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h2. Keys to Applicability

Can be applied to any system for which the change in [mechanical energy] can be attributed to [work|work] done by [non conservative forces|non-conservative] (as opposed to processes like heat transfer, radiative losses, etc.). The non-conservative forces can be external forces exerted on the system or internal forces resulting from the interactions between the elements inside the system. It is specially useful for systems where the non-conservative work is zero, in which case the [mechanical energy] of the system is constant. 


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]

h4. Vocabulary
* [system]
* [internal force]
* [external force]
* [conservative force]
* [non-conservative]
* [kinetic energy]
* [gravitational potential energy]
* [elastic potential energy]
* [mechanical energy]

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h2. Model Specification

h4. System Structure

*[Constituents|system constituent]:*  One or more [point particles|point particle] or [rigid bodies|rigid body]. Technically, the system must be defined in such a way as to contain all objects that participate in any non-negligible [conservative|conservative force] interactions that are present.  
{note}For example, for systems subject to earth's gravity, the earth should technically be included in the system, though it is usually sufficient to treat it as a rigid body that is at rest and has infinite mass.  If this approximation is made, the earth will have zero kinetic energy (it will not change its velocity, since it has infinite mass).{note}  \\

*[Interactions|interaction]:*   All forces that do [non-conservative] [work] on the system must be considered, _including_ [internal forces|internal force] that perform such work.  [Conservative forces|conservative force] that are present should have their interaction represented by a [potential energy] rather than by [work].  

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h4. Descriptors

*[Object Variables|object variable]*:  Mass orNone.
{note}Object masses and moment of inertia forcan eachtechnically objectchange aboutin athis givenmodel, axisso ofthey rotation, (_m{_}{^}j^) or (_I{^}j{^}{~}Q{~}_). (????If the objects in the system interact with a spring then the spring constant.)

State Variablesare state variables.{note}
*[State Variables|state variable]*:   Kinetic energy for each element of the system and the potential energy of the system. (? Or alternatively, linear speed or angular speed, (_v{_}{^}j^) or (_w{^}j{^}) Mass (_m_^j^) and possibly moment of inertia (_I_{^}j{^}) for each object plus  linear (_v_^j^) and possibly rotational (ω^j^) speeds for each object, insideor the system and alternatively, the positionkinetic of each of the objects in the system).

Interaction Variablesenergy (_K_^j^) may be specified directly.  

*[Interaction Variables|interaction variable]*:   External and internal non conservative forces, _F{_}{~}NC,ext{~} and _F{_}{~}NC,int{~}) or, alternately, the work done by the external and internal non conservative forces.

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h2. Model Equations

h4. Laws of Interaction
Here should go the possible type of forces, friction, tension, etcs
{latex}\begin{large}$ $\end{large}{latex}


h4. Laws of Change

{latex}
\begin
{large} $E_{f} = E_{i} + W_{i,f}^{NC} $ \end{large}{latex}\\

where _W{^}NC{^}{~}i,f{~}_ is the [work] done by the all the non-conservative forces on the system between the initial state defined by _E{~}i{~}_ and the final state defined by _E{~}f{~}_ and is given by

{latex}\begin{large}$ W_{i,f}^{NC} = \int_{i}^{f} \sum \vec{F}^{NC} . d\vec{r}  $ \end{large}{latex}

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