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}.
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