There's some exciting news about a product I've lived with—and sometimes praised, sometimes cursed—for decades: Mathcad, PTC's premier math analysis tool.

Regular readers know that most of my columns are math-oriented, as is most of my work. For that reason, I'm a heavy user of Mathcad. For more than 15 years, I've maintained a love-hate relationship with Mathcad. I've mentioned it many times in my columns, in terms ranging from wholehearted endorsements to heated, curmudgeonly rants. Although I often curse Mathcad as I use it, the r......

Physicists know that many problems can be treated as though the dynamical event happened instantaneously. Examples might include the impact of a hammer and nail, two billiard balls colliding, or a baseball bat hitting the ball. Deep down, we know that there is a complex interaction involve. Materials get deformed, forces get exerted, and velocities get changed. But we don't need to know the details or the time history of the collision. From our perspective, the scale of time is so short that it might as well be zero.

We call such collisions impulsive. From our perspe......

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This is not an unreasonable approach, as long as you don't mind the 90 W part. A vertical descent is what we used for Surveyor and other unmanned missions. It simplifies the automated landing quite a bit, and you can change that landing longitude by making only the slightest tweaks to the outbound trajectory.

The vertical descent is simple to automate, but it's not very efficient. When you're landing vertically, your rocket motor expends a lot of fuel fighting gravity. With a grazing, nearly horizontal approa......

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This approach is, in fact, the same one adopted by Euler, Lagrange, and company. In their formulation of the RTBP, they wrote the equations of motion in the rotating system, which meant that they had to add centrifugal and Coriolis terms to the equations. We don't really have to do that. It's easier to compute things in an inertial system; we only need to use the rotating one during input and output transformations.

In 1960, I was using a simulation of the RTBP to study the circumlunar trajectory. I found it pre......

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The three-body problem

One look at figure 1, though, tells you that this ain't your grandfathers ellipse. It's a strange and complicated trajectory, bending left, then right, then around the moon, in a sinuous path perhaps more familiar to a figure skater than an astronaut.

The trajectory is not an ellipse because this isn't a two-body problem, it's a three-body problem. As soon as the early astronomers—which included such mathematical giants as Gauss, Euler, Lagrange, and Poincaré......

We have a new topic this month, and it has absolutely nothing—well, almost nothing—to do with the topics we've been discussing lately—software development, testing, and the like. On the other hand, it certainly has to do with embedded systems and software. Systems that tend to be rather remote. Like 240,000 miles remote.

If you happened to see m......

[Continued from How I test software, again and again (Part 1)]

Hand checks

Now we get to the real meat of the issue, which is how to do hand checks. I've been telling you for some time now that I do a lot of testing, including testing every single line of code, usually as I write it. When I say testing, I mean give the code under test some inputs and verify that it gives the right outputs.

But where do those inputs come from? From a test case, of course.

Now, almost all of my software tends to be mathematical in nature—old-time readers know that. So my test cases tend......

This is the continuation of my article, "How I Test Software". We have a lot to cover this time, so let's get right to it. I'll begin with some topics that don't fit neatly into the mainstream flow.

Test whose software?
As with my previous article, "How I Test Software", I need to make clear that the chosen pronoun in the title is the right one. This is not a tutorial on software testing methodologies. I'm describing the way I test my software.

Does this mean that I only write software solo and for my own use? Not at all. I've worked on many large projects. But when I do, I try to carve out a piece that I ca......

Do you get the impression from my previous column that I'm not a big fan of mediocrity? You're right.

I'm old enough to remember the days when there were no such things as franchise motels. Your average "motel" was more likely to be a collection of little cottages, much like an RV park of today. You paid your money, you got to sleep in one of the cottages, and the term "quality" was interpreted as, no roaches crawling across your nose. Maid service? Surely you jest.

Then along came the Interstate Highways. And with the highways, this wonderful franchise known as the Holid......

The U.S. Declaration of Independence says "All [people] are created equal." That's very true, but we don't all stay equal. Or, to paraphrase Animal Farm's pig Napoleon, all people are equal, but some people are more equal than others.

I'm not talking about politics here, though that might be an interesting topic for another day. I'm talking about variances in people's abilities to produce a product. More specifically, a high-quality software product.

Over the years, I've known a lot of software folk – some good, some bad, some mediocre. I've known a few who......