On March 14, 2011 I traveled to PTC's world headquarters in Needham, MA to record a PTC customer presentation, Nonlinear Dynamics Using Mathcad Prime 1.0.
You will be able to view the 16-minute presentation by registering for the PlanetPTC Virtual Mathcad User Event to be held on Thursday, April 14, 2011 from 1:00 to 5:00 p.m. EDT. (The link is
http://events.unisfair.com/index.jsp?eid=522&seid=611&code=iss
in case you missed Dan Marotta's announcement at the top of the Mathcad Community Web Page:-)
By participating in this PlanetPTC Event, you will have the opportunity to view presentations by Dr. Jakov Kucan, Mr. Mark Walker, and me, as well to visit the exhibit hall, vendor booths, and more.
As you view my presentation, which will start at 2:15 EDT, be sure to note that you can ask questions live anytime from 2:15 to 2:45 EDT. And you will be able to download my presentation worksheets there, too -- look in the lower left corner of the presentation window for Files and Content.
While Mona Zeftel and I were attending Moderator/Speaker training today, Mona said that she thought it might be a good idea if I posted my presentation files here as well.
So here is an overview of the presentation and the files.
1. In Demo_Intro.mcdx, I describe how and why, as an aerospace engineer, I use Mathad 15 and Mathcad Prime 1.0.
2. I show a Mathcad 15 animation of the motions of three Newtonian particles in three dimensions, N=3_2D_Cusps.xmcd.avi. You can also view it as the PlanetPTC video, Bouncing Planets.
3. N=3_2D_Cusps.mcdx is the Mathcad Prime 1.0 worksheet, "Numerical Integration of the Motions of Three Newtonian Particles in Three Dimensions."
In 1912, the Finnish mathematician Sundman proved the existence of an analytical (vs. numerical) solution to the "Newtonian N-body problem" for N=3. However, the solution, in the form of a slowly-convergent power series in time t raised to the 1/3 power, is considered to be so cumbersome that direct numerical integration is the preferred approach.
But even for N=3, to attempt a numerical solution was a dauntingly tedious task in the days before computers. And even as late as the mid-1970s, you could use a mainframe computer to calculate the motions, but few mainframe computers back then had the capability to illustrate the motions graphically.
Today, with Mathcad and a desktop or laptop computer, we can not only find numerical solutions in a matter of seconds for varying masses, initial positions, and initial velocities, but we can also plot the graphs and even animate the plots.
4. In Demo_Deriv.mcdx, I show how I used "reduction of order" to reduce a system of three second-order ODEs to a system of six first-order ODEs. This is needed so that the N=3_2D_Cusps.mcdx worksheet can call Mathcad Prime's Radau numerical integrator directly (vs. using Odesolve, which is easier to set up, but hides the details).
5. OrbitalMotion.pdf is a reference paper that I cite in my presentation.
Question: Would it be useful for me to post the worksheets as .pdf files, so that Mathcad users who haven't upgraded to Mathcad 15 or Mathcad Prime 1.0 can also see the worksheets?
