According to the "Frequency response of nonlinear oscillator" written by Prof. Hilmeijer, I can easily draw the amplitude-frequency response curve, but the problem now is that the force is "γcos(ωt)+γsin(2ωt)". I don't know if the method is correct? i.e., u′ = −ωv + u(1 − u² − v²), v′ = ωu + v(1 − u² − v²); u1′ = −2ωv1 + u1(1 − u1² − v1²), v1′ = 2ωu1 + v1(1 − u1² − v1²)?
However, as I wrote it, the result cannot be continued and displays "Current step size too small (point 1)". I don't know where the problem comes from? Can you give me some advice?
Thanks to everyone in advance.
Best regards,
Yanders
Last edit: yanders 2021-08-01
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
I would use the double-angle formulas as follows.
You already added u,v to model a single oscillator.
Let u=cos(t), v=sin(t), then, in the code defining your model, you can use
cos(2wt)=uu-vv
and
sin(2wt)=u*v/2
You can extend this approach to harmonics of higher order.
Best regards, Hil
From: yanders lyfyanger@users.sourceforge.net
Sent: Friday, July 30, 2021 4:50 PM
To: [matcont:discussion]
Subject: [matcont:discussion] multi-harmonic functions
Dear matcont community,
According to the "Frequency response of nonlinear oscillator" written by Prof. Hilmeijer, I can easily draw the amplitude-frequency response curve, but the problem now is that the force is "γcos(ωt)+γcos(2ωt)". I don't know if the method I wrote in the attachment is correct? i.e., u′ = −ωv + u(1 − u² − v²), v′ = ωu + v(1 − u² − v²); u1′ = −2ωv1 + u1(1 − u1² − v1²), v1′ = 2ωu1 + v1(1 − u1² − v1²)?
However, as I wrote it, the result cannot be continued and displays "Current step size too small (point 1)". I don't know where the problem comes from? Can you give me some advice?
Dear Hil
You are right. For special functions, double-angle formulas can indeed be used, but for example,"γcos(ωt)+γcos(1.1ω*t)", the double-angle formulas is no longer applicable. So what should we do by MATCONT?
Best regards
yanders
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Dear matcont community,
According to the "Frequency response of nonlinear oscillator" written by Prof. Hilmeijer, I can easily draw the amplitude-frequency response curve, but the problem now is that the force is "γcos(ωt)+γsin(2ωt)". I don't know if the method is correct? i.e., u′ = −ωv + u(1 − u² − v²), v′ = ωu + v(1 − u² − v²); u1′ = −2ωv1 + u1(1 − u1² − v1²), v1′ = 2ωu1 + v1(1 − u1² − v1²)?
However, as I wrote it, the result cannot be continued and displays "Current step size too small (point 1)". I don't know where the problem comes from? Can you give me some advice?
Thanks to everyone in advance.
Best regards,
Yanders
Last edit: yanders 2021-08-01
I would use the double-angle formulas as follows.
You already added u,v to model a single oscillator.
Let u=cos(t), v=sin(t), then, in the code defining your model, you can use
cos(2wt)=uu-vv
and
sin(2wt)=u*v/2
You can extend this approach to harmonics of higher order.
Best regards, Hil
From: yanders lyfyanger@users.sourceforge.net
Sent: Friday, July 30, 2021 4:50 PM
To: [matcont:discussion]
Subject: [matcont:discussion] multi-harmonic functions
Dear matcont community,
According to the "Frequency response of nonlinear oscillator" written by Prof. Hilmeijer, I can easily draw the amplitude-frequency response curve, but the problem now is that the force is "γcos(ωt)+γcos(2ωt)". I don't know if the method I wrote in the attachment is correct? i.e., u′ = −ωv + u(1 − u² − v²), v′ = ωu + v(1 − u² − v²); u1′ = −2ωv1 + u1(1 − u1² − v1²), v1′ = 2ωu1 + v1(1 − u1² − v1²)?
However, as I wrote it, the result cannot be continued and displays "Current step size too small (point 1)". I don't know where the problem comes from? Can you give me some advice?
Thanks to everyone in advance.
Best regards,
Yangders
multi-harmonic functions
Sent from sourceforge.net because you indicated interest in https://sourceforge.net/p/matcont/discussion/762214/
To unsubscribe from further messages, please visit https://sourceforge.net/auth/subscriptions/
Dear Hil
You are right. For special functions, double-angle formulas can indeed be used, but for example,"γcos(ωt)+γcos(1.1ω*t)", the double-angle formulas is no longer applicable. So what should we do by MATCONT?
Best regards
yanders
Last edit: yanders 2021-09-14