Classical mechanics

• Hamilton’s Principal and Characteristic Functions: What’s the Difference?
  Hamilton’s principal function S depends on position and time; for a time-independent system, its characteristic function W satisfies a fixed-energy equation.
• How Does Hamilton’s Principle Work with Semiholonomic Constraints?
  For nonintegrable velocity constraints, distinguish Hamilton’s principle on constrained paths from the d’Alembert variation used for ideal constraints.
• How Is the Lagrangian Derived in Classical Mechanics?
  Derive the Euler–Lagrange equations from the stationary-action principle, see why L = T − V works, and follow a worked spring example.