1 #LyX 2.1 created this file. For more info see http://www.lyx.org/
8 \usepackage[all, knot]{xy}
16 \usetikzlibrary{scopes}
18 \use_default_options false
19 \maintain_unincluded_children false
21 \language_package default
26 \font_typewriter default
28 \font_default_family default
29 \use_non_tex_fonts false
35 \default_output_format pdf
37 \bibtex_command default
38 \index_command default
39 \paperfontsize default
44 \use_package amsmath 1
45 \use_package amssymb 1
48 \use_package mathdots 1
49 \use_package mathtools 0
51 \use_package stackrel 0
52 \use_package stmaryrd 0
53 \use_package undertilde 0
55 \cite_engine_type default
59 \paperorientation portrait
69 \paragraph_separation indent
70 \paragraph_indentation default
71 \quotes_language english
74 \paperpagestyle default
75 \tracking_changes false
88 \begin_layout Standard
89 In order to properly typeset the document and have instant preview working,
90 the following packages have to be installed:
93 \begin_layout LyX-Code
94 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf, etex
97 \begin_layout Standard
98 Due to the use of postscript specials in Section
99 \begin_inset CommandInset ref
101 reference "sec:PSTricks"
105 , only the Postscript or PDF (ps2pdf) output formats will correctly render
107 However, the PDF (XeTeX) output seems to also work, while trying to typeset
116 will generate errors.
119 \begin_layout Section
123 \begin_layout Standard
124 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
126 \begin_inset Flex URL
129 \begin_layout Plain Layout
131 http://www.math.columbia.edu/~lauda/xy/
139 \begin_layout Description
143 \begin_layout Standard
146 \begin_layout Standard
150 \begin_layout Plain Layout
157 \begin_layout Plain Layout
159 (5,10)*{}; (-10,-10)*{} **
164 \begin_layout Plain Layout
181 \begin_layout Plain Layout
183 "y"+(0,-1); (2,-10)*{} **
192 \begin_layout Plain Layout
199 \begin_layout Plain Layout
206 \begin_layout Plain Layout
213 \begin_layout Plain Layout
220 \begin_layout Plain Layout
237 \begin_layout Description
241 \begin_layout Standard
244 \begin_layout Standard
248 \begin_layout Plain Layout
255 \begin_layout Plain Layout
260 \begin_layout Plain Layout
265 \begin_layout Plain Layout
269 crv{~*=<.5pt>{.} (0,30)}?(.75)*
274 \begin_layout Plain Layout
279 \begin_layout Plain Layout
284 \begin_layout Plain Layout
288 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
293 \begin_layout Plain Layout
298 \begin_layout Plain Layout
303 \begin_layout Plain Layout
307 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
312 \begin_layout Plain Layout
317 \begin_layout Plain Layout
322 \begin_layout Plain Layout
326 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
331 \begin_layout Plain Layout
336 \begin_layout Plain Layout
341 \begin_layout Plain Layout
345 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
350 \begin_layout Plain Layout
367 \begin_layout Description
371 \begin_layout Standard
374 \begin_layout Standard
378 \begin_layout Plain Layout
385 \begin_layout Plain Layout
394 \begin_layout Plain Layout
401 \begin_layout Plain Layout
408 \begin_layout Plain Layout
415 \begin_layout Plain Layout
432 \begin_layout Description
436 \begin_layout Standard
439 \begin_layout Standard
443 \begin_layout Plain Layout
450 \begin_layout Plain Layout
457 \begin_layout Plain Layout
461 ellipse(3,1)__,=:a(-180){-};
464 \begin_layout Plain Layout
471 \begin_layout Plain Layout
478 \begin_layout Plain Layout
485 \begin_layout Plain Layout
489 ellipse(3,1)__,=:a(-180){-};
492 \begin_layout Plain Layout
496 ellipse(3,1)__,=:a(-180){-};
499 \begin_layout Plain Layout
503 ellipse(3,1)__,=:a(180){-};
506 \begin_layout Plain Layout
513 \begin_layout Plain Layout
520 \begin_layout Plain Layout
525 \begin_layout Plain Layout
530 \begin_layout Plain Layout
535 \begin_layout Plain Layout
540 \begin_layout Plain Layout
547 \begin_layout Plain Layout
552 \begin_layout Plain Layout
557 \begin_layout Plain Layout
562 \begin_layout Plain Layout
567 \begin_layout Plain Layout
574 \begin_layout Plain Layout
581 \begin_layout Plain Layout
588 \begin_layout Plain Layout
592 crv{(-8,7) & (-3,5)};
595 \begin_layout Plain Layout
600 \begin_layout Plain Layout
605 \begin_layout Plain Layout
610 \begin_layout Plain Layout
614 crv{(3,-10) & (9,-10)};
617 \begin_layout Plain Layout
622 \begin_layout Plain Layout
627 \begin_layout Plain Layout
631 crv{(-3,-10) & (-9,-10)};
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
659 \begin_layout Plain Layout
664 \begin_layout Plain Layout
671 \begin_layout Plain Layout
678 \begin_layout Plain Layout
682 crv{(13,-6) & (2,-8)};
685 \begin_layout Plain Layout
689 crv{(-13,-6) & (-2,-8)};
692 \begin_layout Plain Layout
709 \begin_layout Standard
713 \begin_layout Plain Layout
720 \begin_layout Plain Layout
724 bullet}="RU"+(1,3)*{x^{
729 \begin_layout Plain Layout
733 bullet}="RD"+(2.5,2)*{x^{
738 \begin_layout Plain Layout
742 bullet}="LU"+(-1,2)*{x};
745 \begin_layout Plain Layout
749 bullet}="LD"+(-1,2)*{x};
752 \begin_layout Plain Layout
756 crv{(4,2) & (4,-1)}; ?(.1)*
763 \begin_layout Plain Layout
767 crv{(-4,-2) & (-4,1)};
770 \begin_layout Plain Layout
779 \begin_layout Plain Layout
781 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
784 \begin_layout Plain Layout
788 crv{(7,-10) & (-7,-10)};
791 \begin_layout Plain Layout
795 bullet}="RDD"+(2.5,-1)*{x^{
800 \begin_layout Plain Layout
804 bullet}="LDD"+(-1,-3)*{x};
807 \begin_layout Plain Layout
811 bullet}="RUD"+(3.5,1)*{x^{
816 \begin_layout Plain Layout
823 \begin_layout Plain Layout
825 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
828 \begin_layout Plain Layout
835 \begin_layout Plain Layout
842 \begin_layout Plain Layout
849 \begin_layout Plain Layout
853 crv{(0,-17)}; ?(.57)*
858 \begin_layout Plain Layout
865 \begin_layout Plain Layout
872 \begin_layout Plain Layout
879 \begin_layout Plain Layout
883 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
888 \begin_layout Plain Layout
905 \begin_layout Description
909 \begin_layout Standard
912 \begin_layout Standard
916 \begin_layout Plain Layout
920 xy (-15,0)*{};(15,0)*{};
923 \begin_layout Plain Layout
930 \begin_layout Plain Layout
941 \begin_layout Plain Layout
943 (-10,12)*{}; (-10,-12)*{}; **
947 dir{<}+(-4,0)*{F(x)};
950 \begin_layout Plain Layout
955 \begin_layout Plain Layout
960 \begin_layout Plain Layout
965 \begin_layout Plain Layout
970 \begin_layout Plain Layout
975 \begin_layout Plain Layout
979 crv{(-4,-21)&(5,-15)};
982 \begin_layout Plain Layout
991 \begin_layout Plain Layout
998 \begin_layout Plain Layout
1004 widetilde{F(i_x)}} ;
1007 \begin_layout Plain Layout
1016 \begin_layout Plain Layout
1023 \begin_layout Plain Layout
1028 \begin_layout Plain Layout
1033 \begin_layout Plain Layout
1037 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1040 \begin_layout Plain Layout
1045 \begin_layout Plain Layout
1050 \begin_layout Plain Layout
1054 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1057 \begin_layout Plain Layout
1074 \begin_layout Description
1078 \begin_layout Standard
1079 \begin_inset Preview
1081 \begin_layout Standard
1085 \begin_layout Plain Layout
1092 \begin_layout Plain Layout
1101 \begin_layout Plain Layout
1108 \begin_layout Plain Layout
1117 \begin_layout Plain Layout
1126 \begin_layout Plain Layout
1141 \begin_layout Plain Layout
1156 \begin_inset Preview
1158 \begin_layout Standard
1162 \begin_layout Plain Layout
1169 \begin_layout Plain Layout
1176 \begin_layout Plain Layout
1183 \begin_layout Plain Layout
1187 ar@/^.9pc/ "1";"2"};
1190 \begin_layout Plain Layout
1194 ar@/_.9pc/ "1";"2"};
1197 \begin_layout Plain Layout
1204 \begin_layout Plain Layout
1211 \begin_layout Plain Layout
1215 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1218 \begin_layout Plain Layout
1222 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1225 \begin_layout Plain Layout
1229 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1232 \begin_layout Plain Layout
1239 \begin_layout Plain Layout
1246 \begin_layout Plain Layout
1253 \begin_layout Plain Layout
1260 \begin_layout Plain Layout
1267 \begin_layout Plain Layout
1274 \begin_layout Plain Layout
1281 \begin_layout Plain Layout
1285 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1288 \begin_layout Plain Layout
1292 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1295 \begin_layout Plain Layout
1312 \begin_layout Description
1316 \begin_layout Standard
1317 \begin_inset Preview
1319 \begin_layout Standard
1323 \begin_layout Plain Layout
1328 Natural transformation between functors.
1331 \begin_layout Plain Layout
1338 \begin_layout Plain Layout
1345 \begin_layout Plain Layout
1352 \begin_layout Plain Layout
1356 ar@/^.25pc/ "a";"b"};
1359 \begin_layout Plain Layout
1363 ar@/_.25pc/"a";"c"};
1366 \begin_layout Plain Layout
1370 ar@/_.15pc/ "b";"c"};
1373 \begin_layout Plain Layout
1378 \begin_layout Plain Layout
1385 \begin_layout Plain Layout
1392 \begin_layout Plain Layout
1399 \begin_layout Plain Layout
1403 ar@/^.25pc/ "ta";"tb"};
1406 \begin_layout Plain Layout
1410 ar@/_.25pc/ "ta";"tc"};
1413 \begin_layout Plain Layout
1417 ar@/_.15pc/ "tb";"tc"};
1420 \begin_layout Plain Layout
1425 \begin_layout Plain Layout
1432 \begin_layout Plain Layout
1439 \begin_layout Plain Layout
1446 \begin_layout Plain Layout
1450 ar@/^.25pc/@{.>} "ba";"bb"};
1453 \begin_layout Plain Layout
1457 ar@/_.25pc/ "ba";"bc"};
1460 \begin_layout Plain Layout
1464 ar@/_.15pc/ "bb";"bc"};
1467 \begin_layout Plain Layout
1472 \begin_layout Plain Layout
1476 ar@/_.15pc/ "ta";"ba"};
1479 \begin_layout Plain Layout
1483 ar@/_.15pc/ "tb";"bb"};
1486 \begin_layout Plain Layout
1490 ar@/_.15pc/ "tc";"bc"};
1493 \begin_layout Plain Layout
1495 %START ARROWS AND LABELS
1498 \begin_layout Plain Layout
1503 \begin_layout Plain Layout
1508 \begin_layout Plain Layout
1512 ar@/^.35pc/^F "DF";"CF"};
1515 \begin_layout Plain Layout
1520 \begin_layout Plain Layout
1525 \begin_layout Plain Layout
1529 ar@/_.35pc/_G "DF";"CF"};
1532 \begin_layout Plain Layout
1537 \begin_layout Plain Layout
1542 \begin_layout Plain Layout
1551 \begin_layout Plain Layout
1556 \begin_layout Plain Layout
1561 \begin_layout Plain Layout
1578 \begin_layout Section
1582 \begin_layout Standard
1583 \begin_inset Preview
1585 \begin_layout Standard
1589 \begin_layout Plain Layout
1593 textipa{Ekspl@"neIS@n}
1606 \begin_layout Section
1610 \begin_layout Standard
1611 \begin_inset Preview
1613 \begin_layout Standard
1617 \begin_layout Plain Layout
1621 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1632 \begin_inset Preview
1634 \begin_layout Standard
1638 \begin_layout Plain Layout
1661 \begin_layout Section
1663 \begin_inset CommandInset label
1672 \begin_layout Standard
1673 Some simple graphing examples.
1676 \begin_layout Subsection
1680 \begin_layout Standard
1681 \begin_inset Preview
1683 \begin_layout Standard
1687 \begin_layout Plain Layout
1691 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1694 \begin_layout Plain Layout
1698 psaxes{->}(0,0)(0,-3)(10,3)
1701 \begin_layout Plain Layout
1705 uput[-90](10,0){$x$}
1707 uput[0](0,3){$f(x)$}
1710 \begin_layout Plain Layout
1714 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1717 \begin_layout Plain Layout
1734 \begin_layout Subsection
1735 Inline data plotting
1738 \begin_layout Standard
1740 \begin_inset Preview
1742 \begin_layout Standard
1747 \begin_layout Plain Layout
1751 begin{pspicture*}(-1.5,-1.5)(11,5)
1754 \begin_layout Plain Layout
1758 psaxes{->}(0,0)(0,0)(10,5)
1761 \begin_layout Plain Layout
1765 psset{linewidth=2.5pt}
1768 \begin_layout Plain Layout
1772 rput(5.0,-1.0){Speed [MPH]}
1775 \begin_layout Plain Layout
1781 begin{rotate}{90}Cost [Dollars]
1786 \begin_layout Plain Layout
1792 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1795 \begin_layout Plain Layout
1799 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1804 \begin_layout Plain Layout
1821 \begin_layout Subsection
1825 \begin_layout Standard
1826 \begin_inset Preview
1828 \begin_layout Standard
1832 \begin_layout Plain Layout
1836 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1839 \begin_layout Plain Layout
1843 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1847 \begin_layout Plain Layout
1862 \begin_inset space \hfill{}
1866 \begin_inset Preview
1868 \begin_layout Standard
1872 \begin_layout Plain Layout
1876 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1879 \begin_layout Plain Layout
1883 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1884 mul cos 100 t mul sin}
1887 \begin_layout Plain Layout
1902 \begin_inset space \hfill{}
1906 \begin_inset Preview
1908 \begin_layout Standard
1912 \begin_layout Plain Layout
1916 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1919 \begin_layout Plain Layout
1923 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1924 mul cos 200 t mul sin}
1927 \begin_layout Plain Layout
1942 \begin_inset space \hfill{}
1946 \begin_inset Preview
1948 \begin_layout Standard
1952 \begin_layout Plain Layout
1956 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1959 \begin_layout Plain Layout
1963 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1964 mul cos 200 t mul sin}
1967 \begin_layout Plain Layout
1984 \begin_layout Section
1988 \begin_layout Standard
1989 \begin_inset Flex URL
1992 \begin_layout Plain Layout
1994 http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
2002 \begin_layout Standard
2003 \begin_inset Preview
2005 \begin_layout Standard
2009 \begin_layout Plain Layout
2015 iangle{35} % Angle of the inclined plane
2018 \begin_layout Plain Layout
2027 \begin_layout Plain Layout
2033 arcr{0.5cm} % Radius of the arc used to indicate angles
2036 \begin_layout Plain Layout
2040 \begin_layout Plain Layout
2047 \begin_layout Plain Layout
2049 force/.style={>=latex,draw=blue,fill=blue},
2052 \begin_layout Plain Layout
2054 axis/.style={densely dashed,gray,font=
2059 \begin_layout Plain Layout
2061 M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2064 \begin_layout Plain Layout
2066 m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2069 \begin_layout Plain Layout
2071 plane/.style={draw=black,fill=blue!10},
2074 \begin_layout Plain Layout
2076 string/.style={draw=red, thick},
2079 \begin_layout Plain Layout
2081 pulley/.style={thick},
2084 \begin_layout Plain Layout
2089 \begin_layout Plain Layout
2093 \begin_layout Plain Layout
2097 matrix[column sep=1cm] {
2100 \begin_layout Plain Layout
2105 \begin_layout Plain Layout
2109 draw[plane] (0,-1) coordinate (base)
2112 \begin_layout Plain Layout
2114 -- coordinate[pos=0.5] (mid) ++(
2116 iangle:3) coordinate (top)
2119 \begin_layout Plain Layout
2124 \begin_layout Plain Layout
2128 path (mid) node[M,rotate=
2130 iangle,yshift=0.25cm] (M) {};
2133 \begin_layout Plain Layout
2137 draw[pulley] (top) -- ++(
2139 iangle:0.25) circle (0.25cm)
2142 \begin_layout Plain Layout
2146 iangle:0.5) coordinate (pulley);
2149 \begin_layout Plain Layout
2153 draw[string] (M.east) -- ++(
2155 iangle:1.5cm) arc (90+
2160 \begin_layout Plain Layout
2162 -- ++(0,-1) node[m] {};
2165 \begin_layout Plain Layout
2169 \begin_layout Plain Layout
2182 \begin_layout Plain Layout
2195 \begin_layout Plain Layout
2200 \begin_layout Plain Layout
2204 \begin_layout Plain Layout
2209 \begin_layout Plain Layout
2211 %% Free body diagram of M
2214 \begin_layout Plain Layout
2218 begin{scope}[rotate=
2223 \begin_layout Plain Layout
2227 node[M,transform shape] (M) {};
2230 \begin_layout Plain Layout
2232 % Draw axes and help lines
2235 \begin_layout Plain Layout
2239 \begin_layout Plain Layout
2244 \begin_layout Plain Layout
2248 draw (0,-1) -- (0,2) node[right] {$+y$};
2251 \begin_layout Plain Layout
2255 draw (M) -- ++(2,0) node[right] {$+x$};
2258 \begin_layout Plain Layout
2261 The code is a bit awkward.
2264 \begin_layout Plain Layout
2268 \begin_layout Plain Layout
2272 draw[solid,shorten >=0.5pt] (
2281 \begin_layout Plain Layout
2294 \begin_layout Plain Layout
2309 \begin_layout Plain Layout
2314 \begin_layout Plain Layout
2318 \begin_layout Plain Layout
2323 \begin_layout Plain Layout
2328 \begin_layout Plain Layout
2330 % Assuming that Mg = 1.
2331 The normal force will therefore be cos(alpha)
2334 \begin_layout Plain Layout
2338 draw (M.center) -- ++(0,{cos(
2340 iangle)}) node[above right] {$N$};
2343 \begin_layout Plain Layout
2347 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2350 \begin_layout Plain Layout
2354 draw (M.east) -- ++(1,0) node[above] {$T$};
2357 \begin_layout Plain Layout
2362 \begin_layout Plain Layout
2366 \begin_layout Plain Layout
2373 \begin_layout Plain Layout
2375 % Draw gravity force.
2376 The code is put outside the rotated
2379 \begin_layout Plain Layout
2381 % scope for simplicity.
2382 No need to do any angle calculations.
2386 \begin_layout Plain Layout
2390 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2393 \begin_layout Plain Layout
2398 \begin_layout Plain Layout
2402 \begin_layout Plain Layout
2407 \begin_layout Plain Layout
2412 \begin_layout Plain Layout
2414 % Free body diagram of m
2417 \begin_layout Plain Layout
2424 \begin_layout Plain Layout
2428 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2431 \begin_layout Plain Layout
2436 \begin_layout Plain Layout
2440 draw (m.north) -- ++(0,1) node[above] {$T'$};
2443 \begin_layout Plain Layout
2447 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2450 \begin_layout Plain Layout
2455 \begin_layout Plain Layout
2459 \begin_layout Plain Layout
2468 \begin_layout Plain Layout
2473 \begin_layout Plain Layout
2480 \begin_layout Plain Layout