Model
In modeling physics a physical model describes the system, the state of its constituents (including perhaps geometric and temporal structure), their internal and external interactions, and has Laws of Change that determine the changes of state (i.e. behavior). Models combine the definitions, concepts, procedures, interactions, laws of nature and other relationships that model some aspect of the physical world. Models intermediate between laws of nature, which are relationships among abstract quantities, and experimental/experiential reality.
Properties of a Physical Model
A physical model is a mentally linked collection of physical laws, concepts, equations, and associated descriptions that relate to a particular common pattern found in nature. Examples are motion with constant acceleration, harmonic motion, mechanical energy conservation, and applying ΣF = ma to a point particle. A model consists of the following pieces:
1. the physical systems/situations where the model applies and vocabulary of involved objects, state variables, and agents (interactions) involved.
2. specification of the independent and dependent (measurable) state variables that characterize the system and which the model interrelates
3. what physical theories underlie the model and the resulting Laws of Change
4. the behavior/change in state (geometric and temporal) and interaction structure
5. descriptions of the model and interpretation of its predictions as expressed in all various useful representations
Law of Change
Definition
A Law of Change is an equation which represents the time evolution of some property of a system.
Example - Momentum
For example, the equation:
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 External 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:
Hierarchy of Models
Restrictions to the Law of Change - Sub-models
The hierarchy of Models presented in this WIKI classifies some models as sub-models or special cases of other models. These sub-models have a Law of Change which is a special case of the model of which it is a sub-model.
Example - Point Particle Dynamics
For example, the Point Particle Dynamics model is a sub-model of the Momentum and External Force model. The differential form of the Law of Change for the Momentum and External Force model is:
For a point particle system, the momentum can be written as:
where the mass is constant. Thus, we can write:
which is the Law of Change for Point Particle Dynamics. In this way, the Law of Change for Point Particle Dynamics is a special case of the Law of Change for Momentum and Force, and so Point Particle Dynamics is a sub-model of Momentum and Force in the hierarchy.