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h2. Description

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{td:align=center|bgcolor=#F2F2F2}*[Model Hierarchy]*
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h2. Assumed Knowledge


h4. Prior Models

* [Point Particle Dynamics]
* [One-Dimensional Motion with Constant Acceleration|1-D Motion (Constant Acceleration)]

h4. Vocabulary

* [system]
* [force]
* [impulse]
* [momentum]
* [acceleration]

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h2. Model Specification


h4. Keys to Applicability

Can be applied to any system for which [external forces|external force] are known, especially useful forThis model is [generally applicable|generally applicable model] (assuming knowledge of the external forces and system constituents), but is especially useful when:

* describing the momentum of systems where theyexternal forces are absent (system momentum conserved for that system) or act only for a short time (Impulse) as in collisions. will be constant).
* estimating the force in a process that occurs in a very short time interval as in collisions (impulse will be easier to determine than force).

{info}"Very short" is a relative expression.  In collisions, we generally use the conservation of the system's momentum to yield information about the _change_ in momentum of the _individual system constituents_.  A "very short" collision is one in which the internal forces produce an impulse on the constituent of interest that is so much larger than the impulse from external forces that the external forces can be neglected.  Of course, that is a relative criterion as well, and will depend on the desired accuracy of the calculation.{info}

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h2. Model Specification

h4. System Structure

Internal Constituents:  System is composed of [Point particles|point particle].
{note}Rigid bodies may be treated as point particles with positions specified by the center of mass positions of the rigid bodies when this model is used.{note}
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Environment:   Only [external forces|external force] need be considered, since [internal forces|internal force] do not change the system's momentum.
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h4. Descriptors

Object Variables:  Mass for each object (_m{_}{^}j^), unless momentum is given directly.

State Variables:   Velocity (_v{_}{^}j^) or momentum (_p{_}{^}j^) for each object inside the system.

Interaction Variables:   External forces (_F{_}{~}ext,k~) or, alternately, impulses may be specified (_J{_}{~}ext,k~).  They may act on any or all particle(s) in the system.


h4h2. LawsModel of InteractionEquations

{latex}\begin{large}\[ \frac{d\vec{p}_{\rm system}}{dt} = \:\sum_{k=1}^{N_{F}} \vec{F}_{ext,k} \]
\[ \endvec{largep}{latex}
where the_{\rm system momentum is the vector sum of the constituent momenta:
{latex}\begin{large}\[,f} = \vec{p}_{\rm system,i} =+ \sum_{jk=1}^{N} \vec{p}^{j} \]\end{large}{latex}
where _N_ is the number of system constituents.  The integral form involves

*Impulse:*

{latex}\begin{large}\[{F}} \vec{J}_{ext,k} = \int \vec{F}_{ext,k}\:dt  \]
\end{large}{latex}

h4. Laws of Change
where the system momentum is the vector sum of the constituent momenta:
{latex}
\begin
{large}\[ \vec{p}_{\rm system,f} = \vec{p}_{\rm system,i} + \sum_{kj=1}^{N_{F}} \vec{Jp}_^{ext,kj} \]\end{large}
{latex}\\
where _N_ is the number of system constituents.  

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h2. Relevant Examples

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