Changes between Version 4 and Version 5 of u/erica/CylindricalGravity


Ignore:
Timestamp:
08/18/14 14:06:33 (10 years ago)
Author:
Erica Kaminski
Comment:

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  • u/erica/CylindricalGravity

    v4 v5  
    88In 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.
    99
    10 '''in Cartesian coordinates:'''
     10'''in Cartesian coordinates (x,y,z):'''
    1111
    1212[[latex($\nabla^2 = \frac{\partial^2f}{\partial x^2} +  \frac{\partial^2f}{\partial y^2} + \frac{\partial^2f}{\partial z^2} $)]]
    1313
    14 '''in Cylindrical coordinates:'''
     14'''in Cylindrical coordinates [[latex($(\rho, \phi, z)$)]]:'''
    1515
    16 [[latex($\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} $)]]
    1717
    18 '''in Spherical'''
     18'''in Spherical [[latex($(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}$)]]
    1921
    2022'''and in 2.5 d:'''