The objective of this chapter is to introduce rotary spectrum analysis for velocity vector time series. When the two components of a velocity vector have different frequencies, the tip of the displacement vector would draw a figure called a Lissajous Figure. A special case of the Lissajous Figure is when the two components oscillate at the same frequency. Vector time series at a given frequency can only have a few basic patterns or a combination of these patterns: the tip of the vector would draw a line segment back and forth repeatedly, or rotate either clockwise or counterclockwise. This makes it necessary to study the rotary spectra for rotations in both directions. A rectilinear motion is a degenerated version or special case of rotary motion.