PHY201 - Classical Mechanics (2022-2023)

Classical Mechanics (PHY 201)
This course introduces students to the Lagrangian and Hamiltonian mechanics. Starting
from the concepts of Newtonian mechanics, the course extends these concepts to a more
systematic description of the mechanics, adapted to complex systems. The course will
mostly use examples from the dynamics and vibrations of mechanical systems, with
progressively increasing complexity. Examples from other fields of physics will be also
proposed (electromagnetism, astrophysics, chaos…)
After a reminder of the classical concepts of point mechanics, the course extends these
concepts to the Lagrangian formalism and to the least action principle. The Lagrangian
formalism will be used to describe the mechanics of rigid bodies. Lagrangian formalism
will then be extended to the Hamiltonian mechanics which is at the core of quantum
physics and other modern theories in physics. We will also present some extensions of
Lagrangian and Hamiltonian mechanics to other fields of physics.
Upon completion of this course, students master equations and principles in analytical
mechanics. They will be able to discuss the relevance of the chosen model, as well as
derive and solve simple models taken from their environment.
Main concepts covered: Fundamental law of dynamics; kinetic and potential energy.
Linearized equations of motion, dynamics of linear coupled oscillators. Constraints and
generalized coordinates, D’Alembert principle, Hamilton principle, Euler-Lagrange
equations of motion, conservations of energy and momentum. Rigid body, center of
mass, Euler angles, Moment of inertia and inertia tensor, Euler equation of motion.
Equations of Hamilton, conservation theorem, canonical transformation, Poisson brackets.



This course introduces students to the Lagrangian and Hamiltonian mechanics. Starting from the concepts of Newtonian mechanics, the course extends these concepts to a more systematic description of the mechanics, adapted to complex systems. The course mostly use examples from the dynamics and vibrations of mechanical systems, with progressively increasing complexity. Examples from other fields of physics will be also proposed (electromagnetism, astrophysics, chaos…)


After a reminder of the classical concepts of point mechanics, the course extends these concepts to the Lagrangian formalism and to the least action principle. The Lagrangian formalism will be used to describe the mechanics of rigid bodies. Lagrangian formalism will then be extended to the Hamiltonian mechanics which is at the core of quantum physics and other modern theories in physics.

 

We will also present some extensions of Lagrangian and Hamiltonian mechanics to other fields of physics. Upon completion of this course, students master equations and principles in analytical mechanics. They will be able to discuss the relevance of the chosen model, as well as derive and solve simple models taken from their environment.