I wanted to use the Matcont to follow the solution for the driven pendulum (This is the example from Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering by Steven H. Strogatz, pp: 268, where comprehensive explanation can be found)
phi'=y
y'=I0-sin(phi)-alpha*y
where coordinates are: phi and y
parameters: I0,alpha
The issue is that the natural phase-space for this problem is a cylinder because the phi coordinate is limited between [0, 2 pi].
So, I am wondering how can I enforce matcont to find the rotary solution, which are limit cycle solutions in the cylindrical phase-space, and fixed solutions, which are the equilibrium points.
Should I rewrite the equations in another format, or should I add external equations?
This is not supported. A little hint, but a lot of work: You may try to modify the limitcycle class yourself in order to have a different boundary value problem. Now it has x(T)=x(0) and you want x(T)-2pi=x(0). Not impossible, but on this forum I am not going to spend much time on it now.
Best regards, Hil Meijer
From: Hesam Sharghi hesamaero@users.sourceforge.net
Sent: Thursday, March 19, 2020 7:11 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Driven pendulum and rotary solutions
I wanted to use the Matcont to follow the solution for the driven pendulum (This is the example from Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering by Steven H. Strogatz, pp: 268, where comprehensive explanation can be found)
phi'=y
y'=I0-sin(phi)-alpha*y
where coordinates are: phi and y
parameters: I0,alpha
The issue is that the natural phase-space for this problem is a cylinder because the phi coordinate is limited between [0, 2 pi].
So, I am wondering how can I enforce matcont to find the rotary solution, which are limit cycle solutions in the cylindrical phase-space, and fixed solutions, which are the equilibrium points.
Should I rewrite the equations in another format, or should I add external equations?
I wanted to use the Matcont to follow the solution for the driven pendulum (This is the example from Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering by Steven H. Strogatz, pp: 268, where comprehensive explanation can be found)
phi'=y
y'=I0-sin(phi)-alpha*y
where coordinates are: phi and y
parameters: I0,alpha
The issue is that the natural phase-space for this problem is a cylinder because the phi coordinate is limited between [0, 2 pi].
So, I am wondering how can I enforce matcont to find the rotary solution, which are limit cycle solutions in the cylindrical phase-space, and fixed solutions, which are the equilibrium points.
Should I rewrite the equations in another format, or should I add external equations?
Dear Hesam,
This is not supported. A little hint, but a lot of work: You may try to modify the limitcycle class yourself in order to have a different boundary value problem. Now it has x(T)=x(0) and you want x(T)-2pi=x(0). Not impossible, but on this forum I am not going to spend much time on it now.
Best regards, Hil Meijer
From: Hesam Sharghi hesamaero@users.sourceforge.net
Sent: Thursday, March 19, 2020 7:11 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Driven pendulum and rotary solutions
I wanted to use the Matcont to follow the solution for the driven pendulum (This is the example from Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering by Steven H. Strogatz, pp: 268, where comprehensive explanation can be found)
phi'=y
y'=I0-sin(phi)-alpha*y
where coordinates are: phi and y
parameters: I0,alpha
The issue is that the natural phase-space for this problem is a cylinder because the phi coordinate is limited between [0, 2 pi].
So, I am wondering how can I enforce matcont to find the rotary solution, which are limit cycle solutions in the cylindrical phase-space, and fixed solutions, which are the equilibrium points.
Should I rewrite the equations in another format, or should I add external equations?
Driven pendulum and rotary solutions
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Dear Hil,
Is it possibe to rewrite equations in the cartesian coordinates? Then, that case I do not have the polar coordinate.
I do not see how, you will have to do that yourself.
Hil
From: Hesam Sharghi hesamaero@users.sourceforge.net
Sent: Friday, March 20, 2020 7:35 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Re: Driven pendulum and rotary solutions
Dear Hil,
Is it possibe to rewrite equations in the cartesian coordinates? Then, that case I do not have the polar coordinate.
Driven pendulum and rotary solutions
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Dear Hil,
Thank you for your suggestion.