I am using MatCont over the command line (for more flexibility) and have successfully run a simple 4-D.o.F. equilibrium continuation for one parameter, which resembles a non-linear ODE for a physical problem where two masses are hydrodynamically coupled . Although the Hopf bifurcation point is found where it is supposed to be, the: Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 5.377909e-18.
appears. Tracing the warning back out of interest, it is been created at:
apparently, when the Lyapunov coefficients are calculated. I understand, that at the Hopf point, a pair of eigenvalues of the Jacobian cross the real axis and we have a non-hyperbolic fixed point, but cannot interpet the warning. The system is in classical first order, state-space form, so how come the matrix badly scaled? Also, where in line 508 of "cont" is the equilibrium beeing called? It seems to be hidden in the cds.curve_process (?)
Thanks, kind regards
lanast
Last edit: lanast 2020-01-28
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I suspect your system has additional properties that we can't see, such as additional eigenvalues rendering the matrix (A-I) singular.
Please provide a minimal working example.
Best regards, Hil Meijer
From: Lysandros Anastasopoulos lanast@users.sourceforge.net
Sent: Tuesday, January 28, 2020 9:01 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Hopf is found where expected - but before that, RCOND warning(s)
Dear MatCont community,
I am using MatCont over the command line (for more flexibility) and have successfully run a simple 4-D.o.F. equilibrium continuation for one parameter. Although the Hopf bifurcation point is found where it is supposed to be, the warning: Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 5.377909e-18.
appears. Tracing the warning back out of interest, it is been created at:
apparently, when the software calculates the Lyapunov coefficients. I understand, that at the Hopf point, a pair of eigenvalues of the Jacobian cross the real axis, but cannot interpet the warning. Why is the problem badly scaled? Can it be ignored? Also, where in line 508 of "cont" is the equilibrium beeing called? It seems to be hidden in the cds.curve_process (?)
Hello Hil,
thanks for the response.
The differential equation describes two masses m1 and m2, elastically coupled by a stiffness K, and both under the influece of gravity g, given in the form F:
% Body 1F(1)=kmrgd(2);% d/dt of horizontal position of mass 1F(2)=K*(kmrgd(5)-kmrgd(1))/m1+Fx/m1;% d/dt of horizontal velocity of mass 1F(3)=kmrgd(4);% d/dt of vertical position of mass 1F(4)=K*(kmrgd(7)-kmrgd(3))/m1+Fy/m1-g;% d/dt of vertical velocity of mass 1% Body 2F(5)=kmrgd(6);% d/dt of horizontal position of mass 2F(6)=-K*(kmrgd(5)-kmrgd(1))/m2;% d/dt of horizontal velocity of mass 2F(7)=kmrgd(8);% d/dt of vertical position of mass 2F(8)=-K*(kmrgd(7)-kmrgd(3))/m2-g;% d/dt of vertical velocity of mass 2
The forces Fx and Fy act only on the one body and are non-linear functions of position and speed. I have written the state form in the standard MatCont convention kmrgd. The nonlinear forces Fx and Fy are called by a custom function, they are a routine.
Br, lanast
Last edit: lanast 2020-01-29
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Note that you only provide part of the equations, and not a true MWE.
To me it looks as if you have actually a double Hopf by default, with the same eigenvalues. You could check that in the eigenvalues (Numeric Window).
That's not generic and then the computation of the normal form coefficient will fail, or complain, indeed.
Best, Hil
From: lanast lanast@users.sourceforge.net
Sent: Wednesday, January 29, 2020 9:09 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Hopf is found where expected - but before that, RCOND warning(s)
The differential equation describes two masses m1 and m2, elastically coupled by a stiffness K, and both under the influece of gravity g in the form F:
% Body 1F(1)=kmrgd(2);% d/dt of horizontal position of mass 1F(2)=K*(kmrgd(5)-kmrgd(1))/m1+Fx/m1;% d/dt of horizontal velocity of mass 1F(3)=kmrgd(4);% d/dt of vertical position of mass 1F(4)=K*(kmrgd(7)-kmrgd(3))/m1+Fy/m1-g;% d/dt of vertical velocity of mass 1% Body 2F(5)=kmrgd(6);% d/dt of horizontal position of mass 2F(6)=-K*(kmrgd(5)-kmrgd(1))/m2;% d/dt of horizontal velocity of mass 2F(7)=kmrgd(8);% d/dt of vertical position of mass 2F(8)=-K*(kmrgd(7)-kmrgd(3))/m2-g;% d/dt of vertical velocity of mass 2
The forces Fx and Fy act only on the one body and are non-linear function of position and speed. I have written the state form in the standard MatCont convention kmrgd.
Thanks a lot, The nature of the nonlinear forces causes differrent stiffness and damping in horizontal / direction, so the eigenvalues should be differrent in this case.
Best,
lanast
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Dear MatCont community,
I am using MatCont over the command line (for more flexibility) and have successfully run a simple 4-D.o.F. equilibrium continuation for one parameter, which resembles a non-linear ODE for a physical problem where two masses are hydrodynamically coupled . Although the Hopf bifurcation point is found where it is supposed to be, the:
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 5.377909e-18.
appears. Tracing the warning back out of interest, it is been created at:
apparently, when the Lyapunov coefficients are calculated. I understand, that at the Hopf point, a pair of eigenvalues of the Jacobian cross the real axis and we have a non-hyperbolic fixed point, but cannot interpet the warning. The system is in classical first order, state-space form, so how come the matrix badly scaled? Also, where in line 508 of "cont" is the equilibrium beeing called? It seems to be hidden in the cds.curve_process (?)
Thanks, kind regards
lanast
Last edit: lanast 2020-01-28
Dear Lysandros,
I suspect your system has additional properties that we can't see, such as additional eigenvalues rendering the matrix (A-I) singular.
Please provide a minimal working example.
Best regards, Hil Meijer
From: Lysandros Anastasopoulos lanast@users.sourceforge.net
Sent: Tuesday, January 28, 2020 9:01 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Hopf is found where expected - but before that, RCOND warning(s)
Dear MatCont community,
I am using MatCont over the command line (for more flexibility) and have successfully run a simple 4-D.o.F. equilibrium continuation for one parameter. Although the Hopf bifurcation point is found where it is supposed to be, the warning:
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 5.377909e-18.
appears. Tracing the warning back out of interest, it is been created at:
apparently, when the software calculates the Lyapunov coefficients. I understand, that at the Hopf point, a pair of eigenvalues of the Jacobian cross the real axis, but cannot interpet the warning. Why is the problem badly scaled? Can it be ignored? Also, where in line 508 of "cont" is the equilibrium beeing called? It seems to be hidden in the cds.curve_process (?)
Thanks, kind regards
lanast
Hopf is found where expected - but before that, RCOND warning(s)
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Hello Hil,
thanks for the response.
The differential equation describes two masses m1 and m2, elastically coupled by a stiffness K, and both under the influece of gravity g, given in the form F:
The forces Fx and Fy act only on the one body and are non-linear functions of position and speed. I have written the state form in the standard MatCont convention kmrgd. The nonlinear forces Fx and Fy are called by a custom function, they are a routine.
Br, lanast
Last edit: lanast 2020-01-29
Note that you only provide part of the equations, and not a true MWE.
To me it looks as if you have actually a double Hopf by default, with the same eigenvalues. You could check that in the eigenvalues (Numeric Window).
That's not generic and then the computation of the normal form coefficient will fail, or complain, indeed.
Best, Hil
From: lanast lanast@users.sourceforge.net
Sent: Wednesday, January 29, 2020 9:09 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Hopf is found where expected - but before that, RCOND warning(s)
The differential equation describes two masses m1 and m2, elastically coupled by a stiffness K, and both under the influece of gravity g in the form F:
The forces Fx and Fy act only on the one body and are non-linear function of position and speed. I have written the state form in the standard MatCont convention kmrgd.
Hopf is found where expected - but before that, RCOND warning(s)
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/
Thanks a lot, The nature of the nonlinear forces causes differrent stiffness and damping in horizontal / direction, so the eigenvalues should be differrent in this case.
Best,
lanast