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.