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## Nonlinear Dynamics Using Mathcad Prime 1.0

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?

1 ACCEPTED SOLUTION

Accepted Solutions

## Re: Nonlinear Dynamics Using Mathcad Prime 1.0

Thank you all for all clarifications. Everything is clear now.

17 REPLIES 17

## Re: Nonlinear Dynamics Using Mathcad Prime 1.0

Thank you for posting the files. I do have MC15 (M005) but I cannot open the posted files. Is there a special trick in order to open them with MC15?

## Re: Nonlinear Dynamics Using Mathcad Prime 1.0

You can't open Mathcad Prime files in Mathcad 15. There is not even any way to convert them to Mathcad 15 files. They can only be opened in Mathcad Prime.

## Re: Nonlinear Dynamics Using Mathcad Prime 1.0

Thanks Richard for the information. How do you convert a file from MC15 to Prime as I do not see the file extension of Prime in my save as options? Or is this option not available because I have not installed Prime?

## Re: Nonlinear Dynamics Using Mathcad Prime 1.0

If you install Mathcad Prime you will also install a converter. It converts files with varying degrees of success, depending on what's in them and how they are laid out.

## Re: Nonlinear Dynamics Using Mathcad Prime 1.0

Hello desomer,

If you want to test drive Mathcad Prime 1.0 or have a look at Roger's worksheet, you can download the 30-day trial.

-Dan

## Re: Nonlinear Dynamics Using Mathcad Prime 1.0

Anyone that buys Mathcad 15 gets a copy of Prime, and vice versa. It just a question of what you choose to install.

## Re: Nonlinear Dynamics Using Mathcad Prime 1.0

Desomer,

Attached is the Mathcad 15 file, N=3_2D_Cusps.xmcd, that I used to generate the animation in my presentation.

As Richard noted, files with extension .mcdx are Mathcad Prime 1.0 files, and there is no way to convert them back to Mathcad 15.

The attached file will open in Mathcad 14 and Mathcad 15. (As Richard has also noted elsewhere, Mathcad 15 files open in Mathcad 14, and vice versa.)

Please answer the question at the bottom of my original post. (Hint: if you have the Adobe reader [doesn't everyone?], you'll be able to view the .pdf versions of the .mcdx files. Even on a Mac.)

Hope to see you all tomorrow, virtually speaking.

Roger

## Re: Nonlinear Dynamics Using Mathcad Prime 1.0

Thank you all for all clarifications. Everything is clear now.

## Re: Nonlinear Dynamics Using Mathcad Prime 1.0

Here are the presentation files as Adobe PDF (Portable Document Format) files.

You should be able to open them with your Adobe PDF file reader (on Wintel PC or Mac).

The 3-body video itself has been posted in the Member Showcase with the new name, Bouncing Planets.

The PTC Virtual Mathcad Event is now wrapping up ... thank you for viewing my customer user presentation.

If you have any questions that were not addressed in the Q&A session with Mark Walker, then please post them here.

Thanks again,

Roger Mansfield

## Re: Nonlinear Dynamics Using Mathcad Prime 1.0

 RogerMansfield wrote:Here are the presentation files as Adobe PDF (Portable Document Format) files..... Roger Mansfield

Thank You very much for Your very Interesting report here - http://events.unisfair.com/index.jsp?eid=522&seid=611

 RogerMansfield wrote:The PTC Virtual Mathcad Event is now wrapping up ... thank you for viewing my customer user presentation.If you have any questions that were not addressed in the Q&A session with Mark Walker, then please post them here.Thanks again,Roger Mansfield

Inertia forces, gavitations forses... And what about Coriolis Forces?

See for example the article "Mathcad and Coriolis Forces"

## Re: Nonlinear Dynamics Using Mathcad Prime 1.0

 RogerMansfield wrote: on April 12, 2011

Do you know what is it this day - April 12, 1961, 50 yeas ago?

http://communities.ptc.com/videos/1651

## Re: Nonlinear Dynamics Using Mathcad Prime 1.0

Dr. Valery F. Ochkov,

Russia was the first nation to place an artificial satellite, Sputnik 1, into Earth orbit on October 4, 1957.

Russia was the first nation to place a human being into Earth orbit, Yuri Gagarin, on April 12, 1961.

Congratulations, Valery, on the successes of your native country, of which you are justifiably proud.

Roger

## Re: Nonlinear Dynamics Using Mathcad Prime 1.0

 RogerMansfield wrote:Dr. Valery F. Ochkov,Russia was the first nation to place an artificial satellite, Sputnik 1, into Earth orbit on October 4, 1957.Russia was the first nation to place a human being into Earth orbit, Yuri Gagarin, on April 12, 1961.Congratulations, Valery, on the successes of your native country, of which you are justifiably proud.Roger

Thanks Roger!

But it was not Russia and not Soviet Union but whole World!

Congratulations to all

## Re: Nonlinear Dynamics Using Mathcad Prime 1.0

Roger, I very much enjoyed your session yesterday. Thank you for posting the files. I only wish I had known yesterday that they would be available before your talk but I did miss Dan Marotta's announcement on the Mathcad Community Web Page. Also many thanks to Valery.

## Re: Nonlinear Dynamics Using Mathcad Prime 1.0

Roger,

Perhaps backdating them to version 14 would benefit a number of users? Thanks.

## Re: Nonlinear Dynamics Using Mathcad Prime 1.0

Tezza,

See my April 13, 2011 post in response to Desomer. The file attached there is a Mathcad 15 file, but it opens in Mathcad 14 and you can generate the Bouncing Planets animation using Mathcad 14.

You can view all of the posted worksheets as PDF files, too -- the Mathcad Prime 1.0 files as well as the Mathcad 14/15 files -- using Adobe's PDF reader.

Roger

P.S. See also Valery Ochkov's animations and worksheets on the Newtonian N-particle problem. In his worksheets, Valery animates the three particles as little black, red, and blue balls. I chose not to do this because the sizes of the balls cannot be made strictly proportional to the masses, and because the added functionality makes the worksheets just a little bit more complicated than I wanted to present at PlanetPTC. But Valery's animation of the balls as well as the trajectories makes his videos just that much more interesting.

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