# 16: Analytical Formulations for Continuous Systems

- Page ID
- 9662

- 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.

- 16.3: The Lagrangian density formulation for continuous systems
- The Lagrangian density formulation for continuous systems in both one and three spatial dimensions.

- 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.

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