CNC milling stability prediction method hallways full third order discretization

In this article, prediction of lobe stability diagram is presented with the new method of 3th degree of full discretization that is based on direct integral. First, the dynamic model of milling with delay is developed from condition form to integral form. Then every period is discretized in limited time sections. Full discretization method is used for manual calculation of system integral. In every small time interval, the Lagrange 3th degree multi term is applied to interpolate the condition part. Furthermore the Lagrange linear multi term is also used for interpolation of delay- and period parts. A discrete dynamic design is achieved.  Now it is possible to determine the matrix of condition transition in a time interval. Using this matrix by Floquet theory, lets to predict the stability lobe diagram. A basic example provides verifying of this method by comparison with results from literatures. The MATLAB program to calculate the problem is attached.