Modeling Theory

A model is a surrogate object, a conceptual representation of a physical system and/or its properties. The models in physics are mathematical models with four components:

1. A set of names for the object and agents that interact with it, as well as for any part of the object represented in the model.
2. A set of descriptive variables (or descriptors) representing properties of the object.
   • object variables (things that do not change: mass, initial position and initial velocity, etc.).
   • state variables (things that do change as a function of time: position, velocity, ).
   • interaction variables (represents the interaction: force, potential energy, work, etc.)
3. Equations of the model describing its structure and time evolution.
   • kinematical laws represent equations of change (dx/dt = vx, d vx/dt = a).
   • dynamical laws specify change by differential equations with interaction laws (a = F/m).
   • interaction laws specify how objects interact with each other (Newton's third law, conservation laws, constraints, etc).
4. Interpretation relating the descriptive variables to properties of some object which the model represents.

References

• David Hestenes, “Toward a modeling theory of physics instruction,” Am. J. Phys. 55, 440 (1987).