M9 · Continuum & relativistic mechanics
A 20-module path through m9 · continuum & relativistic mechanics, in study order from foundations to the frontier.
Modules
- Discrete Loaded String and the Continuum Limit
- The One-Dimensional Wave Equation
- Normal Modes and Standing Waves on a String
- Lagrangian Density and Continuum Lagrangian Formalism
- Euler–Lagrange Equations for Fields
- Hamiltonian Density and Canonical Field Momentum
- Strain Tensor and Deformation of Continua
- Stress Tensor and Cauchy's Relation
- Linear Elasticity and Hooke's Law for Solids
- Elastic Waves in Solids
- Special Relativity Postulates and the Lorentz Transformation
- Relativistic Kinematics: Time Dilation, Length Contraction, and Velocity Addition
- Four-Vectors and Minkowski Spacetime
- Four-Velocity, Four-Momentum, and Mass-Energy Equivalence
- Relativistic Dynamics and the Four-Force
- The Relativistic Lagrangian for a Free and Charged Particle
- Ideal Fluid Kinematics and the Continuity Equation
- Euler's Equations and Bernoulli's Theorem
- Vorticity, Circulation, and Potential Flow
- The Navier–Stokes Equations and Viscous Flow