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 1
55 \use_package stackrel 1
56 \use_package stmaryrd 1
57 \use_package undertilde 1
59 \cite_engine_type default
63 \paperorientation portrait
74 \paragraph_separation indent
75 \paragraph_indentation default
77 \math_numbering_side default
82 \paperpagestyle default
83 \tracking_changes false
96 \begin_layout Standard
97 In order to properly typeset the document and have instant preview working,
98 the following packages have to be installed:
101 \begin_layout LyX-Code
102 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf, etex
105 \begin_layout Standard
106 Due to the use of postscript specials in Section
107 \begin_inset CommandInset ref
109 reference "sec:PSTricks"
113 , only the Postscript or PDF (ps2pdf) output formats will correctly render
115 However, the PDF (Xe\SpecialChar TeX
116 ) output seems to also work, while trying to typeset
125 will generate errors.
128 \begin_layout Section
132 \begin_layout Standard
133 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
135 \begin_inset Flex URL
138 \begin_layout Plain Layout
140 https://www.ctan.org/tex-archive/macros/generic/diagrams/xypic/doc/xyguide.pdf
148 \begin_layout Description
152 \begin_layout Standard
155 \begin_layout Standard
159 \begin_layout Plain Layout
166 \begin_layout Plain Layout
168 (5,10)*{}; (-10,-10)*{} **
173 \begin_layout Plain Layout
190 \begin_layout Plain Layout
192 "y"+(0,-1); (2,-10)*{} **
201 \begin_layout Plain Layout
208 \begin_layout Plain Layout
215 \begin_layout Plain Layout
222 \begin_layout Plain Layout
229 \begin_layout Plain Layout
246 \begin_layout Description
250 \begin_layout Standard
253 \begin_layout Standard
257 \begin_layout Plain Layout
264 \begin_layout Plain Layout
269 \begin_layout Plain Layout
274 \begin_layout Plain Layout
278 crv{~*=<.5pt>{.} (0,30)}?(.75)*
283 \begin_layout Plain Layout
288 \begin_layout Plain Layout
293 \begin_layout Plain Layout
297 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.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>{.} (17.67,-24.19)}?(.7)*
340 \begin_layout Plain Layout
345 \begin_layout Plain Layout
350 \begin_layout Plain Layout
354 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
359 \begin_layout Plain Layout
376 \begin_layout Description
380 \begin_layout Standard
383 \begin_layout Standard
387 \begin_layout Plain Layout
394 \begin_layout Plain Layout
403 \begin_layout Plain Layout
410 \begin_layout Plain Layout
417 \begin_layout Plain Layout
424 \begin_layout Plain Layout
441 \begin_layout Description
445 \begin_layout Standard
448 \begin_layout Standard
452 \begin_layout Plain Layout
459 \begin_layout Plain Layout
466 \begin_layout Plain Layout
470 ellipse(3,1)__,=:a(-180){-};
473 \begin_layout Plain Layout
480 \begin_layout Plain Layout
487 \begin_layout Plain Layout
494 \begin_layout Plain Layout
498 ellipse(3,1)__,=:a(-180){-};
501 \begin_layout Plain Layout
505 ellipse(3,1)__,=:a(-180){-};
508 \begin_layout Plain Layout
512 ellipse(3,1)__,=:a(180){-};
515 \begin_layout Plain Layout
522 \begin_layout Plain Layout
529 \begin_layout Plain Layout
534 \begin_layout Plain Layout
539 \begin_layout Plain Layout
544 \begin_layout Plain Layout
549 \begin_layout Plain Layout
556 \begin_layout Plain Layout
561 \begin_layout Plain Layout
566 \begin_layout Plain Layout
571 \begin_layout Plain Layout
576 \begin_layout Plain Layout
583 \begin_layout Plain Layout
590 \begin_layout Plain Layout
597 \begin_layout Plain Layout
601 crv{(-8,7) & (-3,5)};
604 \begin_layout Plain Layout
609 \begin_layout Plain Layout
614 \begin_layout Plain Layout
619 \begin_layout Plain Layout
623 crv{(3,-10) & (9,-10)};
626 \begin_layout Plain Layout
631 \begin_layout Plain Layout
636 \begin_layout Plain Layout
640 crv{(-3,-10) & (-9,-10)};
643 \begin_layout Plain Layout
648 \begin_layout Plain Layout
653 \begin_layout Plain Layout
658 \begin_layout Plain Layout
663 \begin_layout Plain Layout
668 \begin_layout Plain Layout
673 \begin_layout Plain Layout
680 \begin_layout Plain Layout
687 \begin_layout Plain Layout
691 crv{(13,-6) & (2,-8)};
694 \begin_layout Plain Layout
698 crv{(-13,-6) & (-2,-8)};
701 \begin_layout Plain Layout
718 \begin_layout Standard
722 \begin_layout Plain Layout
729 \begin_layout Plain Layout
733 bullet}="RU"+(1,3)*{x^{
738 \begin_layout Plain Layout
742 bullet}="RD"+(2.5,2)*{x^{
747 \begin_layout Plain Layout
751 bullet}="LU"+(-1,2)*{x};
754 \begin_layout Plain Layout
758 bullet}="LD"+(-1,2)*{x};
761 \begin_layout Plain Layout
765 crv{(4,2) & (4,-1)}; ?(.1)*
772 \begin_layout Plain Layout
776 crv{(-4,-2) & (-4,1)};
779 \begin_layout Plain Layout
788 \begin_layout Plain Layout
790 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
793 \begin_layout Plain Layout
797 crv{(7,-10) & (-7,-10)};
800 \begin_layout Plain Layout
804 bullet}="RDD"+(2.5,-1)*{x^{
809 \begin_layout Plain Layout
813 bullet}="LDD"+(-1,-3)*{x};
816 \begin_layout Plain Layout
820 bullet}="RUD"+(3.5,1)*{x^{
825 \begin_layout Plain Layout
832 \begin_layout Plain Layout
834 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
837 \begin_layout Plain Layout
844 \begin_layout Plain Layout
851 \begin_layout Plain Layout
858 \begin_layout Plain Layout
862 crv{(0,-17)}; ?(.57)*
867 \begin_layout Plain Layout
874 \begin_layout Plain Layout
881 \begin_layout Plain Layout
888 \begin_layout Plain Layout
892 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
897 \begin_layout Plain Layout
914 \begin_layout Description
918 \begin_layout Standard
921 \begin_layout Standard
925 \begin_layout Plain Layout
929 xy (-15,0)*{};(15,0)*{};
932 \begin_layout Plain Layout
939 \begin_layout Plain Layout
950 \begin_layout Plain Layout
952 (-10,12)*{}; (-10,-12)*{}; **
956 dir{<}+(-4,0)*{F(x)};
959 \begin_layout Plain Layout
964 \begin_layout Plain Layout
969 \begin_layout Plain Layout
974 \begin_layout Plain Layout
979 \begin_layout Plain Layout
984 \begin_layout Plain Layout
988 crv{(-4,-21)&(5,-15)};
991 \begin_layout Plain Layout
1000 \begin_layout Plain Layout
1007 \begin_layout Plain Layout
1013 widetilde{F(i_x)}} ;
1016 \begin_layout Plain Layout
1025 \begin_layout Plain Layout
1032 \begin_layout Plain Layout
1037 \begin_layout Plain Layout
1042 \begin_layout Plain Layout
1046 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1049 \begin_layout Plain Layout
1054 \begin_layout Plain Layout
1059 \begin_layout Plain Layout
1063 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1066 \begin_layout Plain Layout
1083 \begin_layout Description
1087 \begin_layout Standard
1088 \begin_inset Preview
1090 \begin_layout Standard
1094 \begin_layout Plain Layout
1101 \begin_layout Plain Layout
1110 \begin_layout Plain Layout
1117 \begin_layout Plain Layout
1126 \begin_layout Plain Layout
1135 \begin_layout Plain Layout
1150 \begin_layout Plain Layout
1165 \begin_inset Preview
1167 \begin_layout Standard
1171 \begin_layout Plain Layout
1178 \begin_layout Plain Layout
1185 \begin_layout Plain Layout
1192 \begin_layout Plain Layout
1196 ar@/^.9pc/ "1";"2"};
1199 \begin_layout Plain Layout
1203 ar@/_.9pc/ "1";"2"};
1206 \begin_layout Plain Layout
1213 \begin_layout Plain Layout
1220 \begin_layout Plain Layout
1224 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1227 \begin_layout Plain Layout
1231 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1234 \begin_layout Plain Layout
1238 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
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
1276 \begin_layout Plain Layout
1283 \begin_layout Plain Layout
1290 \begin_layout Plain Layout
1294 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1297 \begin_layout Plain Layout
1301 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1304 \begin_layout Plain Layout
1321 \begin_layout Description
1325 \begin_layout Standard
1326 \begin_inset Preview
1328 \begin_layout Standard
1332 \begin_layout Plain Layout
1337 Natural transformation between functors.
1340 \begin_layout Plain Layout
1347 \begin_layout Plain Layout
1354 \begin_layout Plain Layout
1361 \begin_layout Plain Layout
1365 ar@/^.25pc/ "a";"b"};
1368 \begin_layout Plain Layout
1372 ar@/_.25pc/"a";"c"};
1375 \begin_layout Plain Layout
1379 ar@/_.15pc/ "b";"c"};
1382 \begin_layout Plain Layout
1387 \begin_layout Plain Layout
1394 \begin_layout Plain Layout
1401 \begin_layout Plain Layout
1408 \begin_layout Plain Layout
1412 ar@/^.25pc/ "ta";"tb"};
1415 \begin_layout Plain Layout
1419 ar@/_.25pc/ "ta";"tc"};
1422 \begin_layout Plain Layout
1426 ar@/_.15pc/ "tb";"tc"};
1429 \begin_layout Plain Layout
1434 \begin_layout Plain Layout
1441 \begin_layout Plain Layout
1448 \begin_layout Plain Layout
1455 \begin_layout Plain Layout
1459 ar@/^.25pc/@{.>} "ba";"bb"};
1462 \begin_layout Plain Layout
1466 ar@/_.25pc/ "ba";"bc"};
1469 \begin_layout Plain Layout
1473 ar@/_.15pc/ "bb";"bc"};
1476 \begin_layout Plain Layout
1481 \begin_layout Plain Layout
1485 ar@/_.15pc/ "ta";"ba"};
1488 \begin_layout Plain Layout
1492 ar@/_.15pc/ "tb";"bb"};
1495 \begin_layout Plain Layout
1499 ar@/_.15pc/ "tc";"bc"};
1502 \begin_layout Plain Layout
1504 %START ARROWS AND LABELS
1507 \begin_layout Plain Layout
1512 \begin_layout Plain Layout
1517 \begin_layout Plain Layout
1521 ar@/^.35pc/^F "DF";"CF"};
1524 \begin_layout Plain Layout
1529 \begin_layout Plain Layout
1534 \begin_layout Plain Layout
1538 ar@/_.35pc/_G "DF";"CF"};
1541 \begin_layout Plain Layout
1546 \begin_layout Plain Layout
1551 \begin_layout Plain Layout
1560 \begin_layout Plain Layout
1565 \begin_layout Plain Layout
1570 \begin_layout Plain Layout
1587 \begin_layout Section
1591 \begin_layout Standard
1592 \begin_inset Preview
1594 \begin_layout Standard
1598 \begin_layout Plain Layout
1602 textipa{Ekspl@"neIS@n}
1615 \begin_layout Section
1619 \begin_layout Standard
1620 \begin_inset Preview
1622 \begin_layout Standard
1626 \begin_layout Plain Layout
1630 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1641 \begin_inset Preview
1643 \begin_layout Standard
1647 \begin_layout Plain Layout
1670 \begin_layout Section
1672 \begin_inset CommandInset label
1681 \begin_layout Standard
1682 Some simple graphing examples.
1685 \begin_layout Subsection
1689 \begin_layout Standard
1690 \begin_inset Preview
1692 \begin_layout Standard
1696 \begin_layout Plain Layout
1700 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1703 \begin_layout Plain Layout
1707 psaxes{->}(0,0)(0,-3)(10,3)
1710 \begin_layout Plain Layout
1714 uput[-90](10,0){$x$}
1716 uput[0](0,3){$f(x)$}
1719 \begin_layout Plain Layout
1723 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1726 \begin_layout Plain Layout
1743 \begin_layout Subsection
1744 Inline data plotting
1747 \begin_layout Standard
1749 \begin_inset Preview
1751 \begin_layout Standard
1756 \begin_layout Plain Layout
1760 begin{pspicture*}(-1.5,-1.5)(11,5)
1763 \begin_layout Plain Layout
1767 psaxes{->}(0,0)(0,0)(10,5)
1770 \begin_layout Plain Layout
1774 psset{linewidth=2.5pt}
1777 \begin_layout Plain Layout
1781 rput(5.0,-1.0){Speed [MPH]}
1784 \begin_layout Plain Layout
1790 begin{rotate}{90}Cost [Dollars]
1795 \begin_layout Plain Layout
1801 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1804 \begin_layout Plain Layout
1808 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1813 \begin_layout Plain Layout
1830 \begin_layout Subsection
1834 \begin_layout Standard
1835 \begin_inset Preview
1837 \begin_layout Standard
1841 \begin_layout Plain Layout
1845 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1848 \begin_layout Plain Layout
1852 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1856 \begin_layout Plain Layout
1871 \begin_inset space \hfill{}
1875 \begin_inset Preview
1877 \begin_layout Standard
1881 \begin_layout Plain Layout
1885 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1888 \begin_layout Plain Layout
1892 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1893 mul cos 100 t mul sin}
1896 \begin_layout Plain Layout
1911 \begin_inset space \hfill{}
1915 \begin_inset Preview
1917 \begin_layout Standard
1921 \begin_layout Plain Layout
1925 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1928 \begin_layout Plain Layout
1932 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1933 mul cos 200 t mul sin}
1936 \begin_layout Plain Layout
1951 \begin_inset space \hfill{}
1955 \begin_inset Preview
1957 \begin_layout Standard
1961 \begin_layout Plain Layout
1965 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1968 \begin_layout Plain Layout
1972 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1973 mul cos 200 t mul sin}
1976 \begin_layout Plain Layout
1993 \begin_layout Section
1997 \begin_layout Standard
1998 \begin_inset Flex URL
2001 \begin_layout Plain Layout
2003 http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
2011 \begin_layout Standard
2012 \begin_inset Preview
2014 \begin_layout Standard
2018 \begin_layout Plain Layout
2024 iangle{35} % Angle of the inclined plane
2027 \begin_layout Plain Layout
2036 \begin_layout Plain Layout
2042 arcr{0.5cm} % Radius of the arc used to indicate angles
2045 \begin_layout Plain Layout
2049 \begin_layout Plain Layout
2056 \begin_layout Plain Layout
2058 force/.style={>=latex,draw=blue,fill=blue},
2061 \begin_layout Plain Layout
2063 axis/.style={densely dashed,gray,font=
2068 \begin_layout Plain Layout
2070 M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2073 \begin_layout Plain Layout
2075 m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2078 \begin_layout Plain Layout
2080 plane/.style={draw=black,fill=blue!10},
2083 \begin_layout Plain Layout
2085 string/.style={draw=red, thick},
2088 \begin_layout Plain Layout
2090 pulley/.style={thick},
2093 \begin_layout Plain Layout
2098 \begin_layout Plain Layout
2102 \begin_layout Plain Layout
2106 matrix[column sep=1cm] {
2109 \begin_layout Plain Layout
2114 \begin_layout Plain Layout
2118 draw[plane] (0,-1) coordinate (base)
2121 \begin_layout Plain Layout
2123 -- coordinate[pos=0.5] (mid) ++(
2125 iangle:3) coordinate (top)
2128 \begin_layout Plain Layout
2133 \begin_layout Plain Layout
2137 path (mid) node[M,rotate=
2139 iangle,yshift=0.25cm] (M) {};
2142 \begin_layout Plain Layout
2146 draw[pulley] (top) -- ++(
2148 iangle:0.25) circle (0.25cm)
2151 \begin_layout Plain Layout
2155 iangle:0.5) coordinate (pulley);
2158 \begin_layout Plain Layout
2162 draw[string] (M.east) -- ++(
2164 iangle:1.5cm) arc (90+
2169 \begin_layout Plain Layout
2171 -- ++(0,-1) node[m] {};
2174 \begin_layout Plain Layout
2178 \begin_layout Plain Layout
2191 \begin_layout Plain Layout
2204 \begin_layout Plain Layout
2209 \begin_layout Plain Layout
2213 \begin_layout Plain Layout
2218 \begin_layout Plain Layout
2220 %% Free body diagram of M
2223 \begin_layout Plain Layout
2227 begin{scope}[rotate=
2232 \begin_layout Plain Layout
2236 node[M,transform shape] (M) {};
2239 \begin_layout Plain Layout
2241 % Draw axes and help lines
2244 \begin_layout Plain Layout
2248 \begin_layout Plain Layout
2253 \begin_layout Plain Layout
2257 draw (0,-1) -- (0,2) node[right] {$+y$};
2260 \begin_layout Plain Layout
2264 draw (M) -- ++(2,0) node[right] {$+x$};
2267 \begin_layout Plain Layout
2270 The code is a bit awkward.
2273 \begin_layout Plain Layout
2277 \begin_layout Plain Layout
2281 draw[solid,shorten >=0.5pt] (
2290 \begin_layout Plain Layout
2303 \begin_layout Plain Layout
2318 \begin_layout Plain Layout
2323 \begin_layout Plain Layout
2327 \begin_layout Plain Layout
2332 \begin_layout Plain Layout
2337 \begin_layout Plain Layout
2339 % Assuming that Mg = 1.
2340 The normal force will therefore be cos(alpha)
2343 \begin_layout Plain Layout
2347 draw (M.center) -- ++(0,{cos(
2349 iangle)}) node[above right] {$N$};
2352 \begin_layout Plain Layout
2356 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2359 \begin_layout Plain Layout
2363 draw (M.east) -- ++(1,0) node[above] {$T$};
2366 \begin_layout Plain Layout
2371 \begin_layout Plain Layout
2375 \begin_layout Plain Layout
2382 \begin_layout Plain Layout
2384 % Draw gravity force.
2385 The code is put outside the rotated
2388 \begin_layout Plain Layout
2390 % scope for simplicity.
2391 No need to do any angle calculations.
2395 \begin_layout Plain Layout
2399 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2402 \begin_layout Plain Layout
2407 \begin_layout Plain Layout
2411 \begin_layout Plain Layout
2416 \begin_layout Plain Layout
2421 \begin_layout Plain Layout
2423 % Free body diagram of m
2426 \begin_layout Plain Layout
2433 \begin_layout Plain Layout
2437 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2440 \begin_layout Plain Layout
2445 \begin_layout Plain Layout
2449 draw (m.north) -- ++(0,1) node[above] {$T'$};
2452 \begin_layout Plain Layout
2456 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2459 \begin_layout Plain Layout
2464 \begin_layout Plain Layout
2468 \begin_layout Plain Layout
2477 \begin_layout Plain Layout
2482 \begin_layout Plain Layout
2489 \begin_layout Plain Layout