Lecture Notes in Classical Mechanics

Review of Newtonian mechanics Coordinate systems. Kinematics Newton's laws. Inertial frames. Galileo's relativity principle Newton's laws Inertial frames Galileo's relativity principle Conservation laws. Conservative forces. Electromagnetic force Conservation laws Conservative forces Gravitational and electrostatic forces Electromagnetic force Motion of a particle in a one-dimensional potential Stability of equilibria. Period of the small oscillations Dynamics of a system of particles. Conservation laws Dynamics of a system of particles Conservation laws Motion in a central potential Two-body problem. Reduction to the equivalent one-body problem Constants of motion. Law of motion and equation of the trajectory. Bounded Orbits Constants of motion Law of motion and equation of the trajectory Bounded orbits Kepler's problem. Planetary motion Kepler's problem Planetary motion Scattering by a central potential. Rutherford's formula Differential scattering cross section Scattering by a central potential Rutherford's formula Lagrangian and Hamiltonian mechanics Introduction to the calculus of variations Fundamental problem of the calculus of variations Euler–Lagrange equations Hamilton's principle for unconstrained systems Hamilton's principle for a particle Hamilton's principle for a system of particles Covariance of the Lagrangian formulation Lagrangian of a charged particle in an electromagnetic field Systems with constraints Motion of a particle on a smooth surface System of N particles with constraints Conservation laws Introduction to Hamiltonian mechanics Hamilton's canonical equations Conservation laws Poisson brackets Motion relative to a non-inertial frame Angular velocity of a reference frame with respect to another Time derivative in the fixed and moving frames Dynamics in a non-inertial reference frame Motion of a particle relative to the rotating Earth Foucault's pendulum Rigid body motion Angular momentum and kinetic energy of a rigid body Degrees of freedom Angular momentum and kinetic energy Inertia tensor Definition and elementary properties Steiner's theorem Principal axes of inertia Equations of motion of a rigid body Equations of motion of a rigid body in an inertial frame Euler's equations Inertial motion of a symmetric top Special relativity The principles of special relativity Lorentz transformations Deduction of the equations of the transformation Relativistic addition of velocities Interval Minkowski product Lorentz group Physical consequences of Lorentz transformations Time dilation Lorentz–Fitzgerald contraction Four-velocity and four-momentum. Relativistic kinetic energy Four-momentum conservation. Relativistic energy Massless particles Relativistic Doppler effect Compton effect Relativistic dynamics Hyperbolic motion