Classical Mechanics

Recommended Prerequisites

Analysis, Linear Algebra and Analytical Geometry, Physics I and II.

Teaching Methods

Lectures, using audiovisual media and balckboard, during which the main concepts, principles and fundamental theories of quantum mechanics are presented and discussed. Application to simple exemples.
Problem classes during which the student is supposed to solve by him/herself , with help whenever necessary, problems  that apply the main concepts of quantum mechanics. Evaluation  consists of a final examination, or a collection of several problem  along the semester, which will be corrected, and a final test.

Learning Outcomes

- Recognize and use basic concepts and principles of classical mechanics, and apply them to simple examples.
- Know how to use the methodologies and techniques appropriate to classical mechanics.
-Analyze, synthesize and process information. Develop critical thinking and autonomous learning. Prepare, process, interpret and communicate physics information, using relevant literature sources and appropriate tools.

Work Placement(s)

No

Syllabus

1- Lagrange formalism. Constraints and generalized coordinates, Newton's laws, d'Alembert principle and Lagrange equations. Hamilton' s principle. Symmetries and conservation laws. Noether's theorem.
2- One dimensional systems and an isolated two particle system. Gravitational interaction. Scattering theory.
3- Systems that undergo small vibrations around a stable equilibrium position. Normal modes of vibration.
4- Rigid body motion. Orthogonal transformations. Euler angles. Euler theorem. Coriolis effect. Tensor of inertia and Steiner's theorem. Euler equations. Free body motion and motion of the heavy symmetrical top with a fixed point.
5- Hamilton formalism. Legendre transformations. Modified Hamilton principle. Canonical transformations. Poisson brackets.

Head Lecturer(s)

Fernando Manuel Silva Nogueira

Assessment Methods

Assessment
Exam: 100.0%

Bibliography

Goldstein, Poole and Safko. (2002). Classical Mechanics. 3rd edition - International edition. Pearson.
Landau and Lifchitz. (1976). Mechanics. Butterworth-Heinemann.