Sorry, but this is not a very exciting post. I’m just going to go over some physics notation and other basic principles so I can reference this in my other posts. I don’t know why the LaTeX stuff looks so weird. I guess I’ll blame wordpress.

# Notation

- A bar over a letter (e.g., ) denotes an average value.
- A boldface letter (e.g., ) denotes a vector.
- A dot above a letter (e.g., ) denotes a time derivative, i.e., .
- A derivative of a vector (e.g., ) denotes derivatives of each of its components, i.e.,
- denotes a sum over all values of . For example, if is allowed to be any integer between 1 and , then is equivalent to
- denotes a sum over all values of except .
- denotes a sum over all values of that are greater than alpha .

# Basic Principles

- We can measure an object’s average velocity () during a time interval by measuring the change in its position () and then computing .
- The natural generalization of average velocity is instantaneous velocity (). To find it, we use .
- We can measure an object’s average acceleration () during a time interval by measuring the change in its instantaneous velocity () and then computing .
- The natural generalization of average acceleration is instantaneous acceleration (). To find it, we use .

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