A. Modified Mathematica Built-in Symbols

Additional Function Definitions

New definitions are made for the built-in Mathematica symbols Direction and Jacobian (options for Limit and FindRoot, respectively). The new functional definitions that are made for these symbols by MechanicalSystems do not interfere with their standard Mathematica usages as option names.
MechanicalSystems also makes additional functional definitions for Cross and Dot. These new definitions do not interfere with the built-in definitions, they simply allow Cross and Dot to automatically convert MechanicalSystems vector objects (Vector, Line, Plane) into normal vectors so that the cross or dot product can be calculated. Further, Modeler2D defines the cross product of a pair of 2-vectors, which is not defined by the built-in definition of Cross.

Additional Derivative Definitions

Definitions are made by MechanicalSystems for the derivative functions of Abs, Sign, Mod, Round, Floor, and Ceiling. The new definitions disregard the discontinuous nature of these functions and they are not valid for complex numbers in general.

Additional Usage of Existing Symbols

MechanicalSystems makes extensive use of a few built-in Mathematica symbols, such as Line and Point, and many standard option names, such as MaxIterations and InterpolationOrder. No new definitions are made for these symbols, they are simply used to carry their arguments or specify options as they are in standard Mathematica.