13.1.3 Load Inspection

Mech load expressions may be rendered invalid by the presence of nonnumeric expressions in the same way as constraint expressions. CheckSystem evaluates the current load expressions, if any exist, subject to the current values of the initial guesses, parameters, and Lagrange multipliers, and reports any nonnumeric expressions found. To demonstrate, a simple load is added to the reciprocating slider model defined in Section 13.1.2.

A force applied to body 2.

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If the symbols k and b are defined at runtime, but not defined in such a way that the expression Exp[k t + b] evaluates to a number, CheckSystem will not be able to determine exactly what is wrong. For example, CheckSystem is limited to recognizing raw symbols only. CheckSystem does not recognize a user-defined variable of the form c[n].

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The load inspection function.

Loads is a Mech function that is used to return all or part of the vector of load expressions that are applied to the current model. Usually, the loads are inspected subject to the values of the current guesses, parameters, and Lagrange multipliers, which shows exactly what CheckSystem saw to be an error.

Here is the current vector of applied loads.

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In all cases, the input shown should return a list of numbers. In this case, the second load expression, the Y component of the force applied to body 2, evaluates to a symbolic expression instead of a single number. Obviously this is due to the definition of b = c[1] given.
However, c[2] does not appear in the applied loads. This is because c[2] (k) is multiplied by time T. The current initial guess for T is T -> 0, so c[2] is canceled entirely. Thus, CheckSystem does not even recognize the presence of c[2] until the initial guesses are perturbed.

We can repair one of the bogus definitions, but the other still remains.

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CheckSystem thinks that all is well, which is definitely not the case. This is an often frustrating flaw in CheckSystem, but it cannot tell what is and is not a number until it evaluates it, and zero times anything is a number. If the value of time is perturbed, CheckSystem sees that the loads are not purely numeric.

If we change the current value of time with SetGuess, CheckSystem recognizes an error.

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Now we repair the other bogus definition.

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Now the loads evaluate to a nested list of numbers, as is required.