Machine tool chatter is a common occurrence in machining environments which can lead to undesirable part outcomes and can even cause damage to the machine. Chatter is a result of regenerative dynamic forces inherent in the machining process which can cause the system to be either stable or unstable depending on the parameters of the cutting operation and the dynamic characteristics of the machine tool. The study of chatter is a common research topic which aims to characterize the dynamic behavior of machining operations so that chatter can be avoided. In this dissertation, a method is developed to analyze the dynamic behavior of cutting processes in the time domain. This approach allows for the tool point behavior to be determined analytically over a finite number of cutting periods. The analytical expressions describing the tool motion are then incorporated into a matrix solution which is used to determine dynamic stability directly without requiring a full time domain solution. These methods are first developed for an orthogonal turning model, and then expanded for the analysis of low radial immersion milling, low radial immersion milling with variable pitch cutters, average angle approximation milling with non-constant number of teeth in the cut, and full milling with variable cutting force directions.