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Description

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[Model Hierarchy]

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The root page Model Hierarchy could not be found in space Modeling Applied to Problem Solving.

Page Contents


Assumed Knowledge

Prior Models

Vocabulary


Model Specification

Keys to Applicability

Can be applied to any system for which external forces are known, especially useful for systems where they are absent (momentum conserved for that system) or act only for a short time (Impulse) as in collisions.

System Structure

Internal Constituents:  System is composed of Point particles.
Environment:  Only external forces need be considered, since internal forces do not change the system's momentum.

Descriptors

Object Variables:  Mass for each object (mj), unless momentum is given directly.

State Variables:  Velocity (vj) or momentum (pj) for each object inside the system.

Interaction Variables:  External forces (Fext,k) or, alternately, impulses may be specified (Jext,k).  They may act on any or all particle(s) in the system.

Laws of Interaction

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\begin

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[ \frac{d\vec

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_{\rm system}}

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= \:\sum_

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^{N_{F}} \vec

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_

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]\end

where the system momentum is the vector sum of the constituent momenta:

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\begin

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[ \vec

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_

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= \sum_

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^

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\vec

^

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]\end

where N is the number of system constituents.  The integral form involves

Impulse:

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\begin

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[ \vec

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_

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= \int \vec

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_

\:dt ]\end

Laws of Change

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\begin

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[ \vec

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_

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= \vec

_

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+ \sum_

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^{N_{F}} \vec

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_

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]\end



Relevant Examples

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RELATE wiki by David E. Pritchard is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.


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