Classical Mechanics

Physics

1. 1. Newton's laws

   Newton's laws

   Newton's laws

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2. 2. Lagrangian formulation

   Lagrangian formulation: D'Alembert's principle, Euler-Lagrange equation, Hamilton's principle, calculus of variations

   D'Alembert's principleEuler-Lagrange equationHamilton's principlecalculus of variations

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3. 3. Symmetry and conservation laws

   Symmetry and conservation laws

   symmetryconservation laws

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4. 4. Central force motion

   Central force motion: Kepler problem and Rutherford scattering

   Kepler problemRutherford scattering

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5. 5. Small oscillations

   Small oscillations: coupled oscillations and normal modes

   coupled oscillationsnormal modes

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6. 6. Rigid body dynamics

   Rigid body dynamics: inertia tensor, orthogonal transformations, Euler angles, Torque free motion of a symmetric top

   inertia tensororthogonal transformationsEuler anglestorque-free symmetric top

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7. 7. Hamiltonian mechanics

   Hamiltonian and Hamilton's equations of motion; Liouville's theorem

   HamiltonianHamilton's equationsLiouville's theorem

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8. 8. Canonical transformations

   Canonical transformations: action-angle variables, Poisson brackets, Hamilton-Jacobi equation

   action-angle variablesPoisson bracketsHamilton-Jacobi equation

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9. 9. Special theory of relativity

   Special theory of relativity: Lorentz transformations, relativistic kinematics, mass-energy equivalence

   Lorentz transformationsrelativistic kinematicsmass-energy equivalence

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