#LyX 2.2 created this file. For more info see http://www.lyx.org/ \lyxformat 501 \begin_document \begin_header \origin /systemlyxdir/examples/ \textclass article \begin_preamble \usepackage{etex} \usepackage[all, knot]{xy} \xyoption{arc} \usepackage{qtree} \usepackage{tipa} \usepackage{pstricks} \usepackage{pst-plot} \usepackage{rotating} \usepackage{tikz} \usetikzlibrary{scopes} \end_preamble \use_default_options false \maintain_unincluded_children false \language english \language_package default \inputencoding auto \fontencoding global \font_roman "lmodern" "default" \font_sans "default" "default" \font_typewriter "default" "default" \font_math "auto" "auto" \font_default_family default \use_non_tex_fonts false \font_sc false \font_osf false \font_sf_scale 100 100 \font_tt_scale 100 100 \graphics default \default_output_format pdf \output_sync 0 \bibtex_command default \index_command default \paperfontsize default \spacing single \use_hyperref false \papersize default \use_geometry false \use_package amsmath 1 \use_package amssymb 1 \use_package cancel 0 \use_package esint 1 \use_package mathdots 1 \use_package mathtools 0 \use_package mhchem 1 \use_package stackrel 0 \use_package stmaryrd 0 \use_package undertilde 0 \cite_engine basic \cite_engine_type default \biblio_style plain \use_bibtopic false \use_indices false \paperorientation portrait \suppress_date false \justification true \use_refstyle 0 \index Index \shortcut idx \color #008000 \end_index \secnumdepth 3 \tocdepth 3 \paragraph_separation indent \paragraph_indentation default \quotes_language english \papercolumns 1 \papersides 1 \paperpagestyle default \tracking_changes false \output_changes false \html_math_output 0 \html_css_as_file 0 \html_be_strict true \end_header \begin_body \begin_layout Section Introduction \end_layout \begin_layout Standard In order to properly typeset the document and have instant preview working, the following packages have to be installed: \end_layout \begin_layout LyX-Code xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf, etex \end_layout \begin_layout Standard Due to the use of postscript specials in Section \begin_inset CommandInset ref LatexCommand ref reference "sec:PSTricks" \end_inset , only the Postscript or PDF (ps2pdf) output formats will correctly render the included images. However, the PDF (Xe\SpecialCharNoPassThru TeX ) output seems to also work, while trying to typeset the document with \family typewriter pdflatex \family default or \family typewriter pdflualatex \family default will generate errors. \end_layout \begin_layout Section Diagrams by XY(-pic) \end_layout \begin_layout Standard Few examples of diagrams were taken from Aaron Landa's archive of xy-pic examples, see \begin_inset Flex URL status collapsed \begin_layout Plain Layout http://www.math.columbia.edu/~lauda/xy/ \end_layout \end_inset . \end_layout \begin_layout Description Braid \end_layout \begin_layout Standard \begin_inset Preview \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash xy \end_layout \begin_layout Plain Layout (5,10)*{}; (-10,-10)*{} ** \backslash crv{(6,-2)&(-12,4)} \end_layout \begin_layout Plain Layout \backslash POS?(.25)*{ \backslash hole}="x" \backslash POS?(.45)*{ \backslash hole}="y" \backslash POS?(.6)*{ \backslash hole}="z"; \end_layout \begin_layout Plain Layout "y"+(0,-1); (2,-10)*{} ** \backslash crv{} \backslash POS?(.2)*{ \backslash hole}="M"; \end_layout \begin_layout Plain Layout (-10,10)*{}; "z" ** \backslash crv{(-9,0)}; \end_layout \begin_layout Plain Layout "z"; "M" ** \backslash crv{}; \end_layout \begin_layout Plain Layout "M"; "x" ** \backslash crv{(5,0)}; \end_layout \begin_layout Plain Layout "x"; "y" ** \backslash crv{(0,7) & (-5,6)}; \end_layout \begin_layout Plain Layout \backslash endxy \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Description Knots \end_layout \begin_layout Standard \begin_inset Preview \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash xy \end_layout \begin_layout Plain Layout (6,9)*{}="1"; \end_layout \begin_layout Plain Layout (-8.5,-1)*{}="2"; \end_layout \begin_layout Plain Layout "1";"2" ** \backslash crv{~*=<.5pt>{.} (0,30)}?(.75)* \backslash dir{>}+(-2,2)*{z}; \end_layout \begin_layout Plain Layout (-6.5,8)*{}="1"; \end_layout \begin_layout Plain Layout (-.5,-9)*{}="2"; \end_layout \begin_layout Plain Layout "1";"2" ** \backslash crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)* \backslash dir{>}+(-2,-2)*{u}; \end_layout \begin_layout Plain Layout (-9.5,-3.35)*{}="1"; \end_layout \begin_layout Plain Layout (8.5,-3)*{}="2"; \end_layout \begin_layout Plain Layout "1";"2" ** \backslash crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)* \backslash dir{>}+(-1,-3)*{x}; \end_layout \begin_layout Plain Layout (1,-10)*{}="1"; \end_layout \begin_layout Plain Layout (6.5,7.13)*{}="2"; \end_layout \begin_layout Plain Layout "1";"2" ** \backslash crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)* \backslash dir{>}+(3,-1)*{y}; \end_layout \begin_layout Plain Layout (11,-1)*{}="1"; \end_layout \begin_layout Plain Layout (-4,8)*{}="2"; \end_layout \begin_layout Plain Layout "1";"2" ** \backslash crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)* \backslash dir{>}+(1,2)*{w}; \end_layout \begin_layout Plain Layout \backslash endxy \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Description Circles \end_layout \begin_layout Standard \begin_inset Preview \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash xy \end_layout \begin_layout Plain Layout (0,0)* \backslash xycircle(14,8){++ \backslash dir{<}}; \end_layout \begin_layout Plain Layout (0,0)* \backslash xycircle<10pt>{{.}}; \end_layout \begin_layout Plain Layout (0,0)* \backslash xycircle(5,2){:}; \end_layout \begin_layout Plain Layout (0,15)* \backslash xycircle(10,4){--}; \end_layout \begin_layout Plain Layout \backslash endxy \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Description Cobordism \end_layout \begin_layout Standard \begin_inset Preview \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash xy \end_layout \begin_layout Plain Layout (0,0)* \backslash ellipse(3,1){.}; \end_layout \begin_layout Plain Layout (0,0)* \backslash ellipse(3,1)__,=:a(-180){-}; \end_layout \begin_layout Plain Layout (-6,-8)* \backslash ellipse(3,1){.}; \end_layout \begin_layout Plain Layout (6,-8)* \backslash ellipse(3,1){.}; \end_layout \begin_layout Plain Layout (0,-8)* \backslash ellipse(3,1){.}; \end_layout \begin_layout Plain Layout (-6,-8)* \backslash ellipse(3,1)__,=:a(-180){-}; \end_layout \begin_layout Plain Layout (6,-8)* \backslash ellipse(3,1)__,=:a(-180){-}; \end_layout \begin_layout Plain Layout (0,-8)* \backslash ellipse(3,1)__,=:a(180){-}; \end_layout \begin_layout Plain Layout (-3,6)* \backslash ellipse(3,1){-}; \end_layout \begin_layout Plain Layout (3,6)* \backslash ellipse(3,1){-}; \end_layout \begin_layout Plain Layout (-3,12)*{}="1"; \end_layout \begin_layout Plain Layout (3,12)*{}="2"; \end_layout \begin_layout Plain Layout (-9,12)*{}="A2"; \end_layout \begin_layout Plain Layout (9,12)*{}="B2"; \end_layout \begin_layout Plain Layout "1";"2" ** \backslash crv{(-3,7) & (3,7)}; \end_layout \begin_layout Plain Layout (-3,0)*{}="A"; \end_layout \begin_layout Plain Layout (3,0)*{}="B"; \end_layout \begin_layout Plain Layout (-3,1)*{}="A1"; \end_layout \begin_layout Plain Layout (3,1)*{}="B1"; \end_layout \begin_layout Plain Layout "A";"A1" ** \backslash dir{-}; \end_layout \begin_layout Plain Layout "B";"B1" ** \backslash dir{-}; \end_layout \begin_layout Plain Layout "B2";"B1" ** \backslash crv{(8,7) & (3,5)}; \end_layout \begin_layout Plain Layout "A2";"A1" ** \backslash crv{(-8,7) & (-3,5)}; \end_layout \begin_layout Plain Layout %REFLECT \end_layout \begin_layout Plain Layout (3,-16)*{}="1"; \end_layout \begin_layout Plain Layout (9,-16)*{}="2"; \end_layout \begin_layout Plain Layout "1";"2" ** \backslash crv{(3,-10) & (9,-10)}; \end_layout \begin_layout Plain Layout (-3,-16)*{}="1"; \end_layout \begin_layout Plain Layout (-9,-16)*{}="2"; \end_layout \begin_layout Plain Layout "1";"2" ** \backslash crv{(-3,-10) & (-9,-10)}; \end_layout \begin_layout Plain Layout (-15,-16)*{}="A2"; \end_layout \begin_layout Plain Layout (15,-16)*{}="B2"; \end_layout \begin_layout Plain Layout (-3,0)*{}="A"; \end_layout \begin_layout Plain Layout (3,0)*{}="B"; \end_layout \begin_layout Plain Layout (-3,-1)*{}="A1"; \end_layout \begin_layout Plain Layout (3,-1)*{}="B1"; \end_layout \begin_layout Plain Layout "A";"A1" ** \backslash dir{-}; \end_layout \begin_layout Plain Layout "B";"B1" ** \backslash dir{-}; \end_layout \begin_layout Plain Layout "B2";"B1" ** \backslash crv{(13,-6) & (2,-8)}; \end_layout \begin_layout Plain Layout "A2";"A1" ** \backslash crv{(-13,-6) & (-2,-8)}; \end_layout \begin_layout Plain Layout \backslash endxy \end_layout \end_inset \end_layout \end_inset \begin_inset Preview \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash xy 0;/r.18pc/: \end_layout \begin_layout Plain Layout (20,2)*{ \backslash bullet}="RU"+(1,3)*{x^{ \backslash ast}}; \end_layout \begin_layout Plain Layout (16,-3)*{ \backslash bullet}="RD"+(2.5,2)*{x^{ \backslash ast}}; \end_layout \begin_layout Plain Layout (-16,2)*{ \backslash bullet}="LU"+(-1,2)*{x}; \end_layout \begin_layout Plain Layout (-20,-3)*{ \backslash bullet}="LD"+(-1,2)*{x}; \end_layout \begin_layout Plain Layout "RU";"RD" ** \backslash crv{(4,2) & (4,-1)}; ?(.1)* \backslash dir{<}; ?(.85)* \backslash dir{<}; \end_layout \begin_layout Plain Layout "LD";"LU" ** \backslash crv{(-4,-2) & (-4,1)}; \end_layout \begin_layout Plain Layout ?(.08)* \backslash dir{<}; ?(.85)* \backslash dir{<}; \end_layout \begin_layout Plain Layout (7.5,0)*{}="x1"; (-7.5,0)*{}="x2"; \end_layout \begin_layout Plain Layout "x1"; "x2" ** \backslash crv{(7,-10) & (-7,-10)}; \end_layout \begin_layout Plain Layout (16,-20)*{ \backslash bullet}="RDD"+(2.5,-1)*{x^{ \backslash ast}}; \end_layout \begin_layout Plain Layout (-20,-20)*{ \backslash bullet}="LDD"+(-1,-3)*{x}; \end_layout \begin_layout Plain Layout (20,-12.5)*{ \backslash bullet}="RUD"+(3.5,1)*{x^{ \backslash ast}}; \end_layout \begin_layout Plain Layout (-16,-15)*{ \backslash bullet}="LUD"; \end_layout \begin_layout Plain Layout (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B"; \end_layout \begin_layout Plain Layout "RD"; "RDD" ** \backslash dir{-}; \end_layout \begin_layout Plain Layout "LD"; "LDD" ** \backslash dir{-}; \end_layout \begin_layout Plain Layout "A"; "LUD" ** \backslash dir{.}; \end_layout \begin_layout Plain Layout "RDD"; "LDD" ** \backslash crv{(0,-17)}; ?(.57)* \backslash dir{>}; \end_layout \begin_layout Plain Layout "RU"; "RUD" ** \backslash dir{-}; \end_layout \begin_layout Plain Layout "LU"; "A" ** \backslash dir{-}; \end_layout \begin_layout Plain Layout "B"; "RUD" ** \backslash crv{(18,-14.15)}; \end_layout \begin_layout Plain Layout "B"; "LUD" ** \backslash crv{~*=<4pt>{.}(0,-18)}; ?(.4)* \backslash dir{<}; \end_layout \begin_layout Plain Layout \backslash endxy \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Description Strings \end_layout \begin_layout Standard \begin_inset Preview \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash xy (-15,0)*{};(15,0)*{}; \end_layout \begin_layout Plain Layout \backslash endxy \end_layout \begin_layout Plain Layout \backslash qquad = \backslash qquad \backslash xy \end_layout \begin_layout Plain Layout (-10,12)*{}; (-10,-12)*{}; ** \backslash dir{-}?(.5)* \backslash dir{<}+(-4,0)*{F(x)}; \end_layout \begin_layout Plain Layout (-2,12)*{}="1"; \end_layout \begin_layout Plain Layout (6,-7) *{}="2"; \end_layout \begin_layout Plain Layout (14,-7) *{}="3"; \end_layout \begin_layout Plain Layout (14,-13)*{}="3'"; \end_layout \begin_layout Plain Layout (18,0) *={}=""; \end_layout \begin_layout Plain Layout "1";"2" ** \backslash crv{(-4,-21)&(5,-15)}; \end_layout \begin_layout Plain Layout ?(.15)* \backslash dir{<}+(5,10)*{ \backslash overline{F(x)}}; \end_layout \begin_layout Plain Layout "2";"3" ** \backslash crv{(6,1)&(14,1)}; \end_layout \begin_layout Plain Layout ?(0)* \backslash dir{<}+(4,8)*{ \backslash widetilde{F(i_x)}} ; \end_layout \begin_layout Plain Layout ?(.95)* \backslash dir{<}+(5,-2)*{F( \backslash overline x)}; \end_layout \begin_layout Plain Layout "3";"3'" ** \backslash dir{-}; \end_layout \begin_layout Plain Layout (-2,6)*{}="X1"; \end_layout \begin_layout Plain Layout (-10,6)*{}="X2"; \end_layout \begin_layout Plain Layout "X1";"X2" ** \backslash crv{~*=<2pt>{.}(-2,-1)&(-10,-1)}; \end_layout \begin_layout Plain Layout (-2,-6)*{}="XA"; \end_layout \begin_layout Plain Layout (-10,-6)*{}="XB"; \end_layout \begin_layout Plain Layout "XA";"XB" ** \backslash crv{~*=<2pt>{.}(-2,1)&(-10,1)}; \end_layout \begin_layout Plain Layout \backslash endxy \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Description Categories \end_layout \begin_layout Standard \begin_inset Preview \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash xymatrix{ \end_layout \begin_layout Plain Layout (x \backslash otimes 1) \backslash otimes y \end_layout \begin_layout Plain Layout \backslash ar[rr]^{a_{x,1,y}} \end_layout \begin_layout Plain Layout \backslash ar[dr]_{r_x \backslash otimes 1_y} \end_layout \begin_layout Plain Layout && x \backslash otimes(1 \backslash otimes y) \end_layout \begin_layout Plain Layout \backslash ar[dl]^{1_x \backslash otimes \backslash ell_y } \backslash \backslash \end_layout \begin_layout Plain Layout & x \backslash otimes y } \end_layout \end_inset \end_layout \end_inset \begin_inset Preview \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash xy \end_layout \begin_layout Plain Layout (-9,0)*+{ \backslash bullet}="1"; \end_layout \begin_layout Plain Layout (0,0)*+{ \backslash bullet}="2"; \end_layout \begin_layout Plain Layout { \backslash ar@/^.9pc/ "1";"2"}; \end_layout \begin_layout Plain Layout { \backslash ar@/_.9pc/ "1";"2"}; \end_layout \begin_layout Plain Layout { \backslash ar@/^2pc/ "1";"2"}; \end_layout \begin_layout Plain Layout { \backslash ar@/_2pc/ "1";"2"}; \end_layout \begin_layout Plain Layout { \backslash ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ; \end_layout \begin_layout Plain Layout { \backslash ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ; \end_layout \begin_layout Plain Layout { \backslash ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ; \end_layout \begin_layout Plain Layout (0,0)*+{ \backslash bullet}="1"; \end_layout \begin_layout Plain Layout (9,0)*+{ \backslash bullet}="2"; \end_layout \begin_layout Plain Layout (18,0)*+{ \backslash bullet}="3"; \end_layout \begin_layout Plain Layout { \backslash ar "1";"2"}; \end_layout \begin_layout Plain Layout { \backslash ar "2";"3"}; \end_layout \begin_layout Plain Layout { \backslash ar@/^1pc/ "1";"2"}; \end_layout \begin_layout Plain Layout { \backslash ar@/_1pc/ "1";"2"}; \end_layout \begin_layout Plain Layout { \backslash ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ; \end_layout \begin_layout Plain Layout { \backslash ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ; \end_layout \begin_layout Plain Layout \backslash endxy \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Description Transformations \end_layout \begin_layout Standard \begin_inset Preview \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash xy %FIG.19. Natural transformation between functors. \end_layout \begin_layout Plain Layout (-26,-2)*+{ \backslash bullet}="a"; \end_layout \begin_layout Plain Layout (-12,3)*+{ \backslash bullet}="b"; \end_layout \begin_layout Plain Layout (-16,-5)*+{ \backslash bullet}="c"; \end_layout \begin_layout Plain Layout { \backslash ar@/^.25pc/ "a";"b"}; \end_layout \begin_layout Plain Layout { \backslash ar@/_.25pc/"a";"c"}; \end_layout \begin_layout Plain Layout { \backslash ar@/_.15pc/ "b";"c"}; \end_layout \begin_layout Plain Layout %START TOP \end_layout \begin_layout Plain Layout (12,10)*+{ \backslash bullet}="ta"; \end_layout \begin_layout Plain Layout (26,15)*+{ \backslash bullet}="tb"; \end_layout \begin_layout Plain Layout (22,8)*+{ \backslash bullet}="tc"; \end_layout \begin_layout Plain Layout { \backslash ar@/^.25pc/ "ta";"tb"}; \end_layout \begin_layout Plain Layout { \backslash ar@/_.25pc/ "ta";"tc"}; \end_layout \begin_layout Plain Layout { \backslash ar@/_.15pc/ "tb";"tc"}; \end_layout \begin_layout Plain Layout %START bottom \end_layout \begin_layout Plain Layout (12,-10)*+{ \backslash bullet}="ba"; \end_layout \begin_layout Plain Layout (26,-5)*+{ \backslash bullet}="bb"; \end_layout \begin_layout Plain Layout (22,-12)*+{ \backslash bullet}="bc"; \end_layout \begin_layout Plain Layout { \backslash ar@/^.25pc/@{.>} "ba";"bb"}; \end_layout \begin_layout Plain Layout { \backslash ar@/_.25pc/ "ba";"bc"}; \end_layout \begin_layout Plain Layout { \backslash ar@/_.15pc/ "bb";"bc"}; \end_layout \begin_layout Plain Layout %START CONNECT \end_layout \begin_layout Plain Layout { \backslash ar@/_.15pc/ "ta";"ba"}; \end_layout \begin_layout Plain Layout { \backslash ar@/_.15pc/ "tb";"bb"}; \end_layout \begin_layout Plain Layout { \backslash ar@/_.15pc/ "tc";"bc"}; \end_layout \begin_layout Plain Layout %START ARROWS AND LABELS \end_layout \begin_layout Plain Layout (-12,6)*{}="DF"; \end_layout \begin_layout Plain Layout (6,10)*{}="CF"; \end_layout \begin_layout Plain Layout { \backslash ar@/^.35pc/^F "DF";"CF"}; \end_layout \begin_layout Plain Layout (-12,-6)*{}="DF"; \end_layout \begin_layout Plain Layout (6,-10)*{}="CF"; \end_layout \begin_layout Plain Layout { \backslash ar@/_.35pc/_G "DF";"CF"}; \end_layout \begin_layout Plain Layout (-2,5)*{}="DF"; \end_layout \begin_layout Plain Layout (-2,-5)*{}="CF"; \end_layout \begin_layout Plain Layout { \backslash ar@{=>}^{ \backslash alpha} "DF";"CF"}; \end_layout \begin_layout Plain Layout (29,3)*{D}; \end_layout \begin_layout Plain Layout (-23,3)*{C}; \end_layout \begin_layout Plain Layout \backslash endxy \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Section IPA \end_layout \begin_layout Standard \begin_inset Preview \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash textipa{Ekspl@"neIS@n} \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Section QTree \end_layout \begin_layout Standard \begin_inset Preview \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ] \end_layout \end_inset \end_layout \end_inset \begin_inset Preview \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Tree [.$ \backslash sigma$ $ \backslash mu$ $ \backslash mu$ ] \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Section PSTricks \begin_inset CommandInset label LatexCommand label name "sec:PSTricks" \end_inset \end_layout \begin_layout Standard Some simple graphing examples. \end_layout \begin_layout Subsection Function plotting \end_layout \begin_layout Standard \begin_inset Preview \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash begin{pspicture*}(-1,-3.5)(10.5,3.5) \end_layout \begin_layout Plain Layout \backslash psaxes{->}(0,0)(0,-3)(10,3) \end_layout \begin_layout Plain Layout \backslash uput[-90](10,0){$x$} \backslash uput[0](0,3){$f(x)$} \end_layout \begin_layout Plain Layout \backslash psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln } \end_layout \begin_layout Plain Layout \backslash end{pspicture*} \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Subsection Inline data plotting \end_layout \begin_layout Standard \align center \begin_inset Preview \begin_layout Standard \align center \begin_inset ERT status open \begin_layout Plain Layout \backslash begin{pspicture*}(-1.5,-1.5)(11,5) \end_layout \begin_layout Plain Layout \backslash psaxes{->}(0,0)(0,0)(10,5) \end_layout \begin_layout Plain Layout \backslash psset{linewidth=2.5pt} \end_layout \begin_layout Plain Layout \backslash rput(5.0,-1.0){Speed [MPH]} \end_layout \begin_layout Plain Layout \backslash rput(-1.0,1.0){ \backslash begin{rotate}{90}Cost [Dollars] \backslash end{rotate}} \end_layout \begin_layout Plain Layout \backslash savedata{ \backslash mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}] \end_layout \begin_layout Plain Layout \backslash dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{ \backslash mydata} \end_layout \begin_layout Plain Layout \backslash end{pspicture*} \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Subsection Lissajous curves \end_layout \begin_layout Standard \begin_inset Preview \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash begin{pspicture*}(-1.1,-1.1)(1.1,1.1) \end_layout \begin_layout Plain Layout \backslash parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul cos 100 t mul sin} \end_layout \begin_layout Plain Layout \backslash end{pspicture*} \end_layout \end_inset \end_layout \end_inset \begin_inset space \hfill{} \end_inset \begin_inset Preview \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash begin{pspicture*}(-1.1,-1.1)(1.1,1.1) \end_layout \begin_layout Plain Layout \backslash parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t mul cos 100 t mul sin} \end_layout \begin_layout Plain Layout \backslash end{pspicture*} \end_layout \end_inset \end_layout \end_inset \begin_inset space \hfill{} \end_inset \begin_inset Preview \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash begin{pspicture*}(-1.1,-1.1)(1.1,1.1) \end_layout \begin_layout Plain Layout \backslash parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t mul cos 200 t mul sin} \end_layout \begin_layout Plain Layout \backslash end{pspicture*} \end_layout \end_inset \end_layout \end_inset \begin_inset space \hfill{} \end_inset \begin_inset Preview \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash begin{pspicture*}(-1.1,-1.1)(1.1,1.1) \end_layout \begin_layout Plain Layout \backslash parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t mul cos 200 t mul sin} \end_layout \begin_layout Plain Layout \backslash end{pspicture*} \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Section TikZ \end_layout \begin_layout Standard \begin_inset Flex URL status collapsed \begin_layout Plain Layout http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset Preview \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash def \backslash iangle{35} % Angle of the inclined plane \end_layout \begin_layout Plain Layout \backslash def \backslash down{-90} \end_layout \begin_layout Plain Layout \backslash def \backslash arcr{0.5cm} % Radius of the arc used to indicate angles \end_layout \begin_layout Plain Layout \end_layout \begin_layout Plain Layout \backslash begin{tikzpicture}[ \end_layout \begin_layout Plain Layout force/.style={>=latex,draw=blue,fill=blue}, \end_layout \begin_layout Plain Layout axis/.style={densely dashed,gray,font= \backslash small}, \end_layout \begin_layout Plain Layout M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin}, \end_layout \begin_layout Plain Layout m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin}, \end_layout \begin_layout Plain Layout plane/.style={draw=black,fill=blue!10}, \end_layout \begin_layout Plain Layout string/.style={draw=red, thick}, \end_layout \begin_layout Plain Layout pulley/.style={thick}, \end_layout \begin_layout Plain Layout ] \end_layout \begin_layout Plain Layout \end_layout \begin_layout Plain Layout \backslash matrix[column sep=1cm] { \end_layout \begin_layout Plain Layout %% Sketch \end_layout \begin_layout Plain Layout \backslash draw[plane] (0,-1) coordinate (base) \end_layout \begin_layout Plain Layout -- coordinate[pos=0.5] (mid) ++( \backslash iangle:3) coordinate (top) \end_layout \begin_layout Plain Layout |- (base) -- cycle; \end_layout \begin_layout Plain Layout \backslash path (mid) node[M,rotate= \backslash iangle,yshift=0.25cm] (M) {}; \end_layout \begin_layout Plain Layout \backslash draw[pulley] (top) -- ++( \backslash iangle:0.25) circle (0.25cm) \end_layout \begin_layout Plain Layout ++ (90- \backslash iangle:0.5) coordinate (pulley); \end_layout \begin_layout Plain Layout \backslash draw[string] (M.east) -- ++( \backslash iangle:1.5cm) arc (90+ \backslash iangle:0:0.25) \end_layout \begin_layout Plain Layout -- ++(0,-1) node[m] {}; \end_layout \begin_layout Plain Layout \end_layout \begin_layout Plain Layout \backslash draw[->] (base)++( \backslash arcr,0) arc (0: \backslash iangle: \backslash arcr); \end_layout \begin_layout Plain Layout \backslash path (base)++( \backslash iangle*0.5: \backslash arcr+5pt) node {$ \backslash alpha$}; \end_layout \begin_layout Plain Layout %% \end_layout \begin_layout Plain Layout \end_layout \begin_layout Plain Layout & \end_layout \begin_layout Plain Layout %% Free body diagram of M \end_layout \begin_layout Plain Layout \backslash begin{scope}[rotate= \backslash iangle] \end_layout \begin_layout Plain Layout \backslash node[M,transform shape] (M) {}; \end_layout \begin_layout Plain Layout % Draw axes and help lines \end_layout \begin_layout Plain Layout \end_layout \begin_layout Plain Layout {[axis,->] \end_layout \begin_layout Plain Layout \backslash draw (0,-1) -- (0,2) node[right] {$+y$}; \end_layout \begin_layout Plain Layout \backslash draw (M) -- ++(2,0) node[right] {$+x$}; \end_layout \begin_layout Plain Layout % Indicate angle. The code is a bit awkward. \end_layout \begin_layout Plain Layout \end_layout \begin_layout Plain Layout \backslash draw[solid,shorten >=0.5pt] ( \backslash down- \backslash iangle: \backslash arcr) \end_layout \begin_layout Plain Layout arc( \backslash down- \backslash iangle: \backslash down: \backslash arcr); \end_layout \begin_layout Plain Layout \backslash node at ( \backslash down-0.5* \backslash iangle:1.3* \backslash arcr) {$ \backslash alpha$}; \end_layout \begin_layout Plain Layout } \end_layout \begin_layout Plain Layout \end_layout \begin_layout Plain Layout % Forces \end_layout \begin_layout Plain Layout {[force,->] \end_layout \begin_layout Plain Layout % Assuming that Mg = 1. The normal force will therefore be cos(alpha) \end_layout \begin_layout Plain Layout \backslash draw (M.center) -- ++(0,{cos( \backslash iangle)}) node[above right] {$N$}; \end_layout \begin_layout Plain Layout \backslash draw (M.west) -- ++(-1,0) node[left] {$f_R$}; \end_layout \begin_layout Plain Layout \backslash draw (M.east) -- ++(1,0) node[above] {$T$}; \end_layout \begin_layout Plain Layout } \end_layout \begin_layout Plain Layout \end_layout \begin_layout Plain Layout \backslash end{scope} \end_layout \begin_layout Plain Layout % Draw gravity force. The code is put outside the rotated \end_layout \begin_layout Plain Layout % scope for simplicity. No need to do any angle calculations. \end_layout \begin_layout Plain Layout \backslash draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$}; \end_layout \begin_layout Plain Layout %% \end_layout \begin_layout Plain Layout \end_layout \begin_layout Plain Layout & \end_layout \begin_layout Plain Layout %%% \end_layout \begin_layout Plain Layout % Free body diagram of m \end_layout \begin_layout Plain Layout \backslash node[m] (m) {}; \end_layout \begin_layout Plain Layout \backslash draw[axis,->] (m) -- ++(0,-2) node[left] {$+$}; \end_layout \begin_layout Plain Layout {[force,->] \end_layout \begin_layout Plain Layout \backslash draw (m.north) -- ++(0,1) node[above] {$T'$}; \end_layout \begin_layout Plain Layout \backslash draw (m.south) -- ++(0,-1) node[right] {$mg$}; \end_layout \begin_layout Plain Layout } \end_layout \begin_layout Plain Layout \end_layout \begin_layout Plain Layout \backslash \backslash \end_layout \begin_layout Plain Layout }; \end_layout \begin_layout Plain Layout \backslash end{tikzpicture} \end_layout \begin_layout Plain Layout \end_layout \end_inset \end_layout \end_inset \end_layout \end_body \end_document