Laws of Motion – University‑Level Study Notes
Physics – Mechanics – Advanced Course (MIT‑style)
Goal – Understand the three Newtonian laws from first principles, connect them to the variational formulation, extend them to relativistic and constrained systems, and master the subtle edge cases that appear in modern physics.
Prerequisites – Vector calculus, special relativity (basic), elementary classical mechanics.
1. Introduction
The laws of motion are the cornerstone of classical mechanics. They describe how a system’s state evolves under the influence of forces. Modern treatments elevate these laws from empirical statements to consequences of deeper principles (symmetries, action principles, and relativity).
The notes below follow a logical progression:
- Newtonian fundamentals – First principles and the three laws.
- Variational formulation – Action, Lagrangian, Euler–Lagrange equations.
- Generalized coordinates & constraints – Holonomic vs. non‑holonomic.
- Non‑inertial frames – Pseudoforces.
- Relativistic dynamics – Momentum, energy, and Lorentz force.
- Edge cases & paradoxes – Zero mass, infinite force, non‑conservative forces.
- Advanced topics – Symmetries, Noether’s theorem,