Solving multiple equations for a symbolic solution Prime 11.0.1.0

Question

I am currently running the trial version of Mathcad Prime 11.0.1.0 (I think only a few days left) to evaluate its capabilities for solving multiple equations with multiple unknowns. I want to verify that it will produce the results that I need before purchasing the software. I have run into a problem getting Mathcad to solve the system equations symbolically. I have looked around the internet for community information on this aspect of Mathcad but have not found anything that addresses my specific topic.

The problem to which is seek a solution arises when modeling the impact between two bodies. Using the impulse-momentum formulation of Newton's 2nd law gives me 6 equations and six unknowns with a point mass (no rotational inertia) impacting a point mass. I put this system into Mathcad and used the solve feature and it produced the desired result. My file is attached. You will see that I took the solution equations Mathcad produced and ported them over to calculate the numerical solutions after defining the various parameters numerically. Mathcad Point Mass.PNG

The next step was to put the 8 equations and 8 unknowns into Mathcad that I get when I model the the impact with rigid bodies (these have rotational inertia, 2 additional equations, 2 more unknowns). I refer to this problem as planar impact mechanics (PIM). Mathcad does not solve this problem but produces an output with an if-else construct. I have not been able to interpret this output or convince Mathcad to produce a solution. My file is attached. I assume the answer I get is revealing, in some manner, an issue it has with the equations. Mathcad PIM.PNG

I am a little confused that there is an issue with the system equations since these two problems are just precursors to more complicated impact problems that I would like to solve in my research (more than 8 equations and 8 unknows). The solutions to these two systems of equations already have known symbolic/analytical solutions. So I can make comparisons to ensure I am on the right track. The point mass solution Mathcad gives me matches the known solution that I have programmed previously.

I need some Mathcad guidance to get Mathcad to produce the solution equations for the PIM problem and that I can use to solve the more complicated problems.

Werner_E · Answer

A lot of your variables are labelled as "Unit" and not as "Variable" or "-" (for automatic). You can tell as units by default are displayed in bold blue.

As this doe not happen normally when you just type in the expressions it must be assumed that it was you who did so unintentionally. Maybe you used a normal equal sign instead of the boolean one in the first place and typed the expressions in the unit place holder?

Prime's symbolics can't deal with units and know nothing about them and so treats them as unknown. A "P" labelled as "Variable" and a "P" labelled as "Unit" are considered two different variables.

Once all variables are labelled correct, Prime comes up with a solution. The red "error" an be considered as a warning - Prime considers the result to be too large and refuses to display it.

Sometimes you have luck as in your case and Prime at least is willing to display the individual results.

It may be a good idea to define the symbolic solution as a function in all (variable) input values:

You may later evaluate this function either symbolically

But you can also use this function with numeric evaluation

And you may also define functions for the individual solution if that's appropriate

As you can see, I didn't bother using units 😉

But then - if the end goal is to derive numeric results, you may consider omitting the symbolics and use Prime's numeric capabilities. By this I mean a solve block with "Find".

You have to provide guess values for the eight unknowns (take care of using correct units here) and if your goal is to make the calculation using different input values and compare the results, then you can parametrize the solve block and turn it into a function, similar to what I did with the symbolic solution above:

Prime 11 sheet attached

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