MaplePrimes - comments on Post, Simple rocket model

MaplePrimes - comments on Post, Simple rocket model http://www.mapleprimes.com/posts/35907-Simple-Rocket-Model en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Fri, 12 Jun 2026 21:40:59 GMT Fri, 12 Jun 2026 21:40:59 GMT The latest comments added to the Post, Simple rocket model http://www.mapleprimes.com/images/mapleprimeswhite.jpg MaplePrimes - comments on Post, Simple rocket model http://www.mapleprimes.com/posts/35907-Simple-Rocket-Model use odeplot to plot solutions to IVPs http://www.mapleprimes.com/posts/35907-Simple-Rocket-Model?ref=Feed:MaplePrimes:Simple rocket model:Comments#comment59846 I can combine your last five commands into a single line that is quite understandable. The key is to be aware of the odeplot command (in the plots package). This command is designed specifically to plot the numerical solution of an initial value problem. Here is my version of your code: <pre> restart; m:=t->M*exp(-gamma*t)+M[0]: rocket_eq:=m(t)*diff(x(t),t,t)+diff(m(t),t)*u+m(t)*g=0: params := [M[0]=0.2, M=1, gamma=10, u=8, g=9.81]: rocket_eq:=eval(rocket_eq,params): ics:=x(0)=0,D(x)(0)=0: sol:=dsolve({rocket_eq,ics},x(t),numeric): plots:-odeplot(sol, [[t,x(t)],[t,diff(x(t),t)]], t=0..2, color=[black,red],legend=["position","velocity"]); <a href="http://www.mapleprimes.com/viewfile/4013"><img alt="" src="http://www.mapleprimes.com/scripts/image.php?image=http://www.mapleprimes.com/files/178_rocket-plot.gif&width=300&height=300" /></a></pre> The odeplot command can do much more than this; see ?plots,odeplot for full details. Doug <pre> --------------------------------------------------------------------- Douglas B. Meade <>< Math, USC, Columbia, SC 29208 E-mail: mailto:meade@math.sc.edu Phone: (803) 777-6183 URL: http://www.math.sc.edu </pre> The latest comments added to the Post, Simple rocket model 59846 Sat, 23 Jan 2010 22:28:07 Z Doug Meade Doug Meade halt event http://www.mapleprimes.com/posts/35907-Simple-Rocket-Model?ref=Feed:MaplePrimes:Simple rocket model:Comments#comment59847 As a simple extension to Doug's suggestion, we can add a halt event when the rocket hits the ground <pre> sol:=dsolve({rocket_eq,ics},x(t),numeric,events=[[x(t), halt]]): tf := eval(t, sol(10)); plots:-odeplot(sol, [[t,x(t)] ,[t,diff(x(t),t)]], t=0..tf, color=[black,red],legend=["position","velocity"]); </pre> The latest comments added to the Post, Simple rocket model 59847 Sun, 24 Jan 2010 00:07:11 Z Joe Riel Joe Riel Cool http://www.mapleprimes.com/posts/35907-Simple-Rocket-Model?ref=Feed:MaplePrimes:Simple rocket model:Comments#comment59848 Thanks Doug and Joe. We'll be using deplot and deplot3d next wee I think so this is good for me to get a little ahead. The latest comments added to the Post, Simple rocket model 59848 Sun, 24 Jan 2010 05:30:15 Z longrob longrob odeplot, deplot, and deplot3d http://www.mapleprimes.com/posts/35907-Simple-Rocket-Model?ref=Feed:MaplePrimes:Simple rocket model:Comments#comment59849 deplot and deplot3d are different from odeplot odeplot is in the plots package (?odeplot) deplot and deplot3d are in the DEtools package (?DEtools, ?DEplot and ?DEplot3d) There are a lot of similarities between the commands, but also some important differences. As in your example, odeplot is a little more flexible when it comes to specifying exactly what you want to plot. I am more likely to use the DEplot command when I want to perform visualize the direction field (to learn, say, how solutions might behave for wide ranges of initial conditions). Doug <pre> --------------------------------------------------------------------- Douglas B. Meade <>< Math, USC, Columbia, SC 29208 E-mail: mailto:meade@math.sc.edu Phone: (803) 777-6183 URL: http://www.math.sc.edu </pre> The latest comments added to the Post, Simple rocket model 59849 Sun, 24 Jan 2010 10:53:17 Z Doug Meade Doug Meade alternative http://www.mapleprimes.com/posts/35907-Simple-Rocket-Model?ref=Feed:MaplePrimes:Simple rocket model:Comments#comment59850 It probably makes sense to express the burn rate as a differential equation and combine it with the others. Knowing little about rocketry I would think that the burn rate is constant, rather than proportional to the fuel (which the exponential implies).  That could be expressed as <pre> deqs := { v(t) = diff(x(t),t), m(t)*diff(v(t),t) + diff(mf(t),t)*u + m(t)*g = 0, m(t) = mb + mf(t), diff(mf(t),t) = -gamma(t) }: ics := {x(0)=0, v(0)=0, mf(0)=mf0, gamma(0)=gamma0}: params := [mb=0.2, mf0=1, gamma0=10, g=9.81, u=8]: sys := eval(deqs union ics, params); sol:=dsolve(sys,numeric , events = [[v(t) = 0 , 'halt'], # halt simulation at apogee [mf(t) = 0, gamma(t)=0] # fuel is spent, set burn rate to 0 ] , discrete_variables = [gamma(t) :: float] ); tf := eval(t, sol(10)); # determine the time at which rocket reaches apogee plots:-odeplot(sol, [[t,x(t)],[t,v(t)]], t=0..tf, color=[black,blue,red],legend=["position","velocity", "fuel"]); plots:-odeplot(sol, [t,mf(t)], t=0..tf, legend=["fuel"]);</pre> The burn rate could be expressed as a piecewise, say gamma(t) = piecewise(mf(t)>0, gamma0, 0), however, I used a second event to switch it off when the fuel (mf) reached zero.  To enable that, gamma(t) is declared a discrete variable (see ?dsolve[Events]).   The latest comments added to the Post, Simple rocket model 59850 Mon, 25 Jan 2010 21:06:08 Z Joe Riel Joe Riel These can be easily http://www.mapleprimes.com/posts/35907-Simple-Rocket-Model?ref=Feed:MaplePrimes:Simple rocket model:Comments#comment59851 These can be easily completed with MapleSim, and you do not need to care about what Maple commands to use, just need to enter the corresponding equation and Initial conditions. The latest comments added to the Post, Simple rocket model 59851 Thu, 28 Jan 2010 07:18:33 Z junlin junlin