M4 · Lagrangian mechanics
A 20-module path through m4 · lagrangian mechanics, in study order from foundations to the frontier.
Modules
- Generalized Coordinates and Configuration Space
- Constraints and Their Classification
- Degrees of Freedom
- Virtual Displacements and the Principle of Virtual Work
- d'Alembert's Principle
- The Lagrangian Function
- The Action Functional
- Hamilton's Principle of Stationary Action
- The Euler-Lagrange Equations
- Generalized Forces and Generalized Momenta
- Cyclic Coordinates and Conservation of Conjugate Momenta
- The Energy Function and Jacobi Integral
- Symmetries and Continuous Transformations
- Noether's Theorem
- Lagrange Multipliers and Constraint Forces
- Nonholonomic Systems and the Lagrange-d'Alembert Method
- Velocity-Dependent and Generalized Potentials
- Rayleigh Dissipation Function
- Gauge Freedom of the Lagrangian
- Calculus of Variations and the Variational Derivative