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These are replies submitted by Earl

@Rouben Rostamian  Another great reply from you!

From an old list of Harvard weekly problems; with a given mass and a uniform density, this shape produces the greatest gravitational force at the origin.

@gkokovidis Based on djc561's recommendation above, I am exploring Micro-Cap at this time.

Depending on how I do, I may go on to explore your recommendation.

@djc I have installed Micro-Cap and begun to practice its capabilities by following Chapter 3 of the user manual.

I am deeply impressed by its sophistication, which is far above my needs. Hopefully I can become familiar enough with its simpler features to do simple circuit analysis.

Thank you very much for the reference

@tomleslie I'll do as you suggest.

@acer I would like to use a component featured circuit analyser but can't justify the cost of MapleSim.


I greatly appreciate the time you have taken to give me an example of a Syrup analysis.

Far from an expert, I have only ever dealt with simple LRC circuits so Syrup may have all the capability I need.

Is there a better free package for simple circuit analysis?

In your example, is LPckt a Spice-like circuit definition? Is it better to use this than the ladder specification of a circuit?

Is there anywhere a collection of Syrup examples to which you can refer me?

@Joe Riel Thanks for the quick response.

I will give the cloud version of Syrup a try.

@acer Thanks for the advice.

I have attempted the same display using fieldplot and it works well.

However I find fieldplot3d's displays are hard to visualize e.g. the magnetic field through a current carrying ring. Do you have any advice for improving the appearance of this kind of display?


@vv Thank you vv. Please see my reply to Carl Love

@Carl Love My intent was to display the magnetic field surrounding two current carrying wires, one coming out of the xy plane, the other going into the xy plane. It seems the third term in the expression Bst should be y rather than zero.

It also seems I do not fully understand the effect in a 2 dimension contourplot of plotting a three term expression.

I thank you for prompting me to re-examine my intent.

BTW, contours show magnetic field lines but without field direction i.e. without showing north vs. south poles. Is there a neat way to add arrow heads to the contours in a contourplot?

@Carl Love Thank you for this. I'm busy now with another project but sometime within the next few days I'll access your post and see if I can adapt it as a higher-level plotting command.

@Rouben Rostamian  Thank you. 

As I replied to Carl Love, I'm guessing your answer implies that there is no way for a procedure invoked by a plot command to pass anything other than the function to be plotted. Is this true?

@Carl Love I'm guessing your answer implies that there is no way for a procedure invoked by a plot command to pass anything other than the function to be plotted. 

@Rouben Rostamian  I very much appreciate that you've taken the time to show me the energy/forces way to find the coaster loop curve.

In the worksheet below, I have corrected my original energy/forces ode equations (which are explicated more clearly in your worksheet) and then use Kepler's equation to reach an identical curve.

Amazing that there seem to be three different approaches yielding the correct curve!


@Rouben Rostamian  In the worksheet below, in the second ODE equation, I corrected the gravity vector. Then I applied Carl's change. The coaster loops now proceed horizontally but successive loops increase in size.

The second odeplot shows velocity increasing in successive loops, which seems to indicate a fault in the first ODE equation describing the system's energy.

Can you detect the error?


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