arXiv subjects

John E. Hurtado

Publications and source records attributed to John E. Hurtado.

3 recordsLinked to original sources

arXiv2023

Understanding the Hamiltonian Function through the Geometry of Partial Legendre Transforms

The relationship between the Hamiltonian and Lagrangean functions in analytical mechanics is a type of duality. The two functions, while distinct, are both descriptive functions encoding the behavior of the same dynamical system. One difference is that the Lagrangean naturally appears as one investigates the fundamental equation of classical dynamics. It is not that way for the Hamiltonian. The Hamiltonian comes after Lagrange's equations have been fully formed, most commonly through a Legendre transform of the Lagrangean function. We revisit the Legendre transform approach and offer a more refined geometrical interpretation than what is commonly shown.

physics.gen-ph↗

arXiv2022

A summary on the UD Kalman Filter

This document contains a concise and unified reference for one of the existing mechanizations of the UD Kalman filter. The associated matrix algorithms are also included along with the corresponding references.

eess.SY↗

arXiv2020

Analytical Dynamics Development of the Canonical Equations

It is most common to construct the Hamiltonian function and Hamilton's canonical equations through a Legendre transformation of the Lagrangean function or through the central equation. These common perspectives, however, seem abstract and detached from classical analytical dynamics. A new and different approach is presented in which the Hamiltonian function is created as one investigates d'Alembert's equation of motion. This formulation directly ties the Hamiltonian function and Hamilton's canonical equations to the root of classical analytical dynamics more than any other approach.

physics.class-ph↗