A Wandering Mathematician personal notes

Indar is finally out! A Python package for the analysis of vibrations

This project started because I wanted to model machining processes such as turning, where estimating the structural parameters of the system — tool holder, workpiece, fixture, and so on — is essential. These structures are usually modeled as linear spring systems, whose dynamics can be solved analytically and used to fit experimental data. Ther... Read more

Kalman filter from Bayes filter

An important problem in engineering is to estimate the evolution of a hidden (latent) variable, such as the trajectory of a rocket, from noisy observations. If the dynamics of the latent variable is known, and also the relationship between the latent variable and the observation, then Bayes filtering is a robust method for estimating the latent ... Read more

Modal Analysis: dynamics

In this follow-up to our post on basic concepts, we will explore the dynamics generated by models of linear vibrations. Linear models of vibrating structures have the form \[\begin{equation} M\ddot{x} + C\dot{x} + Kx = F, \label{eq:basic_vibrations} \end{equation}\] where $x(t) \in \R^N$ is a vector function representing the displacement from... Read more

Modal Analysis: the basics

Vibrating mechanical systems are modelled by the equation \[\begin{equation} M\ddot{x} + C\dot{x} + Kx = F,\label{eq:basic_vibration} \end{equation}\] where $x(t) \in \R^N$ is a vector function representing the displacement from equilibrium, $F$ are external forces, $M$ is the mass, $C$ is the damping, and $K$ is the stiffness. The dimension $... Read more

Envelopes of Solids of Revolution

Flank milling is a manufacturing process in which material is removed from the workpiece using a cutter rotating at high speed. Since the cutter rotates much faster than the feed rate of the tool, the cutter can be thought of as a solid of revolution, and the envelope swept by this solid becomes the final surface of the workpiece. Numerous book... Read more