Notes on Lagrangian Mechanics

An introduction to Lagrangian and Hamiltonian mechanics

These notes are dedicated to Dr. Frank Berkshire whose enthusiasm and knowledge inspired me as a student. The lecture notes herein, are largely based on the first half of Frank's Dynamics course that I attended as a third year undergraduate at Imperial College in the Autumn term of 1989. Preface Newtonian mechanics took the Apollo astronauts to the moon. It also took the voyager spacecraft to t...

Math 439 Course Notes Lagrangian Mechanics, Dynamics, and Control

Lagrangian and Hamiltonian Formulation of the Classical Electromagnetic Field

In Notes 38, we derived the classical Hamiltonian description of the classical electromagnetic field by starting with the equations of motion and making a series of guesses for the Hamiltonian and the canonical variables. A more systematic, but more lengthy, procedure is to start with the classical Lagrangian for the field and proceed through the Legendre transformation. This procedure is outli...

Dynamic Fracture Analysis Using an Uncoupled Arbitrary Lagrangian Eulerian Finite Element Formulation

This paper deals with the implementation of an efficient Arbitrary Lagrangian Eulerian (ALE) formulation for the three dimensional finite element modeling of mode I self-similar dynamic fracture process. Contrary to the remeshing technique, the presented algorithm can continuously advance the crack with the one mesh topology. The uncoupled approach is employed to treat the equations. So, each t...

Contents 1 Elementary Mechanics 3 2 Lagrangian and Hamiltonian Dynamics 9 3 Oscillations 23

version of the lecture notes. Corrections are listed by section. Many thanks to students who have informed me of errors and typos.