Plotting Phase Graphs/Diagrams of PDE's in Maple

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SUMMARY

The discussion focuses on plotting phase diagrams for ordinary differential equations (ODEs) in Maple, specifically for the damped harmonic motion represented by the equation ay" + by' + cy = 0. The user successfully created a phase diagram using the "dsolve" function to obtain solutions for displacement and velocity. The main challenge lies in plotting a 3D representation of velocity versus displacement over time, aiming for a spiral effect that converges to a vertical line. The user seeks assistance with the "plot3d" function in Maple to achieve this visualization.

PREREQUISITES
  • Understanding of ordinary differential equations (ODEs)
  • Familiarity with Maple software and its plotting functions
  • Knowledge of phase diagrams and their significance in dynamical systems
  • Experience with 3D plotting techniques in mathematical software
NEXT STEPS
  • Research the "dsolve" function in Maple for solving ODEs
  • Explore the "plot3d" function in Maple for 3D visualizations
  • Learn about phase diagrams and their applications in oscillatory systems
  • Investigate the "implicitplot3d" function in Maple for complex 3D plots
USEFUL FOR

This discussion is beneficial for mathematicians, engineers, and students working with ordinary differential equations, particularly those interested in visualizing dynamic systems using Maple software.

Woland
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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.
 
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try implicitplot3d =]

For the record its an ODE not a PDE
 

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