In our version of modeling physics, a model is a specific Law of Change that is applied to a system.
Page Contents |
|---|
Many Definitions of Model
The word "model" has many meanings in everyday language, and it has many meanings in physics as well. The Models in Physics page gives a summary of what is usually called the modeling approach to mechanics. In this WIKI, however, we will use a more narrow definition of model. We will use it to refer to a specific Law of Change (which may have more than one equivalent form) that can be applied to systems which meet certain specified restrictions.
Law of Change
Definition
A Law of Change is an equation which expresses the time evolution of some property of a system.
Example – Momentum
For example, the equation:
\begin
[ \vec
_
= \vec
_
+ \int_{t_{i}}^{t_{f}} \vec
^
\;dt]\end
expresses the time evolution of the momentum of a system in terms of the external forces acting on the system. It is therefore a Law of Change (in this case, belonging to the [Momentum and Force] model).
Integral vs. Differential
Many Laws of Change can be equivalently expressed using derivatives or using integrals (or using explicitly integrated quantities).
Example – Momentum
For example, the Law of Change from the momentum model that was discussed above is an integral form. This Law could also be expressed as:
\begin
[ \frac{d\vec{p}}
= \vec
^
]\end
Hierarchy of Models
Restrictions to the Law of Change – Sub-models
The [Model Hierarchy] presented in this WIKI classifies some models as sub-models or special cases of other models.