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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

Internal Constituents:*[Constituents|system constituent]:*  One or more [Pointpoint particles|point particle] or [rigid objectsbodies|rigid objectbody]. \\

Environment:*[Interactions|interaction]:*   [External forces|external force] that do non-conservative work on the system. (??? If I want to be consisten with all the model structure I should leave here only the external forces. My concern is that leaving it in this way may give the impression to the student that they only need to think about the external non conservative forces and forget the possible work done by internal non-conservative forces, what do you thin??)

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h4. Descriptors

Object Variables:  Mass or moment of inertia for each object about a given axis of rotation, (_m{_}{^}j^) or (_I{^}j{^}{~}Q{~}_). (????If the objects in the system interact with a spring then the spring constant.)

State Variables:   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{^}) for each object inside the system and the position of each of the objects in the system).

Interaction Variables:   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.

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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