_layout Plain Layout
396 \begin_layout Plain Layout
403 \begin_layout Plain Layout
420 \begin_layout Description
424 \begin_layout Standard
427 \begin_layout Standard
431 \begin_layout Plain Layout
438 \begin_layout Plain Layout
445 \begin_layout Plain Layout
449 ellipse(3,1)__,=:a(-180){-};
452 \begin_layout Plain Layout
459 \begin_layout Plain Layout
466 \begin_layout Plain Layout
473 \begin_layout Plain Layout
477 ellipse(3,1)__,=:a(-180){-};
480 \begin_layout Plain Layout
484 ellipse(3,1)__,=:a(-180){-};
487 \begin_layout Plain Layout
491 ellipse(3,1)__,=:a(180){-};
494 \begin_layout Plain Layout
501 \begin_layout Plain Layout
508 \begin_layout Plain Layout
513 \begin_layout Plain Layout
518 \begin_layout Plain Layout
523 \begin_layout Plain Layout
528 \begin_layout Plain Layout
535 \begin_layout Plain Layout
540 \begin_layout Plain Layout
545 \begin_layout Plain Layout
550 \begin_layout Plain Layout
555 \begin_layout Plain Layout
562 \begin_layout Plain Layout
569 \begin_layout Plain Layout
576 \begin_layout Plain Layout
580 crv{(-8,7) & (-3,5)};
583 \begin_layout Plain Layout
588 \begin_layout Plain Layout
593 \begin_layout Plain Layout
598 \begin_layout Plain Layout
602 crv{(3,-10) & (9,-10)};
605 \begin_layout Plain Layout
610 \begin_layout Plain Layout
615 \begin_layout Plain Layout
619 crv{(-3,-10) & (-9,-10)};
622 \begin_layout Plain Layout
627 \begin_layout Plain Layout
632 \begin_layout Plain Layout
637 \begin_layout Plain Layout
642 \begin_layout Plain Layout
647 \begin_layout Plain Layout
652 \begin_layout Plain Layout
659 \begin_layout Plain Layout
666 \begin_layout Plain Layout
670 crv{(13,-6) & (2,-8)};
673 \begin_layout Plain Layout
677 crv{(-13,-6) & (-2,-8)};
680 \begin_layout Plain Layout
697 \begin_layout Standard
701 \begin_layout Plain Layout
708 \begin_layout Plain Layout
712 bullet}="RU"+(1,3)*{x^{
717 \begin_layout Plain Layout
721 bullet}="RD"+(2.5,2)*{x^{
726 \begin_layout Plain Layout
730 bullet}="LU"+(-1,2)*{x};
733 \begin_layout Plain Layout
737 bullet}="LD"+(-1,2)*{x};
740 \begin_layout Plain Layout
744 crv{(4,2) & (4,-1)}; ?(.1)*
751 \begin_layout Plain Layout
755 crv{(-4,-2) & (-4,1)};
758 \begin_layout Plain Layout
767 \begin_layout Plain Layout
769 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
772 \begin_layout Plain Layout
776 crv{(7,-10) & (-7,-10)};
779 \begin_layout Plain Layout
783 bullet}="RDD"+(2.5,-1)*{x^{
788 \begin_layout Plain Layout
792 bullet}="LDD"+(-1,-3)*{x};
795 \begin_layout Plain Layout
799 bullet}="RUD"+(3.5,1)*{x^{
804 \begin_layout Plain Layout
811 \begin_layout Plain Layout
813 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
816 \begin_layout Plain Layout
823 \begin_layout Plain Layout
830 \begin_layout Plain Layout
837 \begin_layout Plain Layout
841 crv{(0,-17)}; ?(.57)*
846 \begin_layout Plain Layout
853 \begin_layout Plain Layout
860 \begin_layout Plain Layout
867 \begin_layout Plain Layout
871 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
876 \begin_layout Plain Layout
893 \begin_layout Description
897 \begin_layout Standard
900 \begin_layout Standard
904 \begin_layout Plain Layout
908 xy (-15,0)*{};(15,0)*{};
911 \begin_layout Plain Layout
918 \begin_layout Plain Layout
929 \begin_layout Plain Layout
931 (-10,12)*{}; (-10,-12)*{}; **
935 dir{<}+(-4,0)*{F(x)};
938 \begin_layout Plain Layout
943 \begin_layout Plain Layout
948 \begin_layout Plain Layout
953 \begin_layout Plain Layout
958 \begin_layout Plain Layout
963 \begin_layout Plain Layout
967 crv{(-4,-21)&(5,-15)};
970 \begin_layout Plain Layout
979 \begin_layout Plain Layout
986 \begin_layout Plain Layout
995 \begin_layout Plain Layout
1004 \begin_layout Plain Layout
1011 \begin_layout Plain Layout
1016 \begin_layout Plain Layout
1021 \begin_layout Plain Layout
1025 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1028 \begin_layout Plain Layout
1033 \begin_layout Plain Layout
1038 \begin_layout Plain Layout
1042 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1045 \begin_layout Plain Layout
1062 \begin_layout Description
1066 \begin_layout Standard
1067 \begin_inset Preview
1069 \begin_layout Standard
1073 \begin_layout Plain Layout
1080 \begin_layout Plain Layout
1089 \begin_layout Plain Layout
1096 \begin_layout Plain Layout
1105 \begin_layout Plain Layout
1114 \begin_layout Plain Layout
1129 \begin_layout Plain Layout
1144 \begin_inset Preview
1146 \begin_layout Standard
1150 \begin_layout Plain Layout
1157 \begin_layout Plain Layout
1164 \begin_layout Plain Layout
1171 \begin_layout Plain Layout
1175 ar@/^.9pc/ "1";"2"};
1178 \begin_layout Plain Layout
1182 ar@/_.9pc/ "1";"2"};
1185 \begin_layout Plain Layout
1192 \begin_layout Plain Layout
1199 \begin_layout Plain Layout
1203 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1206 \begin_layout Plain Layout
1210 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1213 \begin_layout Plain Layout
1217 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1220 \begin_layout Plain Layout
1227 \begin_layout Plain Layout
1234 \begin_layout Plain Layout
1241 \begin_layout Plain Layout
1248 \begin_layout Plain Layout
1255 \begin_layout Plain Layout
1262 \begin_layout Plain Layout
1269 \begin_layout Plain Layout
1273 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1276 \begin_layout Plain Layout
1280 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1283 \begin_layout Plain Layout
1300 \begin_layout Description
1304 \begin_layout Standard
1305 \begin_inset Preview
1307 \begin_layout Standard
1311 \begin_layout Plain Layout
1316 Natural transformation between functors.
1319 \begin_layout Plain Layout
1326 \begin_layout Plain Layout
1333 \begin_layout Plain Layout
1340 \begin_layout Plain Layout
1344 ar@/^.25pc/ "a";"b"};
1347 \begin_layout Plain Layout
1351 ar@/_.25pc/"a";"c"};
1354 \begin_layout Plain Layout
1358 ar@/_.15pc/ "b";"c"};
1361 \begin_layout Plain Layout
1366 \begin_layout Plain Layout
1373 \begin_layout Plain Layout
1380 \begin_layout Plain Layout
1387 \begin_layout Plain Layout
1391 ar@/^.25pc/ "ta";"tb"};
1394 \begin_layout Plain Layout
1398 ar@/_.25pc/ "ta";"tc"};
1401 \begin_layout Plain Layout
1405 ar@/_.15pc/ "tb";"tc"};
1408 \begin_layout Plain Layout
1413 \begin_layout Plain Layout
1420 \begin_layout Plain Layout
1427 \begin_layout Plain Layout
1434 \begin_layout Plain Layout
1438 ar@/^.25pc/@{.>} "ba";"bb"};
1441 \begin_layout Plain Layout
1445 ar@/_.25pc/ "ba";"bc"};
1448 \begin_layout Plain Layout
1452 ar@/_.15pc/ "bb";"bc"};
1455 \begin_layout Plain Layout
1460 \begin_layout Plain Layout
1464 ar@/_.15pc/ "ta";"ba"};
1467 \begin_layout Plain Layout
1471 ar@/_.15pc/ "tb";"bb"};
1474 \begin_layout Plain Layout
1478 ar@/_.15pc/ "tc";"bc"};
1481 \begin_layout Plain Layout
1483 %START ARROWS AND LABELS
1486 \begin_layout Plain Layout
1491 \begin_layout Plain Layout
1496 \begin_layout Plain Layout
1500 ar@/^.35pc/^F "DF";"CF"};
1503 \begin_layout Plain Layout
1508 \begin_layout Plain Layout
1513 \begin_layout Plain Layout
1517 ar@/_.35pc/_G "DF";"CF"};
1520 \begin_layout Plain Layout
1525 \begin_layout Plain Layout
1530 \begin_layout Plain Layout
1539 \begin_layout Plain Layout
1544 \begin_layout Plain Layout
1549 \begin_layout Plain Layout
1566 \begin_layout Section
1570 \begin_layout Standard
1571 \begin_inset Preview
1573 \begin_layout Standard
1577 \begin_layout Plain Layout
1581 textipa{Ekspl@"neIS@n}
1594 \begin_layout Section
1598 \begin_layout Standard
1599 \begin_inset Preview
1601 \begin_layout Standard
1605 \begin_layout Plain Layout
1609 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1620 \begin_inset Preview
1622 \begin_layout Standard
1626 \begin_layout Plain Layout
1649 \begin_layout Section
1651 \begin_inset CommandInset label
1660 \begin_layout Standard
1661 Some simple graphing examples.
1664 \begin_layout Subsection
1668 \begin_layout Standard
1669 \begin_inset Preview
1671 \begin_layout Standard
1675 \begin_layout Plain Layout
1679 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1682 \begin_layout Plain Layout
1686 psaxes{->}(0,0)(0,-3)(10,3)
1689 \begin_layout Plain Layout
1693 uput[-90](10,0){$x$}
1695 uput[0](0,3){$f(x)$}
1698 \begin_layout Plain Layout
1702 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1705 \begin_layout Plain Layout
1722 \begin_layout Subsection
1723 Inline data plotting
1726 \begin_layout Standard
1728 \begin_inset Preview
1730 \begin_layout Standard
1735 \begin_layout Plain Layout
1739 begin{pspicture*}(-1.5,-1.5)(11,5)
1742 \begin_layout Plain Layout
1746 psaxes{->}(0,0)(0,0)(10,5)
1749 \begin_layout Plain Layout
1753 psset{linewidth=2.5pt}
1756 \begin_layout Plain Layout
1760 rput(5.0,-1.0){Speed [MPH]}
1763 \begin_layout Plain Layout
1769 begin{rotate}{90}Cost [Dollars]
1774 \begin_layout Plain Layout
1780 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1783 \begin_layout Plain Layout
1787 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1792 \begin_layout Plain Layout
1809 \begin_layout Subsection
1813 \begin_layout Standard
1814 \begin_inset Preview
1816 \begin_layout Standard
1820 \begin_layout Plain Layout
1824 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1827 \begin_layout Plain Layout
1831 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1835 \begin_layout Plain Layout
1850 \begin_inset space \hfill{}
1854 \begin_inset Preview
1856 \begin_layout Standard
1860 \begin_layout Plain Layout
1864 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1867 \begin_layout Plain Layout
1871 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1872 mul cos 100 t mul sin}
1875 \begin_layout Plain Layout
1890 \begin_inset space \hfill{}
1894 \begin_inset Preview
1896 \begin_layout Standard
1900 \begin_layout Plain Layout
1904 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1907 \begin_layout Plain Layout
1911 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1912 mul cos 200 t mul sin}
1915 \begin_layout Plain Layout
1930 \begin_inset space \hfill{}
1934 \begin_inset Preview
1936 \begin_layout Standard
1940 \begin_layout Plain Layout
1944 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1947 \begin_layout Plain Layout
1951 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1952 mul cos 200 t mul sin}
1955 \begin_layout Plain Layout
1972 \begin_layout Section
1976 \begin_layout Standard
1977 \begin_inset Flex URL
1980 \begin_layout Plain Layout
1982 http://media.texample.net/tikz/examples/TEX/free-body-diagrams.tex
1990 \begin_layout Standard
1991 \begin_inset Preview
1993 \begin_layout Standard
1997 \begin_layout Plain Layout
2003 iangle{35} % Angle of the inclined plane
2006 \begin_layout Plain Layout
2015 \begin_layout Plain Layout
2021 arcr{0.5cm} % Radius of the arc used to indicate angles
2024 \begin_layout Plain Layout
2028 \begin_layout Plain Layout
2035 \begin_layout Plain Layout
2037 force/.style={>=latex,draw=blue,fill=blue},
2040 \begin_layout Plain Layout
2042 axis/.style={densely dashed,gray,font=
2047 \begin_layout Plain Layout
2049 M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2052 \begin_layout Plain Layout
2054 m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2057 \begin_layout Plain Layout
2059 plane/.style={draw=black,fill=blue!10},
2062 \begin_layout Plain Layout
2064 string/.style={draw=red, thick},
2067 \begin_layout Plain Layout
2069 pulley/.style={thick},
2072 \begin_layout Plain Layout
2077 \begin_layout Plain Layout
2081 \begin_layout Plain Layout
2085 matrix[column sep=1cm] {
2088 \begin_layout Plain Layout
2093 \begin_layout Plain Layout
2097 draw[plane] (0,-1) coordinate (base)
2100 \begin_layout Plain Layout
2102 -- coordinate[pos=0.5] (mid) ++(
2104 iangle:3) coordinate (top)
2107 \begin_layout Plain Layout
2112 \begin_layout Plain Layout
2116 path (mid) node[M,rotate=
2118 iangle,yshift=0.25cm] (M) {};
2121 \begin_layout Plain Layout
2125 draw[pulley] (top) -- ++(
2127 iangle:0.25) circle (0.25cm)
2130 \begin_layout Plain Layout
2134 iangle:0.5) coordinate (pulley);
2137 \begin_layout Plain Layout
2141 draw[string] (M.east) -- ++(
2143 iangle:1.5cm) arc (90+
2148 \begin_layout Plain Layout
2150 -- ++(0,-1) node[m] {};
2153 \begin_layout Plain Layout
2157 \begin_layout Plain Layout
2170 \begin_layout Plain Layout
2183 \begin_layout Plain Layout
2188 \begin_layout Plain Layout
2192 \begin_layout Plain Layout
2197 \begin_layout Plain Layout
2199 %% Free body diagram of M
2202 \begin_layout Plain Layout
2206 begin{scope}[rotate=
2211 \begin_layout Plain Layout
2215 node[M,transform shape] (M) {};
2218 \begin_layout Plain Layout
2220 % Draw axes and help lines
2223 \begin_layout Plain Layout
2227 \begin_layout Plain Layout
2232 \begin_layout Plain Layout
2236 draw (0,-1) -- (0,2) node[right] {$+y$};
2239 \begin_layout Plain Layout
2243 draw (M) -- ++(2,0) node[right] {$+x$};
2246 \begin_layout Plain Layout
2249 The code is a bit awkward.
2252 \begin_layout Plain Layout
2256 \begin_layout Plain Layout
2260 draw[solid,shorten >=0.5pt] (
2269 \begin_layout Plain Layout
2282 \begin_layout Plain Layout
2297 \begin_layout Plain Layout
2302 \begin_layout Plain Layout
2306 \begin_layout Plain Layout
2311 \begin_layout Plain Layout
2316 \begin_layout Plain Layout
2318 % Assuming that Mg = 1.
2319 The normal force will therefore be cos(alpha)
2322 \begin_layout Plain Layout
2326 draw (M.center) -- ++(0,{cos(
2328 iangle)}) node[above right] {$N$};
2331 \begin_layout Plain Layout
2335 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2338 \begin_layout Plain Layout
2342 draw (M.east) -- ++(1,0) node[above] {$T$};
2345 \begin_layout Plain Layout
2350 \begin_layout Plain Layout
2354 \begin_layout Plain Layout
2361 \begin_layout Plain Layout
2363 % Draw gravity force.
2364 The code is put outside the rotated
2367 \begin_layout Plain Layout
2369 % scope for simplicity.
2370 No need to do any angle calculations.
2374 \begin_layout Plain Layout
2378 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2381 \begin_layout Plain Layout
2386 \begin_layout Plain Layout
2390 \begin_layout Plain Layout
2395 \begin_layout Plain Layout
2400 \begin_layout Plain Layout
2402 % Free body diagram of m
2405 \begin_layout Plain Layout
2412 \begin_layout Plain Layout
2416 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2419 \begin_layout Plain Layout
2424 \begin_layout Plain Layout
2428 draw (m.north) -- ++(0,1) node[above] {$T'$};
2431 \begin_layout Plain Layout
2435 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2438 \begin_layout Plain Layout
2443 \begin_layout Plain Layout
2447 \begin_layout Plain Layout
2456 \begin_layout Plain Layout
2461 \begin_layout Plain Layout
2468 \begin_layout Plain Layout