1 #LyX 2.4 created this file. For more info see https://www.lyx.org/
5 \save_transient_properties true
6 \origin /systemlyxdir/examples/Graphics_and_Insets/
10 \usepackage[all, knot]{xy}
18 \usetikzlibrary{scopes}
20 \use_default_options false
21 \maintain_unincluded_children no
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
35 \font_typewriter_osf false
36 \font_sf_scale 100 100
37 \font_tt_scale 100 100
39 \use_dash_ligatures false
41 \default_output_format pdf
43 \bibtex_command default
44 \index_command default
45 \paperfontsize default
50 \use_package amsmath 1
51 \use_package amssymb 1
54 \use_package mathdots 1
55 \use_package mathtools 1
57 \use_package stackrel 1
58 \use_package stmaryrd 1
59 \use_package undertilde 1
61 \cite_engine_type default
65 \paperorientation portrait
77 \paragraph_separation indent
78 \paragraph_indentation default
80 \math_numbering_side default
85 \paperpagestyle default
87 \tracking_changes false
90 \postpone_fragile_content false
94 \docbook_table_output 0
95 \docbook_mathml_prefix 1
100 \begin_layout Section
104 \begin_layout Standard
105 In order to properly typeset the document and have instant preview working,
106 the following packages have to be installed:
109 \begin_layout LyX-Code
121 \begin_layout Standard
122 Due to the use of postscript specials in Section
123 \begin_inset CommandInset ref
125 reference "sec:PSTricks"
131 only the Postscript or PDF (ps2pdf) output formats will correctly render the included images.
132 Starting with TeX Live 2021,
133 you may need to add the flag
135 -dALLOWPSTRANSPARENCY
142 The PDF (Xe\SpecialChar TeX
143 ) output seems to also work,
144 while trying to typeset the document with
152 will generate errors.
155 \begin_layout Section
159 \begin_layout Standard
160 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic examples,
162 \begin_inset Flex URL
165 \begin_layout Plain Layout
167 https://www.ctan.org/tex-archive/macros/generic/diagrams/xypic/doc/xyguide.pdf
175 \begin_layout Description
179 \begin_layout Standard
182 \begin_layout Standard
186 \begin_layout Plain Layout
193 \begin_layout Plain Layout
201 \begin_layout Plain Layout
218 \begin_layout Plain Layout
230 \begin_layout Plain Layout
238 \begin_layout Plain Layout
246 \begin_layout Plain Layout
254 \begin_layout Plain Layout
262 \begin_layout Plain Layout
279 \begin_layout Description
283 \begin_layout Standard
286 \begin_layout Standard
290 \begin_layout Plain Layout
297 \begin_layout Plain Layout
302 \begin_layout Plain Layout
307 \begin_layout Plain Layout
311 crv{~*=<.5pt>{.} (0,30)}?(.75)*
316 \begin_layout Plain Layout
321 \begin_layout Plain Layout
326 \begin_layout Plain Layout
330 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
335 \begin_layout Plain Layout
340 \begin_layout Plain Layout
345 \begin_layout Plain Layout
349 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
354 \begin_layout Plain Layout
359 \begin_layout Plain Layout
364 \begin_layout Plain Layout
368 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
373 \begin_layout Plain Layout
378 \begin_layout Plain Layout
383 \begin_layout Plain Layout
387 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
392 \begin_layout Plain Layout
409 \begin_layout Description
413 \begin_layout Standard
416 \begin_layout Standard
420 \begin_layout Plain Layout
427 \begin_layout Plain Layout
436 \begin_layout Plain Layout
443 \begin_layout Plain Layout
450 \begin_layout Plain Layout
457 \begin_layout Plain Layout
474 \begin_layout Description
478 \begin_layout Standard
481 \begin_layout Standard
485 \begin_layout Plain Layout
492 \begin_layout Plain Layout
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
527 \begin_layout Plain Layout
531 ellipse(3,1)__,=:a(-180){-};
534 \begin_layout Plain Layout
538 ellipse(3,1)__,=:a(-180){-};
541 \begin_layout Plain Layout
545 ellipse(3,1)__,=:a(180){-};
548 \begin_layout Plain Layout
555 \begin_layout Plain Layout
562 \begin_layout Plain Layout
567 \begin_layout Plain Layout
572 \begin_layout Plain Layout
577 \begin_layout Plain Layout
582 \begin_layout Plain Layout
589 \begin_layout Plain Layout
594 \begin_layout Plain Layout
599 \begin_layout Plain Layout
604 \begin_layout Plain Layout
609 \begin_layout Plain Layout
616 \begin_layout Plain Layout
623 \begin_layout Plain Layout
630 \begin_layout Plain Layout
634 crv{(-8,7) & (-3,5)};
637 \begin_layout Plain Layout
642 \begin_layout Plain Layout
647 \begin_layout Plain Layout
652 \begin_layout Plain Layout
656 crv{(3,-10) & (9,-10)};
659 \begin_layout Plain Layout
664 \begin_layout Plain Layout
669 \begin_layout Plain Layout
673 crv{(-3,-10) & (-9,-10)};
676 \begin_layout Plain Layout
681 \begin_layout Plain Layout
686 \begin_layout Plain Layout
691 \begin_layout Plain Layout
696 \begin_layout Plain Layout
701 \begin_layout Plain Layout
706 \begin_layout Plain Layout
713 \begin_layout Plain Layout
720 \begin_layout Plain Layout
724 crv{(13,-6) & (2,-8)};
727 \begin_layout Plain Layout
731 crv{(-13,-6) & (-2,-8)};
734 \begin_layout Plain Layout
751 \begin_layout Standard
755 \begin_layout Plain Layout
762 \begin_layout Plain Layout
766 bullet}="RU"+(1,3)*{x^{
771 \begin_layout Plain Layout
775 bullet}="RD"+(2.5,2)*{x^{
780 \begin_layout Plain Layout
784 bullet}="LU"+(-1,2)*{x};
787 \begin_layout Plain Layout
791 bullet}="LD"+(-1,2)*{x};
794 \begin_layout Plain Layout
807 \begin_layout Plain Layout
811 crv{(-4,-2) & (-4,1)};
814 \begin_layout Plain Layout
824 \begin_layout Plain Layout
830 \begin_layout Plain Layout
835 crv{(7,-10) & (-7,-10)};
838 \begin_layout Plain Layout
842 bullet}="RDD"+(2.5,-1)*{x^{
847 \begin_layout Plain Layout
851 bullet}="LDD"+(-1,-3)*{x};
854 \begin_layout Plain Layout
858 bullet}="RUD"+(3.5,1)*{x^{
863 \begin_layout Plain Layout
870 \begin_layout Plain Layout
876 \begin_layout Plain Layout
884 \begin_layout Plain Layout
892 \begin_layout Plain Layout
900 \begin_layout Plain Layout
911 \begin_layout Plain Layout
919 \begin_layout Plain Layout
927 \begin_layout Plain Layout
935 \begin_layout Plain Layout
940 crv{~*=<4pt>{.}(0,-18)};
946 \begin_layout Plain Layout
963 \begin_layout Description
967 \begin_layout Standard
970 \begin_layout Standard
974 \begin_layout Plain Layout
978 xy (-15,0)*{};(15,0)*{};
981 \begin_layout Plain Layout
988 \begin_layout Plain Layout
999 \begin_layout Plain Layout
1007 dir{<}+(-4,0)*{F(x)};
1010 \begin_layout Plain Layout
1015 \begin_layout Plain Layout
1020 \begin_layout Plain Layout
1025 \begin_layout Plain Layout
1030 \begin_layout Plain Layout
1035 \begin_layout Plain Layout
1039 crv{(-4,-21)&(5,-15)};
1042 \begin_layout Plain Layout
1051 \begin_layout Plain Layout
1058 \begin_layout Plain Layout
1064 widetilde{F(i_x)}} ;
1067 \begin_layout Plain Layout
1076 \begin_layout Plain Layout
1083 \begin_layout Plain Layout
1088 \begin_layout Plain Layout
1093 \begin_layout Plain Layout
1097 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1100 \begin_layout Plain Layout
1105 \begin_layout Plain Layout
1110 \begin_layout Plain Layout
1114 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1117 \begin_layout Plain Layout
1134 \begin_layout Description
1138 \begin_layout Standard
1139 \begin_inset Preview
1141 \begin_layout Standard
1145 \begin_layout Plain Layout
1152 \begin_layout Plain Layout
1161 \begin_layout Plain Layout
1168 \begin_layout Plain Layout
1177 \begin_layout Plain Layout
1186 \begin_layout Plain Layout
1201 \begin_layout Plain Layout
1216 \begin_inset Preview
1218 \begin_layout Standard
1222 \begin_layout Plain Layout
1229 \begin_layout Plain Layout
1236 \begin_layout Plain Layout
1243 \begin_layout Plain Layout
1247 ar@/^.9pc/ "1";"2"};
1250 \begin_layout Plain Layout
1254 ar@/_.9pc/ "1";"2"};
1257 \begin_layout Plain Layout
1264 \begin_layout Plain Layout
1271 \begin_layout Plain Layout
1275 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1278 \begin_layout Plain Layout
1282 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1285 \begin_layout Plain Layout
1289 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1292 \begin_layout Plain Layout
1299 \begin_layout Plain Layout
1306 \begin_layout Plain Layout
1313 \begin_layout Plain Layout
1320 \begin_layout Plain Layout
1327 \begin_layout Plain Layout
1334 \begin_layout Plain Layout
1341 \begin_layout Plain Layout
1345 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1348 \begin_layout Plain Layout
1352 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1355 \begin_layout Plain Layout
1372 \begin_layout Description
1376 \begin_layout Standard
1377 \begin_inset Preview
1379 \begin_layout Standard
1383 \begin_layout Plain Layout
1388 Natural transformation between functors.
1391 \begin_layout Plain Layout
1398 \begin_layout Plain Layout
1405 \begin_layout Plain Layout
1412 \begin_layout Plain Layout
1416 ar@/^.25pc/ "a";"b"};
1419 \begin_layout Plain Layout
1423 ar@/_.25pc/"a";"c"};
1426 \begin_layout Plain Layout
1430 ar@/_.15pc/ "b";"c"};
1433 \begin_layout Plain Layout
1438 \begin_layout Plain Layout
1445 \begin_layout Plain Layout
1452 \begin_layout Plain Layout
1459 \begin_layout Plain Layout
1463 ar@/^.25pc/ "ta";"tb"};
1466 \begin_layout Plain Layout
1470 ar@/_.25pc/ "ta";"tc"};
1473 \begin_layout Plain Layout
1477 ar@/_.15pc/ "tb";"tc"};
1480 \begin_layout Plain Layout
1485 \begin_layout Plain Layout
1492 \begin_layout Plain Layout
1499 \begin_layout Plain Layout
1506 \begin_layout Plain Layout
1510 ar@/^.25pc/@{.>} "ba";"bb"};
1513 \begin_layout Plain Layout
1517 ar@/_.25pc/ "ba";"bc"};
1520 \begin_layout Plain Layout
1524 ar@/_.15pc/ "bb";"bc"};
1527 \begin_layout Plain Layout
1532 \begin_layout Plain Layout
1536 ar@/_.15pc/ "ta";"ba"};
1539 \begin_layout Plain Layout
1543 ar@/_.15pc/ "tb";"bb"};
1546 \begin_layout Plain Layout
1550 ar@/_.15pc/ "tc";"bc"};
1553 \begin_layout Plain Layout
1555 %START ARROWS AND LABELS
1558 \begin_layout Plain Layout
1563 \begin_layout Plain Layout
1568 \begin_layout Plain Layout
1572 ar@/^.35pc/^F "DF";"CF"};
1575 \begin_layout Plain Layout
1580 \begin_layout Plain Layout
1585 \begin_layout Plain Layout
1589 ar@/_.35pc/_G "DF";"CF"};
1592 \begin_layout Plain Layout
1597 \begin_layout Plain Layout
1602 \begin_layout Plain Layout
1611 \begin_layout Plain Layout
1616 \begin_layout Plain Layout
1621 \begin_layout Plain Layout
1638 \begin_layout Section
1642 \begin_layout Standard
1643 \begin_inset Preview
1645 \begin_layout Standard
1649 \begin_layout Plain Layout
1653 textipa{Ekspl@"neIS@n}
1666 \begin_layout Section
1670 \begin_layout Standard
1671 \begin_inset Preview
1673 \begin_layout Standard
1677 \begin_layout Plain Layout
1681 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1692 \begin_inset Preview
1694 \begin_layout Standard
1698 \begin_layout Plain Layout
1721 \begin_layout Section
1723 \begin_inset CommandInset label
1732 \begin_layout Standard
1733 Some simple graphing examples.
1736 \begin_layout Subsection
1740 \begin_layout Standard
1741 \begin_inset Preview
1743 \begin_layout Standard
1747 \begin_layout Plain Layout
1751 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1754 \begin_layout Plain Layout
1758 psaxes{->}(0,0)(0,-3)(10,3)
1761 \begin_layout Plain Layout
1765 uput[-90](10,0){$x$}
1767 uput[0](0,3){$f(x)$}
1770 \begin_layout Plain Layout
1774 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1777 \begin_layout Plain Layout
1794 \begin_layout Subsection
1795 Inline data plotting
1798 \begin_layout Standard
1800 \begin_inset Preview
1802 \begin_layout Standard
1807 \begin_layout Plain Layout
1811 begin{pspicture*}(-1.5,-1.5)(11,5)
1814 \begin_layout Plain Layout
1818 psaxes{->}(0,0)(0,0)(10,5)
1821 \begin_layout Plain Layout
1825 psset{linewidth=2.5pt}
1828 \begin_layout Plain Layout
1832 rput(5.0,-1.0){Speed [MPH]}
1835 \begin_layout Plain Layout
1841 begin{rotate}{90}Cost [Dollars]
1846 \begin_layout Plain Layout
1852 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1855 \begin_layout Plain Layout
1859 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1864 \begin_layout Plain Layout
1881 \begin_layout Subsection
1885 \begin_layout Standard
1886 \begin_inset Preview
1888 \begin_layout Standard
1892 \begin_layout Plain Layout
1896 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1899 \begin_layout Plain Layout
1903 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul cos 100 t mul sin}
1906 \begin_layout Plain Layout
1921 \begin_inset space \hfill{}
1925 \begin_inset Preview
1927 \begin_layout Standard
1931 \begin_layout Plain Layout
1935 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1938 \begin_layout Plain Layout
1942 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t mul cos 100 t mul sin}
1945 \begin_layout Plain Layout
1960 \begin_inset space \hfill{}
1964 \begin_inset Preview
1966 \begin_layout Standard
1970 \begin_layout Plain Layout
1974 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1977 \begin_layout Plain Layout
1981 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t mul cos 200 t mul sin}
1984 \begin_layout Plain Layout
1999 \begin_inset space \hfill{}
2003 \begin_inset Preview
2005 \begin_layout Standard
2009 \begin_layout Plain Layout
2013 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
2016 \begin_layout Plain Layout
2020 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t mul cos 200 t mul sin}
2023 \begin_layout Plain Layout
2040 \begin_layout Section
2044 \begin_layout Standard
2045 \begin_inset Flex URL
2048 \begin_layout Plain Layout
2050 http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
2058 \begin_layout Standard
2059 \begin_inset Preview
2061 \begin_layout Standard
2065 \begin_layout Plain Layout
2071 iangle{35} % Angle of the inclined plane
2074 \begin_layout Plain Layout
2083 \begin_layout Plain Layout
2089 arcr{0.5cm} % Radius of the arc used to indicate angles
2092 \begin_layout Plain Layout
2096 \begin_layout Plain Layout
2103 \begin_layout Plain Layout
2105 force/.style={>=latex,draw=blue,fill=blue},
2108 \begin_layout Plain Layout
2110 axis/.style={densely dashed,gray,font=
2115 \begin_layout Plain Layout
2117 M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2120 \begin_layout Plain Layout
2122 m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2125 \begin_layout Plain Layout
2127 plane/.style={draw=black,fill=blue!10},
2130 \begin_layout Plain Layout
2132 string/.style={draw=red,
2136 \begin_layout Plain Layout
2138 pulley/.style={thick},
2141 \begin_layout Plain Layout
2146 \begin_layout Plain Layout
2150 \begin_layout Plain Layout
2154 matrix[column sep=1cm] {
2157 \begin_layout Plain Layout
2162 \begin_layout Plain Layout
2166 draw[plane] (0,-1) coordinate (base)
2169 \begin_layout Plain Layout
2171 -- coordinate[pos=0.5] (mid) ++(
2173 iangle:3) coordinate (top)
2176 \begin_layout Plain Layout
2181 \begin_layout Plain Layout
2185 path (mid) node[M,rotate=
2187 iangle,yshift=0.25cm] (M) {};
2190 \begin_layout Plain Layout
2194 draw[pulley] (top) -- ++(
2196 iangle:0.25) circle (0.25cm)
2199 \begin_layout Plain Layout
2203 iangle:0.5) coordinate (pulley);
2206 \begin_layout Plain Layout
2210 draw[string] (M.east) -- ++(
2212 iangle:1.5cm) arc (90+
2217 \begin_layout Plain Layout
2219 -- ++(0,-1) node[m] {};
2222 \begin_layout Plain Layout
2226 \begin_layout Plain Layout
2239 \begin_layout Plain Layout
2252 \begin_layout Plain Layout
2257 \begin_layout Plain Layout
2261 \begin_layout Plain Layout
2266 \begin_layout Plain Layout
2268 %% Free body diagram of M
2271 \begin_layout Plain Layout
2275 begin{scope}[rotate=
2280 \begin_layout Plain Layout
2284 node[M,transform shape] (M) {};
2287 \begin_layout Plain Layout
2289 % Draw axes and help lines
2292 \begin_layout Plain Layout
2296 \begin_layout Plain Layout
2301 \begin_layout Plain Layout
2305 draw (0,-1) -- (0,2) node[right] {$+y$};
2308 \begin_layout Plain Layout
2312 draw (M) -- ++(2,0) node[right] {$+x$};
2315 \begin_layout Plain Layout
2318 The code is a bit awkward.
2321 \begin_layout Plain Layout
2325 \begin_layout Plain Layout
2329 draw[solid,shorten >=0.5pt] (
2338 \begin_layout Plain Layout
2351 \begin_layout Plain Layout
2366 \begin_layout Plain Layout
2371 \begin_layout Plain Layout
2375 \begin_layout Plain Layout
2380 \begin_layout Plain Layout
2385 \begin_layout Plain Layout
2387 % Assuming that Mg = 1.
2388 The normal force will therefore be cos(alpha)
2391 \begin_layout Plain Layout
2395 draw (M.center) -- ++(0,{cos(
2397 iangle)}) node[above right] {$N$};
2400 \begin_layout Plain Layout
2404 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2407 \begin_layout Plain Layout
2411 draw (M.east) -- ++(1,0) node[above] {$T$};
2414 \begin_layout Plain Layout
2419 \begin_layout Plain Layout
2423 \begin_layout Plain Layout
2430 \begin_layout Plain Layout
2432 % Draw gravity force.
2433 The code is put outside the rotated
2436 \begin_layout Plain Layout
2438 % scope for simplicity.
2439 No need to do any angle calculations.
2443 \begin_layout Plain Layout
2447 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2450 \begin_layout Plain Layout
2455 \begin_layout Plain Layout
2459 \begin_layout Plain Layout
2464 \begin_layout Plain Layout
2469 \begin_layout Plain Layout
2471 % Free body diagram of m
2474 \begin_layout Plain Layout
2481 \begin_layout Plain Layout
2485 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2488 \begin_layout Plain Layout
2493 \begin_layout Plain Layout
2497 draw (m.north) -- ++(0,1) node[above] {$T'$};
2500 \begin_layout Plain Layout
2504 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2507 \begin_layout Plain Layout
2512 \begin_layout Plain Layout
2516 \begin_layout Plain Layout
2525 \begin_layout Plain Layout
2530 \begin_layout Plain Layout
2537 \begin_layout Plain Layout