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system of algebric equations with parameter
Posted 2010/06/04 5:21 GMT-4 3 Replies
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Hi,
I'd like to solve an algebric system of two equations ((1) and (2)) with two unknown (u and v). My system is
2*omega * u + 4* v = 0 (1)
u + 3*omega *v = 0 (2)
The problem is that this system has solutions only for some value of omega. Basically I can solve this problem by writing fist that the determinant of the system is zero (I obtain the values of omega possible such as u and v different of zero). Then I find u and v by using (1) and (2)...I would like use COMSOL to perform the solution (find omega, u and v).
How COMSOL can find the values of omega for which the system has solutions ? then find u and v for each omega found ?
The documentation written by COMSOL doesn't talk about this problem...
Thank you for your help !
Best
Pierre Simon
I'd like to solve an algebric system of two equations ((1) and (2)) with two unknown (u and v). My system is
2*omega * u + 4* v = 0 (1)
u + 3*omega *v = 0 (2)
The problem is that this system has solutions only for some value of omega. Basically I can solve this problem by writing fist that the determinant of the system is zero (I obtain the values of omega possible such as u and v different of zero). Then I find u and v by using (1) and (2)...I would like use COMSOL to perform the solution (find omega, u and v).
How COMSOL can find the values of omega for which the system has solutions ? then find u and v for each omega found ?
The documentation written by COMSOL doesn't talk about this problem...
Thank you for your help !
Best
Pierre Simon
3 Replies Last Post 2010/06/07 7:46 GMT-4
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Posted:
2 decades ago
Hi
when I see these two equations, I understand mainly 3 unknown and two equations, then no boundary value, so its no full BVP like that, I'm missing a third equations and/or some boundary conditions to be "Comsol applicant", no ?
Perhaps the hypothesis Omega = cte, that is d/dx(Omega) = 0 (o whatever dimension) could add an equation, still what to put on the borders ?
I assume that you are using COMSOL standard notation of generalise dependent variables u and v the "general displacements" in 1,2 or 3D (of general coordinates x,y,z) and Omega some kind of value independent of the spatial dimensions (but no eigenvalue, time harmonic development) ? and not u,v the x, respective y displacements
Ivar
when I see these two equations, I understand mainly 3 unknown and two equations, then no boundary value, so its no full BVP like that, I'm missing a third equations and/or some boundary conditions to be "Comsol applicant", no ?
Perhaps the hypothesis Omega = cte, that is d/dx(Omega) = 0 (o whatever dimension) could add an equation, still what to put on the borders ?
I assume that you are using COMSOL standard notation of generalise dependent variables u and v the "general displacements" in 1,2 or 3D (of general coordinates x,y,z) and Omega some kind of value independent of the spatial dimensions (but no eigenvalue, time harmonic development) ? and not u,v the x, respective y displacements
Ivar
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Posted:
2 decades ago
Hi Ivar,
Thank you for your answer,
This problem describes the dynamic of two oscillators coupled. I look the eigenmodes of this system. It is a system of two equations with two unknowns which depends on the pulsation w (A11(w)*u + A12(w)*v = 0 AND A21(w)*u+A22(w)*v=0). When the determinant of the system is different of zero, this system admits the trivial solution u = v = 0. When the determinant of this system is zero (which defines the possibles w, I mean the eigenfrequencies of my coupled-oscillator) then there are non-zero solutions. There are two equations and two unknowns and this problem is easily solved by hand ! I would like use COMSOL to solve it for me ... that means finding w why this sytem to non-zero solutions and for each w find u and v. Remark that this system is not of the form A*u=lamda*u but it is of the form A*u=0.
Best
Pierre
Thank you for your answer,
This problem describes the dynamic of two oscillators coupled. I look the eigenmodes of this system. It is a system of two equations with two unknowns which depends on the pulsation w (A11(w)*u + A12(w)*v = 0 AND A21(w)*u+A22(w)*v=0). When the determinant of the system is different of zero, this system admits the trivial solution u = v = 0. When the determinant of this system is zero (which defines the possibles w, I mean the eigenfrequencies of my coupled-oscillator) then there are non-zero solutions. There are two equations and two unknowns and this problem is easily solved by hand ! I would like use COMSOL to solve it for me ... that means finding w why this sytem to non-zero solutions and for each w find u and v. Remark that this system is not of the form A*u=lamda*u but it is of the form A*u=0.
Best
Pierre
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Posted:
2 decades ago
Hi
you are two here trying something simular (see the other thread), again what puzzles me is that to have Comsol finding solutions, you must tell it which are (all) the variables to solve for, so all three Lambda, u,v must be defined as unknown, and then the corresponding equations bust be entered.
And as Lambda i not depending on x,y,z, (while COMSOL assumes all unknown are related, if not told othervise), and if I read you correctly, then this must also be "told" to COMSOL via an appropriate equation(s)
Have fun Comsoling
ivar
you are two here trying something simular (see the other thread), again what puzzles me is that to have Comsol finding solutions, you must tell it which are (all) the variables to solve for, so all three Lambda, u,v must be defined as unknown, and then the corresponding equations bust be entered.
And as Lambda i not depending on x,y,z, (while COMSOL assumes all unknown are related, if not told othervise), and if I read you correctly, then this must also be "told" to COMSOL via an appropriate equation(s)
Have fun Comsoling
ivar