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16: Analytical Formulations for Continuous Systems

Last updated

Nov 21, 2020
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- 15.S: Advanced Hamiltonian mechanics (Summary)
- 16.1: Introduction

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16.1: Introduction
Lagrangian and Hamiltonian mechanics have been used to determine the equations of motion for discrete systems having a finite number of discrete variables $q_i$ where $1 \leq i \leq n$ . There are important classes of systems where it is more convenient to treat the system as being continuous. Fluid and gas dynamics, as well as electromagnetic fields, are other important classes of continuous systems.
16.2: The Continuous Uniform Linear Chain
16.3: The Lagrangian density formulation for continuous systems
The Lagrangian density formulation for continuous systems in both one and three spatial dimensions.
16.4: The Hamiltonian density formulation for continuous systems
16.5: Linear Elastic Solids
Stress and strain tensors. Moduli of elasticity.
16.6: Electromagnetic Field Theory
Maxwell stress tensor. Momentum in electromagnetic field.
16.7: Ideal Fluid Dynamics
Continuity equation. Euler's hydronamic equation. Irrotational flow and Bernoulli's equation. Gas flow.
16.8: Viscous Fluid Dynamics
Navier-Stokes equation. Reynolds number. Laminar and turbulent fluid flow.
16.9: Summary and Implications

Thumbnail: Rubber bands are one type of elastic solid that can be described with continuous formalism. (CC BY-SA 3.0; Bill Ebbesen)

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