# Glossary

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., $\bar{v}$) denotes an average value.
• A boldface letter (e.g., $\bf r$) denotes a vector.
• A dot above a letter (e.g., $\dot {\bf r}$) denotes a time derivative, i.e., $\dot {\bf r} = \frac{d}{dt}{\bf r}$.
• A derivative of a vector (e.g., $\dot {\bf r}$) denotes derivatives of each of its components, i.e., $\dot {\bf r} = \dot{r}_x \hat{\bf x} + \dot{r}_y \hat{\bf y} + \dot{r}_z \hat{\bf z}$
• $\sum_{\beta}$ denotes a sum over all values of $\beta$. For example, if $\beta$ is allowed to be any integer between 1 and $N$, then $\sum_{\beta}$ is equivalent to $\sum_{\beta=1}^{N}$
• $\sum_{\beta \neq \alpha}$ denotes a sum over all values of $\beta$ except $\alpha$.
• $\sum_{\beta > \alpha}$ denotes a sum over all values of $\beta$ that are greater than alpha $\alpha$.

# Basic Principles

• We can measure an object’s average velocity ($\bar{\bf v}$) during a time interval $\Delta t$ by measuring the change in its position ($\Delta {\bf r}$) and then computing $\bar{{\bf v}} \equiv \frac{\Delta {\bf r}}{\Delta t}$.
• The natural generalization of average velocity is instantaneous velocity ($\bf v$). To find it, we use ${\bf v} = \dot{\bf r}$.
• We can measure an object’s average acceleration ($\bar{\bf a}$) during a time interval $\Delta t$ by measuring the change in its instantaneous velocity ($\Delta {\bf v}$) and then computing $\bar{{\bf a}} \equiv \frac{\Delta {\bf v}}{\Delta t}$.
• The natural generalization of average acceleration is instantaneous acceleration ($\bf a$). To find it, we use ${\bf a} = \dot{\bf v} = \ddot{\bf r}$.