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DieterSchmidt1-Visitor
1-Visitor
November 3, 2018
Solved

Solving a non-linear differentialsystem 2.order

  • November 3, 2018
  • 2 replies
  • 3395 views

Greetings,

i am trying so solve the attachted differentialsystem in Mathcad 15. Note, that im not THAT familiar with the program.The last few days i spent searching this forum, but i couldnt get any clue. The error massage seems to vary within an Hour Smiley LOL

 

Some Background:

This is a differentialsystem, which describes the motion of an impacted panel and the impactor.

 

Thanks in advance Smiley Happy

 

 

Best answer by Werner_E

OK, I played around with your sheet and at first I found out that your system solves without any problems if I reduce the value of q significantly. The highest value I was able to use was just 119 Pa

B0.png

Then playing further I saw that I can use higher values for q if I reduce the end time t.e.

For the system with the values given to solve you have to reduce t.e down to just 11 microseconds.

B1.png

So it seems the you are not allowed to go farther with t.e than to the point where the two curves meet. If you do the solve block fails. If y gets larger than x the radikand, the expression under the root, gets negative and the result is non-real. Obviously something odesolve can't deal with.

The values of x and y are in the range of micrometer now - not sure if thats what you expect. If not you might want to check your values.

Of course this all works in Prime, too, with the benefit of being able to use real units.

 

Mathcad 15 file attached.

 

2 replies

W
Werner_E25-Diamond I
25-Diamond I
November 3, 2018

I guess you will have to strip the units off as Mathcad 15 usually does not allow units in a solve block with odesolve.

(This is one of the very few advantages of Prime as Prime would allow for units here)

W
Werner_E25-Diamond I
25-Diamond I
November 3, 2018

I just gave it a try and after omitting the units the block still fails and also the file converted to Prime fails with strange error messages.

B1.png

 The error message varies depending on the algorithm chosen. For Adams/BDF and for Radau I get the "The return value of this function must match the problem size" which is shown in the picture.

Choosing Fixed or Adaptive changes the message to "This value must be real.".

 

B2.png

 

W
Werner_E25-Diamond IAnswer
25-Diamond I
November 3, 2018

OK, I played around with your sheet and at first I found out that your system solves without any problems if I reduce the value of q significantly. The highest value I was able to use was just 119 Pa

B0.png

Then playing further I saw that I can use higher values for q if I reduce the end time t.e.

For the system with the values given to solve you have to reduce t.e down to just 11 microseconds.

B1.png

So it seems the you are not allowed to go farther with t.e than to the point where the two curves meet. If you do the solve block fails. If y gets larger than x the radikand, the expression under the root, gets negative and the result is non-real. Obviously something odesolve can't deal with.

The values of x and y are in the range of micrometer now - not sure if thats what you expect. If not you might want to check your values.

Of course this all works in Prime, too, with the benefit of being able to use real units.

 

Mathcad 15 file attached.

 

F
Fred_Kohlhepp23-Emerald I
23-Emerald I
November 3, 2018

This makes sense, since this is supposedly a collision, "impacted panel and impactor."  

 

One wonders why the impactor doesn't rebound rather that travel thru the panel. . .

W
Werner_E25-Diamond I
25-Diamond I
November 3, 2018
@Fred_Kohlhepp wrote:

This makes sense, since this is supposedly a collision, "impacted panel and impactor." 

... what the used equations evidently do not consider

 

 

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