Analytical mechanics II

Duration

Part A : 12h Th, 15h Pr
Part B : 18h Th, 15h Pr

Number of credits

Lecturer

Part A : Pierre Dauby
Part B : Pierre Dauby

Coordinator

Pierre Dauby

Language(s) of instruction

French language

Organisation and examination

Teaching in the first semester, review in January

Schedule

Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

The Lagrangian formulation of mechanics is intimately connected to the introduction of generalized coordinates which are used to describe the motion of a system of particles (including the solids) by elimination of possible constraints restricting their motions. We first introduce the Lagrange's equations and apply this formalism to several different problems (e.g. study of the symmetric top, known as the Lagrange-Poisson problem). Then, we consider the symmetries of a problem and determine the associated conserved quantities. The Hamilton variational principle is also discussed.
One of the major interests of the Hamiltonian formulation of dynamics comes from the importance of this formalism in the elaboration of modern physical theories such as quantum mechanics or to describe the fundamental interactions between particles. In this part of the course, we derive the Hamilton canonical equations and we discuss the importance of the canonical transformations in order to solve various mechanical problems. The equations of dynamics are also expressed in terms of the Poisson brackets. Several applications are considered. Finally, we present the Hamilton-Jacobi method for solving mechanical problems.
The chapter on special relativity starts with a brief description of the difficulties encountered while attempting to interpret various physical experiments at the end of the XIXth century. We then introduce the Lorentz transformations and the Minkowski space-time. Time dilation and length contraction are discussed and analyzed in depth. The dynamical equations of a particle are also derived in the framework of special relativity.

Learning outcomes of the learning unit

At the end of the course, the students will have understood the physical concepts and principles of lagrangian and hamiltonian mechanics and of special relativity. They will also be able to solve problems related to these subjects.

Prerequisite knowledge and skills

It is assumed that the course Analytical Mechanics I is familiar to the students.

Planned learning activities and teaching methods

The theoretical part of the course is presented as lectures (30h). Practical work sessions are also devoted to solving problems and making exercices (30h).

Mode of delivery (face to face, distance learning, hybrid learning)

Face-to-face teaching.

Organisational adjustments related to the current health context

Recommended or required readings

Notes and slides (in French) can be downloaded from eCampus. A printed version of the notes can also be provided on demand.
   

Assessment methods and criteria

Below you will find information on the evaluation methods planned for in-person and remote exams as well as those planned for hybrid sessions. Depending on how the health crisis evolves, the chosen method will be communicated to you no later than one month before the start of the exam session.

Written exam.
 
> Remote written exam and oral online exams (details on eCampus) (update 11/12/2020)

Work placement(s)

None

Organizational remarks

Practical details will be provided on eCampus.
   

Contacts

• Pierre C. DAUBY, Professeur Institut de Physique (local 2/57), Bât. B5a, Allée du 6 août 19, B-4000 Liège  Tel.: 04/366.23.57 E-mail: PC.Dauby@uliege.be
• Sophie ROSU, research and teaching assistant, Tel.: 04/366.97.78  E-mail: Sophie.Rosu@uliege.be