Context Navigation

CylindricalGravity

-              v6
+              v7
 [[latex($\nabla^2 = \frac{1}{\rho} \frac{\partial}{\partial \rho}(\rho \frac{\partial f}{\partial \rho}) +  \frac{1}{\rho ^2}\frac{\partial^2 f }{\partial \phi^2}  + \frac{\partial^2f}{\partial z^2} $)]]
 '''in Spherical [[latex($(r, \theta, \phi)$)]]:'''
+'''in Spherical [[latex($(r, \theta, \phi)$)]] coordinates:'''
 [[latex($\nabla^2 = \frac{1}{r ^2} \frac{\partial}{\partial r}(r^2 \frac{\partial f}{\partial r}) +  \frac{1}{r ^2 \sin \theta}\frac{\partial}{\partial \theta}(\sin \theta \frac{\partial f}{\partial \theta}) + \frac{1}{r^2 \sin^2 \theta} \frac{\partial^2 f}{\partial \phi ^2}$)]]
+'''and in 2.5 d:'''
+Currently astrobear is configured for gravity in Cartesian coordinates. I will be modifying the code so that it can solve for gravity in 2.5D (aka cylindrical, axisymmetric symmetry) and 1D spherical geometry (aka spherical coordinates with polar and azimuthal symmetry). With these symmetries, the Laplacian becomes:
+'''in 2.5 d:'''
+'''in 1d, spherical:'''