Undergraduate-to-advanced notes on Lagrangian mechanics. Constraints, generalized coordinates, and the Euler-Lagrange equation are derived, then used on Atwood, beads on wires, and small oscillations.

For students leaving Newtonian mechanics for Goldstein-level courses.

• Holonomic constraints and virtual work
• Euler-Lagrange with and without multipliers
• Small oscillations and normal modes
• Noether’s theorem at the notes level
• Fully worked multi-degree-of-freedom examples