Leonard Susskind: Classical Mechanics
Stanford University - 10 comprehensive lectures on Lagrangian and Hamiltonian mechanics
About This Series
Professor Leonard Susskind's classical mechanics course goes far beyond introductory Newtonian mechanics. These lectures develop the Lagrangian and Hamiltonian formulations of classical mechanics - elegant mathematical frameworks that form the foundation for quantum mechanics, quantum field theory, and statistical physics.
Susskind's teaching style combines physical intuition with mathematical rigor, making advanced concepts accessible while maintaining depth. He emphasizes the principle of least action, symmetries and conservation laws (Noether's theorem), and the geometric structure of phase space.
Why this matters: The concepts in these lectures are not just about classical particles. They provide the mathematical language and conceptual framework for all of modern theoretical physics:
- • Quantum Mechanics: Canonical quantization replaces Poisson brackets with commutators
- • Quantum Field Theory: Lagrangian formalism extends to fields, path integrals generalize the action principle
- • Statistical Mechanics: Phase space is the arena for ensembles and Liouville's theorem
- • General Relativity: Einstein-Hilbert action uses variational principles
Complete Lecture Series (10 Lectures)
Classical Mechanics - Lecture 1
Introduction to the course. Newton's laws revisited. Configuration space and state space. Introduction to the principle of least action and motivation for Lagrangian mechanics. Why we need to go beyond F = ma for modern physics.
Video Lecture
Classical Mechanics Lecture 1
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Classical Mechanics - Lecture 2
Action principle and Hamilton's principle. Derivation of the Euler-Lagrange equations from the principle of least action. Simple examples: free particle, harmonic oscillator. Generalized coordinates and constraints.
Video Lecture
Classical Mechanics Lecture 2
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Classical Mechanics - Lecture 3
Symmetries and conservation laws. Noether's theorem: the profound connection between continuous symmetries and conserved quantities. Time translation → energy conservation, space translation → momentum conservation, rotational symmetry → angular momentum conservation.
Video Lecture
Classical Mechanics Lecture 3
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Classical Mechanics - Lecture 4
Introduction to Hamiltonian mechanics. Legendre transformation from Lagrangian L(q, q̇) to Hamiltonian H(q, p). Conjugate momenta p = ∂L/∂q̇. Hamilton's equations of motion. Physical meaning of the Hamiltonian as total energy.
Video Lecture
Classical Mechanics Lecture 4
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Classical Mechanics - Lecture 5
Phase space: the fundamental arena of Hamiltonian mechanics. Phase space trajectories. Liouville's theorem: phase space volume is preserved under Hamiltonian evolution. This theorem is crucial for statistical mechanics and connects to quantum mechanics.
Video Lecture
Classical Mechanics Lecture 5
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Classical Mechanics - Lecture 6
Poisson brackets: the mathematical structure of classical mechanics. {q, p} = 1. How Poisson brackets encode the geometry of phase space. Time evolution using Poisson brackets. Connection to quantum commutators in canonical quantization.
Video Lecture
Classical Mechanics Lecture 6
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Classical Mechanics - Lecture 7
Central force problems and orbital mechanics. Effective potential for radial motion. Conservation of angular momentum and energy. Kepler problem: planetary orbits and gravitational physics. Virial theorem and its applications.
Video Lecture
Classical Mechanics Lecture 7
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Classical Mechanics - Lecture 8
Rigid body dynamics. Inertia tensor and principal axes. Euler angles describing rotation. Euler's equations for rigid body motion. Angular momentum and torque in rotating frames. Applications to spinning tops and gyroscopes.
Video Lecture
Classical Mechanics Lecture 8
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Classical Mechanics - Lecture 9
Canonical transformations and generating functions. Transformations that preserve the Hamiltonian structure of mechanics. Action-angle variables. Hamilton-Jacobi theory and the connection to quantum mechanics (semiclassical approximation).
Video Lecture
Classical Mechanics Lecture 9
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Classical Mechanics - Lecture 10
Advanced topics and connections to modern physics. Path to quantum mechanics through canonical quantization. Extension to field theory via Lagrangian densities. Chaos in classical mechanics. Summary of key concepts and looking forward to quantum theory.
Video Lecture
Classical Mechanics Lecture 10
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Study Guide
Before Watching:
- • Review calculus (partial derivatives, chain rule, integration by parts)
- • Familiarize yourself with Newton's laws and basic physics concepts
- • Have pencil and paper ready to work through derivations alongside Susskind
During the Lectures:
- • Pause frequently to work through calculations yourself
- • Pay special attention to Lectures 2-3 (Euler-Lagrange, Noether's theorem)
- • Lectures 4-6 on Hamiltonian mechanics are crucial for quantum mechanics
- • Take notes on key concepts and mark sections to review
After Watching:
- • Work problems from a textbook (Goldstein, Taylor, or Landau)
- • Master the harmonic oscillator in both Lagrangian and Hamiltonian formulations
- • Verify Noether's theorem for specific symmetries
- • Connect concepts to quantum mechanics (if you know QM already)
Key Concept to Master: The relationship between symmetries and conservation laws (Noether's theorem) is one of the most profound principles in all of physics. Make sure you understand it deeply—it appears in every area of modern theoretical physics.
Recommended Textbooks
The standard graduate textbook. Comprehensive coverage, excellent problems.
Best undergraduate text. Clear explanations, many worked examples.
Elegant and concise. Starts from least action principle. More advanced.