Solving Damped Driven Pendulum ODEs

[HansBu]

Homework Statement

Hello everyone! I am having some confusions with regards to my problem, whether or not the differential equations presented to me are inclined to damped driven pendulum. From the differential equations given, I can see that these equations are part of the convection equations made my Lorenz dubbed as Lorenz equations.

Relevant Equations

The relevant equations are presented in the attempt to the solution part.

Here are the nonlinear and coupling ordinary differential equations:

I was given values of a, b, and c as well as some initial values for x, y, and z. If ever the equations above are related to the pendulum, I can think of a as the damping factor, b as the forcing amplitude, and c as the driving frequency. On the other hand, initial values of x and y represent initial angular displacement and initial angular velocity, respectively. Can you help me verify this thought of mine? I have gone through a lot of resources and I am now confused. I am hoping that this forum might clear any confusions I have on mind. Thank you so much! A sample output shown below might be a help.

NOTE: I was able to come up with the source code in order to print out the graph below. My only concern here is the concept behind it.

 

[Frodo]

Have you searched the forum with damped pendulum? Does anything help?

 

[HansBu]

Have you searched the forum with damped pendulum? Does anything help?

Yes sir, I did only to see the standard differential equation of a damped driven pendulum in normalized version. Now, I am really confused. The graph above, from the problem, says that those are chaotic solutions. I understand what the problem means, but chaotic solutions of what system?

 

[wrobel]

Homework Statement:: Hello everyone! I am having some confusions with regards to my problem, whether or not the differential equations presented to me are inclined to damped driven pendulum. From the differential equations given, I can see that these equations are part of the convection equations made my Lorenz dubbed as Lorenz equations.
Relevant Equations:: The relevant equations are presented in the attempt to the solution part.

Can you help me verify this thought of mine?

To verify what? You have not formulated anything verifiable. If you for example present other system and make hypothesis on how its solutions approximate the Lorenz solutions then the matter of discussion will appear.

 

[HansBu]

To verify what? You have not formulated anything verifiable. If you for example present other system and make hypothesis on how its solutions approximate the Lorenz solutions then the matter of discussion will appear.

Hello, Wrobel! Can you enlighten me more on what you are trying to imply?