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    <title>MaplePrimes - answers and comments on Question, how to plot with DEplot and odeplot in the polar coordinate?</title>
    <link>http://www.mapleprimes.com/questions/133621-How-To-Plot-With-DEplot-And-Odeplot</link>
    <language>en-us</language>
    <copyright>2026 Maplesoft, A Division of Waterloo Maple Inc.</copyright>
    <generator>Maplesoft Document System</generator>
    <lastBuildDate>Wed, 10 Jun 2026 10:33:13 GMT</lastBuildDate>
    <pubDate>Wed, 10 Jun 2026 10:33:13 GMT</pubDate>
    <itunes:subtitle />
    <itunes:summary />
    <description>The latest answers and comments added to the Question, how to plot with DEplot and odeplot in the polar coordinate?</description>
    <image>
      <url>http://www.mapleprimes.com/images/mapleprimeswhite.jpg</url>
      <title>MaplePrimes - answers and comments on Question, how to plot with DEplot and odeplot in the polar coordinate?</title>
      <link>http://www.mapleprimes.com/questions/133621-How-To-Plot-With-DEplot-And-Odeplot</link>
    </image>
    <item>
      <title>Not directly with DEplot or odeplot</title>
      <link>http://www.mapleprimes.com/questions/133621-How-To-Plot-With-DEplot-And-Odeplot?ref=Feed:MaplePrimes:how to plot with DEplot and odeplot in the polar coordinate?:Comments#answer133622</link>
      <itunes:summary>&lt;p&gt;If you want to use the option coords = polar, then you must use the "normal" plot-command, to plot r(theta).&lt;/p&gt;
&lt;pre&gt;q1 := dsolve( {sys1, theta(0)=Pi, r(0)=2}, numeric, output=listprocedure);&lt;/pre&gt;
&lt;p&gt;This gives you numeric procedures for r(t) and theta(t).&lt;/p&gt;
&lt;pre&gt;Theta := subs(q1,theta(t)): R := subs(q1,r(t)):
plot( [R(t),Theta(t),t=0..10], coords=polar, axiscoordinates=polar );

&lt;/pre&gt;</itunes:summary>
      <description>&lt;p&gt;If you want to use the option coords = polar, then you must use the "normal" plot-command, to plot r(theta).&lt;/p&gt;
&lt;pre&gt;q1 := dsolve( {sys1, theta(0)=Pi, r(0)=2}, numeric, output=listprocedure);&lt;/pre&gt;
&lt;p&gt;This gives you numeric procedures for r(t) and theta(t).&lt;/p&gt;
&lt;pre&gt;Theta := subs(q1,theta(t)): R := subs(q1,r(t)):
plot( [R(t),Theta(t),t=0..10], coords=polar, axiscoordinates=polar );

&lt;/pre&gt;</description>
      <guid>133622</guid>
      <pubDate>Tue, 01 May 2012 12:39:02 Z</pubDate>
      <itunes:author>Adri vanderMeer
 van der Meer</itunes:author>
      <author>Adri vanderMeer
 van der Meer</author>
    </item>
    <item>
      <title>a work around for DEplot in other coordinate syste...</title>
      <link>http://www.mapleprimes.com/questions/133621-How-To-Plot-With-DEplot-And-Odeplot?ref=Feed:MaplePrimes:how to plot with DEplot and odeplot in the polar coordinate?:Comments#answer206204</link>
      <itunes:summary>&lt;p&gt;Here is another way to do it.&lt;br /&gt;&lt;br /&gt;&lt;/p&gt;
&lt;p&gt;L1:= op(indets(DEplot({diff(x(t),t)=x(t)+x(t)^3-x(t)^5,diff(y(t),t)=1}, &lt;br /&gt;[x(t),y(t)], t=0 .. 12, [[x(0)=2.5,y(0)=1]],numpoints=1000),list(list(numeric)))):&lt;/p&gt;
&lt;p&gt;plot(L1,coords=polar,scaling=constrained);&lt;/p&gt;</itunes:summary>
      <description>&lt;p&gt;Here is another way to do it.&lt;br /&gt;&lt;br /&gt;&lt;/p&gt;
&lt;p&gt;L1:= op(indets(DEplot({diff(x(t),t)=x(t)+x(t)^3-x(t)^5,diff(y(t),t)=1}, &lt;br /&gt;[x(t),y(t)], t=0 .. 12, [[x(0)=2.5,y(0)=1]],numpoints=1000),list(list(numeric)))):&lt;/p&gt;
&lt;p&gt;plot(L1,coords=polar,scaling=constrained);&lt;/p&gt;</description>
      <guid>206204</guid>
      <pubDate>Wed, 07 May 2014 18:55:03 Z</pubDate>
      <itunes:author>John  Starrett</itunes:author>
      <author>John  Starrett</author>
    </item>
    <item>
      <title>transformation</title>
      <link>http://www.mapleprimes.com/questions/133621-How-To-Plot-With-DEplot-And-Odeplot?ref=Feed:MaplePrimes:how to plot with DEplot and odeplot in the polar coordinate?:Comments#answer206208</link>
      <itunes:summary>&lt;p&gt;Could you not transform the plots with cartesian coordinates?&lt;/p&gt;
&lt;p&gt;&lt;br&gt; &lt;/p&gt;
&lt;form name="worksheet_form"&gt;&lt;input type="hidden" name="md.ref" value="BACDDC00F4245E46FF37194197206C9E"&gt;
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&lt;td&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;restart:&lt;br&gt; &lt;/span&gt;&lt;/p&gt;
&lt;/td&gt;
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&lt;table style="margin-left: 0px; margin-right: 0px;"&gt;
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&lt;td&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;sys := diff(x(t), t) = -y(t)+x(t)*(1-2*x(t)^2-3*y(t)^2),&lt;br&gt; &lt;/span&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;diff(y(t), t) = x(t)+y(t)*(1-2*x(t)^2-3*y(t)^2):&lt;br&gt; &lt;/span&gt;&lt;/p&gt;
&lt;/td&gt;
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&lt;td&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;sys1 := diff(r(t), t) = r(t)*(1-2*r(t)^2-r(t)^2*sin(theta(t))^2),&lt;br&gt; &lt;/span&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;diff(theta(t), t) = 1:&lt;br&gt; &lt;/span&gt;&lt;/p&gt;
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&lt;td&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;conv:=plottools:-transform((a,b)-&amp;gt;[a*cos(b),a*sin(b)]):&lt;br&gt; &lt;/span&gt;&lt;/p&gt;
&lt;/td&gt;
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&lt;td&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;P0:=DEtools[DEplot]({sys1},[r(t),theta(t)],t=0..10,[[theta(0)=Pi,r(0)=2]],&lt;br&gt; &lt;/span&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;arrows=none,thickness=1,linecolor=burgundy):&lt;br&gt; &lt;/span&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&lt;br&gt; &lt;/span&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;plots:-display(conv(P0),axiscoordinates=polar);&lt;/span&gt;&lt;/p&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="border: none;" src="/view.aspx?sf=206208_Answer/a4f6b61cdcf27ef6e543cf1bba307d88.gif" alt="" width="400" height="400" align="middle"&gt;&lt;/p&gt;
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&lt;td&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;q1 := dsolve([sys1, theta(0) = Pi, r(0) = 2], numeric, [theta(t), r(t)]):&lt;br&gt; &lt;/span&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;P:=plots:-odeplot(q1, [r(t), theta(t)], t = 0 .. 10):&lt;br&gt; &lt;/span&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&lt;br&gt; &lt;/span&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;plots:-display(conv(P),axiscoordinates=polar);&lt;/span&gt;&lt;/p&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="border: none;" src="/view.aspx?sf=206208_Answer/49da356206e9a2cea2ecfe75d5949322.gif" alt="" width="400" height="400" align="middle"&gt;&lt;/p&gt;
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&lt;td&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
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&lt;input type="hidden" name="sequence" value="1"&gt; &lt;input type="hidden" name="cmd" value="none"&gt;&lt;/form&gt;
&lt;p&gt;&lt;br&gt; &lt;/p&gt;
&lt;p&gt;&lt;a href="/view.aspx?sf=206208_Answer/polarde.mw"&gt;Download polarde.mw&lt;/a&gt;&lt;/p&gt;
&lt;!--break--&gt;
&lt;p&gt;acer&lt;/p&gt;</itunes:summary>
      <description>&lt;p&gt;Could you not transform the plots with cartesian coordinates?&lt;/p&gt;
&lt;p&gt;&lt;br&gt; &lt;/p&gt;
&lt;form name="worksheet_form"&gt;&lt;input type="hidden" name="md.ref" value="BACDDC00F4245E46FF37194197206C9E"&gt;
&lt;table style="width: 768px;" align="center"&gt;
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&lt;td&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;restart:&lt;br&gt; &lt;/span&gt;&lt;/p&gt;
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&lt;td&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;sys := diff(x(t), t) = -y(t)+x(t)*(1-2*x(t)^2-3*y(t)^2),&lt;br&gt; &lt;/span&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;diff(y(t), t) = x(t)+y(t)*(1-2*x(t)^2-3*y(t)^2):&lt;br&gt; &lt;/span&gt;&lt;/p&gt;
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&lt;td&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;sys1 := diff(r(t), t) = r(t)*(1-2*r(t)^2-r(t)^2*sin(theta(t))^2),&lt;br&gt; &lt;/span&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;diff(theta(t), t) = 1:&lt;br&gt; &lt;/span&gt;&lt;/p&gt;
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&lt;td&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;conv:=plottools:-transform((a,b)-&amp;gt;[a*cos(b),a*sin(b)]):&lt;br&gt; &lt;/span&gt;&lt;/p&gt;
&lt;/td&gt;
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&lt;td&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;P0:=DEtools[DEplot]({sys1},[r(t),theta(t)],t=0..10,[[theta(0)=Pi,r(0)=2]],&lt;br&gt; &lt;/span&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;arrows=none,thickness=1,linecolor=burgundy):&lt;br&gt; &lt;/span&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&lt;br&gt; &lt;/span&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;plots:-display(conv(P0),axiscoordinates=polar);&lt;/span&gt;&lt;/p&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="border: none;" src="/view.aspx?sf=206208_Answer/a4f6b61cdcf27ef6e543cf1bba307d88.gif" alt="" width="400" height="400" align="middle"&gt;&lt;/p&gt;
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&lt;td&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;q1 := dsolve([sys1, theta(0) = Pi, r(0) = 2], numeric, [theta(t), r(t)]):&lt;br&gt; &lt;/span&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;P:=plots:-odeplot(q1, [r(t), theta(t)], t = 0 .. 10):&lt;br&gt; &lt;/span&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&lt;br&gt; &lt;/span&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;plots:-display(conv(P),axiscoordinates=polar);&lt;/span&gt;&lt;/p&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="border: none;" src="/view.aspx?sf=206208_Answer/49da356206e9a2cea2ecfe75d5949322.gif" alt="" width="400" height="400" align="middle"&gt;&lt;/p&gt;
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&lt;td&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt; &amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;span style="color: #78000e; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
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&lt;input type="hidden" name="sequence" value="1"&gt; &lt;input type="hidden" name="cmd" value="none"&gt;&lt;/form&gt;
&lt;p&gt;&lt;br&gt; &lt;/p&gt;
&lt;p&gt;&lt;a href="/view.aspx?sf=206208_Answer/polarde.mw"&gt;Download polarde.mw&lt;/a&gt;&lt;/p&gt;
&lt;!--break--&gt;
&lt;p&gt;acer&lt;/p&gt;</description>
      <guid>206208</guid>
      <pubDate>Wed, 07 May 2014 20:36:13 Z</pubDate>
      <itunes:author>acer</itunes:author>
      <author>acer</author>
    </item>
  </channel>
</rss>