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Description
Unknown macro: {table} Unknown macro: {tr} Unknown macro: {td} [Model Hierarchy]
Unknown macro: {tr} Unknown macro: {td}
The root page Model Hierarchy could not be found in space Modeling Applied to Problem Solving.
Assumed Knowledge
Prior Models
Vocabulary
Model Specification
System Structure
Internal Constituents: Point particles.
Environment: Only external forces need be considered, since internal forces do not change the system momentum.
Descriptors
Object Variables: Mass for each object (mj), unless momentum is given directly.
State Variables: Velocity (vj) or momentum (pj) for each object.
Interaction Variables: External forces (Fext,k) or, alternately, impulses may be specified (Jext,k).
Laws of Interaction
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Unknown macro: {large} [ \vec
Unknown macro: {J}
_
Unknown macro: {ext,k} = \int \vec
Unknown macro: {F}
_
\:dt ]
[ \frac{d\vec
Unknown macro: {p}
_{\rm system}}
Unknown macro: {dt}
= \:\sum_
Unknown macro: {k=1}
^{N_{F}} \vec
Unknown macro: {F}
_
Unknown macro: {ext,k}
]\end
where the system momentum is the vector sum of the constituent momenta:
Unknown macro: {latex} \begin
Unknown macro: {large} [ \vec
Unknown macro: {p} _
Unknown macro: {rm system}
= \sum_
Unknown macro: {j=1}
^
Unknown macro: {N}
\vec
^
Unknown macro: {j}
]\end
where N is the number of system constituents.
Laws of Change
Unknown macro: {latex} \begin
Unknown macro: {large} [ \vec
Unknown macro: {p} _
Unknown macro: {rm system,f}
= \vec
_
Unknown macro: {rm system,i}
+ \sum_
Unknown macro: {k=1}
^{N_{F}} \vec
Unknown macro: {J}
_
Unknown macro: {ext,k}
]\end
Relevant Examples
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