Help Solving a System of Differential Equations

[dnordemann]

I’m having trouble solving this system of differential equations. I’m pretty new to Mathcad and I don’t really have that much experience with differential equations either so I’m really off to a great start.

I’m trying to calculate the flight path of a spinning tennis ball being launched at 45 deg. I am working with some numbers now but they are partially placeholders. I removed units for now just to take out one level of complexity.

Feel free to check my equations but the real problem I’m having is with my initial conditions (I think). I keep getting the error message “Unknown error: dae%_­inital%­_condition%_error.” and I'm not sure how to fix it.

I’ve attached the file below. I'm using Mathcad prime 3.1

Thanks

[Fred_Kohlhepp]

Unless 3.1 has suddenly broken with tradition the error message rarely hints at the actual problem.  If you can "Trace Error," you may get a clue where the problem actually lies.  Otherwise the error means "it won't compute."  This is unfortunately especially true in solve blocks.

You're using 3.1, since I only have 3.0 (and cannot, therefore, actually see your file) you'll have to wait for a more up-to-date user to provide a better clue.  These angels exist--be patient!

[vlehner · Accepted solution]

Hallo Dan,

See attached File, hope it will be helpful.

I'm using MathCad Prime 3.1 as well.

Volker

[ValeryOchkov]

Welcome Celestial mechanics with Mathcad (Небесная механика с Mathcad)

[dnordemann]

Wow, thanks, everyone!

Haha Fred, that point about the error messages is all too true.

Volker, you are a god among men. That is exactly what I needed. I should be able to modify that with no problem at all.

Valery, thanks, I will definitely check that out.

-Dan

[vlehner]

Thanks Dan,

here another example to use the solve block with differential Equations and with Units.

...have Fun driving the beetle...

Greets, Volker

[-MFra-]

Hello Dan,

if you're interested, here is the analytical solution. As you see the problem is very simple ...

[dnordemann]

Volker, thanks more examples are always better. I'm starting to get a hang of how this works. 

F.M., thanks that is really interesting. Did you ever calculate exactly how different the numerical solution is to the analytical one?

Sorry to the both of you for not responding sooner I was traveling.

[-MFra-]

Hi Dan,

the relative error, practically, is null.

Bye