This is a spinoff issue from #96 .
A partial fix to problem 2.) described there is to extend https://github.com/sandialabs/LCM/blob/main/src/evaluators/bc/PHAL_ExprEvalSDBC_Def.hpp to compute using symbolic differentiation the time-derivatives of the prescribed time-dependent DBC specified in the input file. To do this, we need to see if STK or Panzer's expression evaluator capabilities can do symbolic differentiation.
A workaround is to have the user specify the analytic form of xdot and xdotdot in the input file.
Getting things to work for non-expression evaluated SDBCs would be more challenging and would require relying on finite differences, as done in SIERRA. We may want to do this at a later point in time.