[Date Index] [Thread Index] [Author Index]
Playing with numerically integrated fields?
I'm experimenting with the fields (gravitational, electric, magnetic) of extended objects that I'm visualizing through VectorPlot/VectorPlot3D, StreamPlot, and ContourPlot and examining the behavior of the motion of particles through. These are all excellent tools, but I have some random questions regarding them. My situation specifically involves the situation where I'm calculating a field strength from a static assemblage of "charge" generators (again, whether it's gravitational or electromagnetic) and then examining the behavior and dynamics of the resulting fields. First, I presume there is no 3D analog for StreamPlot? So StreamPlot can only visualize two-dimensional cross-sections? Second, I'd like to show a ContourPlot of the potential of some of these fields fields, but sometimes the equation of the field strength has to be numerically integrated (with NIntegrate) at each point rather than having a simple, closed-form solution that I could pump through DSolve to solve for the potential from the field strength. Any suggestions here? Third, sometimes I want to look at dynamics of particles responding to these fields, and I've seen numerical integration of the dynamics of closed-form fields. But how do I tackle the numerical integration of the path of a particle responding to forces on it from a field when the field itself has to be numerically integrated at each point? If this is all too abstract I'll give examples, but hopefully I'm making my intentions clear. Thanks. -- Erik Max Francis && max at alcyone.com && http://www.alcyone.com/max/ San Jose, CA, USA && 37 18 N 121 57 W && AIM, Y!M erikmaxfrancis Tomorrow does not exist. Twenty tomorrows is a long time. -- Lady Mariko