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{td:align=center|bgcolor=#F2F2F2}*[Model Hierarchy]*
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h2. Description and Assumptions

{excerpt}This model is [generally applicable|generally applicable model], but mathematically very complicated.  In introductory mechanics it will only be used to describe the motion of a gyroscope.{excerpt}


h2. Problem Cues

Only used in problems involving a gyroscope.

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h2. Prerequisite Knowledge

h4. Prior Models

* [1-D Angular Momentum and Torque]
* [Uniform Circular Motion]


h4. Vocabulary

* [torque (one-dimensional)]
* [angular momentum (one-dimensional)]

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h2. System

h4. Constituents

A single [point particle|point particle] (or a system treated as a point particle with position specified by the center of mass).

h4. State Variables

Time (_t_), axial angular momentum (_L_), axial angular velocity (ω), precessional angular velocity (Ω), axial moment of inertia (_I_), mass (_m_).

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h2. Interactions

h4. Relevant Types

Some time-varying external influence that is confined to one dimension.

h4. Interaction Variables

Acceleration (_a_(_t_)).

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h2. Model

h4. Laws of Change

Differential Forms:
\\
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{latex}\begin{large}\[ \frac{dv}{dt} = a\]\end{large}{latex}\\
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{latex}\begin{large}\[ \frac{dx}{dt} = v\]\end{large}{latex}\\
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Integral Forms:
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{latex}\begin{large}\[ v(t) = v(t_{0})+\int_{t_{0}}^{t} a\;dt\]\end{large}{latex}\\
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{latex}\begin{large}\[ x(t) = x(t_{0})+\int_{t_{0}}^{t} v\;dt\]\end{large}{latex}\\

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h2. Diagrammatical Representations

* Acceleration versus time graph.
* Velocity versus time graph.
* Position versus time graph.

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h2. Relevant Examples

None yet.
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