Position-Velocity phase plane portrait in MATLAB?

[currently]

TL;DR

How to graph a Position-Velocity phase plane portrait?

For example, how would I graph a Position-Velocity phase portrait of a nodal sink or spiral sink?
Given form of mx'' = -cx' - kx + βx^3.

 

[jedishrfu]

To get a plot you’ll have to numerically integrate it using MATLAB using rk4 or something similar.

If you look online at the Matlab site or do a google search you should be able to find examples to base your solution on.

 

[jedishrfu]

Here’s a link to an example using rk4 aka ode45

https://www.mathworks.com/matlabcentral/answers/221857-how-do-i-integrate-a-differential-equation

 

[currently]

Here’s a link to an example using rk4 aka ode45

https://www.mathworks.com/matlabcentral/answers/221857-how-do-i-integrate-a-differential-equation

Ok, thank you. I will keep this in mind. it seems I have another step to do before actually graphing, but it's no worry to you. Thanks again.

 

[Master1022]

Summary:: How to graph a Position-Velocity phase plane portrait?

For example, how would I graph a Position-Velocity phase portrait of a nodal sink or spiral sink?
Given form of mx'' = -cx' - kx + βx^3.

You could also create the system within Simulink and link it to an interactive live Matlab script.

For example, here is a 2nd-order system with some damping (you could also include some extra blocks for your other term)

Then we link it to the Matlab script:
1. Define our variables
2. Run the simulation and extract the data
3. Plot the data

1.

2.

3.

Hope that is of some help.

Note: there will be a few more things to define within Simulink, but a youtube introductory video should show you how to use the blocks