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The exhaustive list of topics in Classical Mechanics in which we provide Help with Homework Assignment and Help with Project is as follows:

  • Mechanics of a system of particles in vector form. Conservation of linear momentum, energy and angular momentum.
  • Degrees of freedom, generalized coordinates and velocities. Lagrangian, action, and the principle of extremal action. Euler-Lagrange equations. Constraints. Applications of the Lagrangian formalism.
  • Legendre transform, generalized momenta. Hamiltonian and Hamilton's equations of motion. Phase space, phase trajectories. Applications to systems with a small number of degrees of freedom.
  • Scattering in a central potential, Rutherford formula, scattering cross section.
  • Charged particle in an electromagnetic field.
  • Non-inertial frames of reference and pseudo-forces: centrifugal, Coriolis and Euler forces.
  • Rotations in three dimensions, Euler angles. Angular momentum. Elements of rigid-body dynamics. The symmetric top.
  • Small oscillations. Normal mode analysis. Normal modes of simple molecules and harmonic chains.
  • Elementary ideas on general dynamical systems: conservative versus dissipative systems. Hamiltonian systems and Liouville's theorem.
  • Constants of the motion and symmetries in classical mechanics. Noether's Theorem and the connection between symmetry, invariance and conservation principles.
  • Canonical transformations, Poisson brackets. Action-angle variables. Integrable Hamiltonians. Non-integrable systems and elements of chaotic motion.
  • Special relativity: Inertial frames. Principle and postulate of Relativity. Lorentz transformations. Length contraction, time dilation and the Doppler effect. Velocity addition formula. Rapidity.
  • Four-vectors and tensors. Energy-momentum of a free particle. Relativistic invariance of physical laws. The wave equation. Transformation properties of electric and magnetic fields. The homogeneous and inhomogeneous Lorentz groups.