Staffan,
Just a guess, but sin(phi) goes negative even for positive values of phi.
You’d have limit the range to 0 <= phi <= pi.
— Arthur
On Mon, Dec 19, 2022 at 1:41 PM Staffan Lundberg <
drstaffan.lundb...@gmail.com> wrote:
> I am working with curvilinear coordinates, especiallt how to determine
> scale factors for spherical coordinates and how to express the unit vectors
> i terms of i, j, k (cartesian base vectors). I submit some code
>
> #
> # curvilinear.py
> #from sympy import *
> x, y, z = symbols("x y z")
> rho= symbols("rho",positive=True,real=True)
> theta = symbols("theta",positive=True,real=True)
>
> phi = symbols("phi",positive=True,real=True)
> # spherical coord
> x=rho*sin(phi)*cos(theta)
> y=rho*sin(phi)*sin(theta)
> z=rho*cos(phi)
>
> A=Matrix([[x],[y],[z]])
> r=A
> dr=diff(r,rho)
> hr=dr.norm()
> hr=simplify(hr)
>
> dphi=diff(r,phi)
> hphi=dphi.norm()
> hphi=simplify(hphi)
>
> dtheta=diff(r,theta)
> htheta=dtheta.norm()
> htheta=simplify(htheta)
>
> r_hat=dr/hr
> fi_hat=dphi/hphi
> th_hat=dtheta/htheta
> print(fi_hat)
> print(th_hat)
> print(r_hat)
> #
> #
>
> Problems with th_hat. Despite telling sympy that phi is positive, I get
> Abs(sin(phi)) instead of sin(phi). Thus python does not cancel the
> factor sin(phi).
>
> Has anyone some hints how to solve this issue. Maybe a bug in sympy?
> /Staffan L
>
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