Changes between Version 4 and Version 5 of u/erica/CylindricalGravity
- Timestamp:
- 08/18/14 14:06:33 (10 years ago)
Legend:
- Unmodified
- Added
- Removed
- Modified
-
u/erica/CylindricalGravity
v4 v5 8 8 In cartesian coordinates, the Laplacian contains only simple derivatives, i.e. does not contain any functions of position as it does in cylindrical or spherical coordinates. 9 9 10 '''in Cartesian coordinates :'''10 '''in Cartesian coordinates (x,y,z):''' 11 11 12 12 [[latex($\nabla^2 = \frac{\partial^2f}{\partial x^2} + \frac{\partial^2f}{\partial y^2} + \frac{\partial^2f}{\partial z^2} $)]] 13 13 14 '''in Cylindrical coordinates :'''14 '''in Cylindrical coordinates [[latex($(\rho, \phi, z)$)]]:''' 15 15 16 [[latex($\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} $)]]16 [[latex($\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} $)]] 17 17 18 '''in Spherical''' 18 '''in Spherical [[latex($(r, \theta, \phi)$)]]:''' 19 20 [[latex($\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}$)]] 19 21 20 22 '''and in 2.5 d:'''