Classical Mechanics (MEC_2F001)
This course covers non-inertial frames and fictitious forces, the Lagrangian and Hamiltonian formulations and rigid body mechanics. It explores velocity fields, kinetic energy decomposition, angular momentum, and conservation laws. With the calculus of variations serving as a mathematical foundation, Lagrangian mechanics is presented as a variational principle for constrained systems, while Hamiltonian mechanics emphasizes energy conservation and its role in quantum physics. Practical examples treated throughout the class include turning tables, Foucault pendulum and rolling disks. The course balances mathematical rigor with physical interpretation. It builds on Newtonian mechanics and vector calculus. By the end of the class, students will derive the fundamental mathematical techniques used in physics and mechanics, and will be acquainted with fun physical phenomena.
Prerequisites: PHY101, PHY102, PHY201, PHY202
The course describes waves in fluids, with a preference for illustrations coming from the Earth system, in particular the atmosphere and ocean. Waves are one essential type of motion present in many fluids. One goal of the course is to demonstrate how one proceeds to obtain wave solutions starting from a physical description of a system and its equations of motion. Acoustic waves will be considered as a first example, surface water waves at different scales (from ripples in the pond to tsunamis) will be derived as further examples. Basics of fluid mechanics (Euler equations, kinematics) will be introduced in order to make these developments possible. Similarities in the behavior of fluid waves and optical waves seen in PHY202 will be discussed.
At the end of the course, the students will understand how one characterizes a family of waves (dispersion relation, polarisation relations), and how to proceed to obtain, in a given system, wave solutions if they exist. Some preliminary considerations for exploring behaviors beyond linearity will have been introduced, as an opening. Finally, some elements of the study of the Earth, and of the atmosphere in particular, will have been introduced.
