Plotting Phase Graphs/Diagrams of PDE's in Maple

[Woland]

Hi everyone,

I believe the term I am looking for is phase diagram. For a oscillating system it is a graph where displacement is on the x-axis and velocity is on the y-axis. My first question is what is the proper name for this type of graph?

I had the following simple PDE: ay" + by' + cy = 0, just a run of the mill damped harmonic motion. To solve I split this up into two 1st order differential equations by the substitution v = y'. Then I basically used "dsolve" to find the y and v solutions. I then successfully plotted them against each other on my phase diagram to get the circular motion dying down towards zero.

Now my real problem starts. I want to plot velocity vs displacement VS time. So I will basically have a 3D version of what is happening. What this should look like is a spiral or spring, which gets more and more narrow as we progress in the z-axis, until it dies down and is just a vertical line along the z-axis. I was trying to use "plot3d" but could not get it to work.

Does anyone know how I can plot this in Maple? Please let me know if you need further clarification. Thank you.

 

[djeitnstine]

try implicitplot3d =]

For the record its an ODE not a PDE

 

[oswaler]

Hi there,

I can provide some guidance on how to plot phase diagrams of PDE's using Maple. Firstly, the proper term for the type of graph you are describing is a phase portrait. This is a graphical representation of the behavior of a system over time, showing how different variables (such as displacement and velocity) change in relation to each other.

To plot a phase portrait in Maple, you can use the "phaseportrait" command. This allows you to specify the differential equations and initial conditions for your system, and it will automatically generate a phase portrait for you. You can then customize the plot using various options, such as changing the color scheme or adding labels.

For your specific problem of wanting to plot velocity vs displacement vs time, you can use the "plot3d" command. This allows you to plot a function of three variables in a three-dimensional space. You can specify your velocity and displacement functions as functions of time, and then plot them together in a 3D plot. You can also use the "animate" command to animate the plot over time, giving you a visual representation of the spiral or spring behavior you are looking for.

I hope this helps. Let me know if you need any further assistance. Good luck with your research!