Classical Mechanics

Classical mechanics is a fundamental branch of physics that describes the motion of macroscopic objects, from projectiles and machinery on Earth to the orbits of planets and stars. Grounded in the principles laid out by Isaac Newton, it utilizes concepts such as force, mass, momentum, and energy to mathematically predict how objects will move when subjected to various influences. This deterministic framework, where the future state of a system can be fully determined from its initial conditions, provides an incredibly accurate model for the everyday world, though its principles are superseded by quantum mechanics at the atomic scale and by relativity at speeds approaching the speed of light.

1. Introduction to Classical Mechanics
   1. Historical Development
      1. Ancient and Medieval Physics
         1. Aristotelian Physics
         2. Medieval Impetus Theory
      2. Pre-Newtonian Physics
         1. Galilean Mechanics
         2. Kepler's Astronomical Work
      3. Newtonian Revolution
         1. Newton's Principia
         2. Mathematical Framework
         3. Unification of Terrestrial and Celestial Mechanics
      4. Post-Newtonian Developments
         1. Lagrangian Formulation
         2. Hamiltonian Formulation
         3. Statistical Mechanics Foundations
   2. Core Concepts and Scope
      1. Definition of Classical Mechanics
      2. Fundamental Quantities
         1. Space and Time
         2. Mass and Force
         3. Energy and Momentum
      3. Systems and Particles
         1. Point Particles
         2. Extended Bodies
         3. Many-Body Systems
      4. Physical Laws and Principles
         1. Conservation Laws
         2. Symmetry Principles
   3. The Deterministic Worldview
      1. Determinism in Classical Physics
         1. Laplace's Demon
         2. Causal Relationships
      2. Predictability and Causality
         1. Initial Conditions
         2. Equations of Motion
   4. Domains of Applicability
      1. Macroscopic vs. Microscopic Scales
         1. Size Limitations
         2. Everyday Objects
      2. Non-relativistic Regime
         1. Velocity Constraints
         2. Speed of Light Considerations
      3. Non-quantum Regime
         1. Action Scales
         2. Planck's Constant Considerations
   5. Limitations of Classical Mechanics
      1. Breakdown at High Speeds
         1. Special Relativity
         2. Relativistic Effects
      2. Breakdown at Small Scales
         1. Quantum Mechanics
         2. Wave-Particle Duality
      3. Chaotic Systems
         1. Sensitive Dependence on Initial Conditions
         2. Limits of Predictability