Thank you so much, for the answer. I have to get the solutions to plot
them. The solutions represent the critical speed of a shaft and there's no
other way. Other students are using other software for their project like
Maple or Mathematica, which they cause less problem. I was using python and
I've written around 50 pages of code in jupyter notebook and i get stuck in
this last calculation. Using Sagemath i've solved the equation and then
i've copied into my python code.
Il giorno venerdì 7 giugno 2019 02:21:52 UTC+2, Oscar ha scritto:
>
> SymPy will find the solution eventually I think.
>
> This is a polynomial of order 8 having only even powers so with a
> substitution omega**2 -> x it's a quartic in x with complicated
> symbolic coefficients. The general formula for a quartic is horrendous
> and in this case your coefficients are already large expressions.
>
> What this means is that the solution will take a while to compute and
> will probably be too complicated to be useful when done anyway. Really
> complicated analytic expressions can be difficult to use without
> substituting numeric values in and it's much easier to find the roots
> if you substitute the numbers in first.
>
> I'm not sure why it is so slow though. You can get to the solutions
> for omega^2 like this:
>
> In [39]: coeffs = Poly(omega_nf_eq.rhs.subs(omega, sqrt(x)),
> x).coeffs()
>
> In [40]: a, b, c, d, e = symbols('a, b, c, d, e')
>
> In [41]: p = Poly(a*x**4+b*x**3+c*x**2+d*x+e, x)
>
> In [42]: rs = solve(p, x)
>
> Print the first root:
>
> In [43]: rs[0].subs(zip((a,b,c,d,e), coeffs))
>
> (output omitted as it's long and complicated)
>
>
> My suggestion is to consider why you need the solutions to this
> equation. There may be a better way to reach your actual end goal then
> getting the solutions in explicit analytic form.
>
> --
> Oscar
>
> On Fri, 7 Jun 2019 at 00:13, pull_over93 <[email protected]
> <javascript:>> wrote:
> >
> > Hi everybody, I'm tring to solve this equation without succes:
> omega_nf_eq = 0
> >
> > import sympy as sym
> >
> m,J_d,J_p,y,Y,omega,Omega,phi,Phi,z,Z,theta,Theta,k_yy,k_zz,k_phiphi,k_yphi,k_ztheta,k_thetatheta,plane_xy1,plane_xy2,plane_xz1,plane_xz2
>
> =
> sym.symbols('m,J_d,J_p,y,Y,omega,Omega,phi,Phi,z,Z,theta,Theta,k_yy,k_zz,k_phiphi,k_yphi,k_ztheta,k_thetatheta,plane_xy1,plane_xy2,plane_xz1,plane_xz2',
>
> real = True)
> > t, omega_nf = sym.symbols('t, omega_nf', real = True)
> >
> > omega_nf_eq = sym.Eq(omega_nf, -J_d**2*k_yy*k_zz*omega**4 +
> 0.382*J_d**2*k_yy*omega**6 + 0.382*J_d**2*k_zz*omega**6 -
> 0.145924*J_d**2*omega**8 + J_d*k_phiphi*k_yy*k_zz*omega**2 -
> 0.382*J_d*k_phiphi*k_yy*omega**4 - 0.382*J_d*k_phiphi*k_zz*omega**4 +
> 0.145924*J_d*k_phiphi*omega**6 + J_d*k_thetatheta*k_yy*k_zz*omega**2 -
> 0.382*J_d*k_thetatheta*k_yy*omega**4 - 0.382*J_d*k_thetatheta*k_zz*omega**4
> + 0.145924*J_d*k_thetatheta*omega**6 - J_d*k_yphi**2*k_zz*omega**2 +
> 0.382*J_d*k_yphi**2*omega**4 - J_d*k_yy*k_ztheta**2*omega**2 +
> 0.382*J_d*k_ztheta**2*omega**4 + J_p**2*Omega**2*k_yy*k_zz*omega**2 -
> 0.382*J_p**2*Omega**2*k_yy*omega**4 - 0.382*J_p**2*Omega**2*k_zz*omega**4 +
> 0.145924*J_p**2*Omega**2*omega**6 - k_phiphi*k_thetatheta*k_yy*k_zz +
> 0.382*k_phiphi*k_thetatheta*k_yy*omega**2 +
> 0.382*k_phiphi*k_thetatheta*k_zz*omega**2 -
> 0.145924*k_phiphi*k_thetatheta*omega**4 + k_phiphi*k_yy*k_ztheta**2 -
> 0.382*k_phiphi*k_ztheta**2*omega**2 + k_thetatheta*k_yphi**2*k_zz -
> 0.382*k_thetatheta*k_yphi**2*omega**2 - k_yphi**2*k_ztheta**2)
> >
> > solution = sym.solve(omega_nf_eq.rhs, omega, dict = True , force=True,
> manual=True, set=True)
> >
> > Even after half an hour, sympy is unable to give a solution.
> > I also tried sage math, but I had the same failure.
> > Suggestions?
> >
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