Duration
Part A : 12h Th, 15h Pr
Part B : 18h Th, 15h Pr
Number of credits
| Bachelor in mathematics | 6 crédits | |||
| Bachelor in physics | 6 crédits |
Lecturer
Part A : Pierre Dauby
Part B : Pierre Dauby
Coordinator
Language(s) of instruction
French language
Organisation and examination
Teaching in the first semester, review in January
Schedule
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.
Part A
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.
Part B
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.
Part A
At the end of the course, the students will have understood the physical concepts and principles of lagrangian mechanics. They will also be able to solve problems related to this subject.
Part B
At the end of the course, the students will have understood the physical concepts and principles of 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.
Part A
It is assumed that the course Analytical Mechanics I is familiar to the students.
Part B
It is assumed that the course Analytical Mechanics I and the course MECA0523-A-a are familiar to the students.
Planned learning activities and teaching methods
The theoretical part of the course is presented as lectures. Practical work sessions are also devoted to solving problems and making exercices.
Part A
The theoretical part of the course is presented as lectures. Practical work sessions are also devoted to solving problems and making exercices.
Part B
See MECA0523-A-a.
Mode of delivery (face to face, distance learning, hybrid learning)
Face-to-face course
Additional information:
Face-to-face teaching (except in the case of problems related to the pandemic).
Part A
Face-to-face course
Additional information:
Face-to-face teaching (except in the case of problems related to the pandemic).
Part B
Face-to-face course
Additional information:
See MECA0523-A-a.
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.
Part A
Notes and slides (in French) can be downloaded from eCampus. A printed version of the notes can also be provided on demand.
Part B
See MECA0523-A-a.
Assessment methods and criteria
Exam(s) in session
Any session
- In-person
written exam
Additional information:
Written exam.
Part A
Exam(s) in session
Any session
- In-person
written exam
Additional information:
Written exam.
Part B
Exam(s) in session
Any session
- In-person
written exam
Additional information:
See MECA0523-A-a.
Work placement(s)
None
Part A
None
Part B
See MECA0523-A-a.
Organizational remarks
Practical details will be provided on eCampus.
Part A
Practical details will be provided on eCampus.
Part B
See MECA0523-A-a.
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 - Guillaume SICORELLO, research and teaching assistant,,
email: guillaume.sicorello@uliege.be
Part A
- 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 - Guillaume SICORELLO, research and teaching assistant,,
email: guillaume.sicorello@uliege.be
Part B
See MECA0523-A-a.