Power Tools

We've pulled together some notes on many topics needed to understand, use and develop this manual. You will mine principles and ideas that can help you build your own models of the activities you enjoy most.

Mathematical modeling weilds mathematical tools on the conceptual material of other disciplines, in this case, physics. The result is a framework within which particular facets of the modeled domain can be studied, often in isolation - a luxury seldom known in the realm of empirical experimentation.

Tools

What are these "power tools"? Some are general tools of mathematics. Others, in this manual, are specializations of mathematical tools to operate on physical concepts. Often the tools take the form of definitions, properties, theorems and laws. Sometimes they are conventions and approaches.

1. Convention Notebook

Notation	Here's a breif explanation of our mathematical notation.
Units	A handy description of the units used in this manual. Conversion to and from standard units is covered.

2. Math notebook

Geometry	A refresher on some points.
Algebra	The fine art of substituting symbols for numbers.
Radius of curvature	A good example of geometry and algebra working together.
Trigonometry	The right triangle for a round world.
Calculus	Expressing cause and effect in a well behaved world.

3. Physics notebook

Newton's Laws of Motion	Inertia, force and reaction.
Rotation	Moment of inertia and arcs
Force, work, energy	What's the difference?
Levers and torque	The bones and muscle of modeling objects.
Trajectory and force centers	Boiling shape and volume down to a few points.
Collisions	Elastic and inelastic encounters of Newton's 3rd kind.