Classical Mechanics I

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- Newtonian Mechanics: Newton's laws, conservation laws, uni-dimensional motion of a conservative system.
2- Central force motion: orbits in a central field, equations of motion, Kepler's problem, binary systems, scattering in a central force field.
3- Mechanics of a system of particles: conservation laws, applications.
4- Lagrange formalism: generalized coordinates, d'Alembert principle, Hamilton' s principle, calculus of variations, Lagrange equations, conservation laws.
5- Kinematics and dynamics of a rigid body: orthogonal transformations, Euler angles, Coriollis force, angular momentum and kinetic energy of a rigid body, tensor  and moment of inertia, eigenvalues and principal axis of the tensor of inertia,  equations of motion of a rigid body,
torque-free motion of a rigid body, motion of a heavy symmetric top with a fixed point.
6- Hamilton's formalis, Legendre transformations, Canonical transformations, Poisson brackets.

Head Lecturer(s)

Fernando Manuel Silva Nogueira

Assessment Methods

Final evaluation
Exam: 100.0%

Continuous evaluation
Resolution Problems: 20.0%
Frequency: 80.0%

Bibliography

MARION, J. B.; e THORNTON, S. T. (1995). Classical Dynamics of Particles and Systems. 4. ed. Academic Press.
FRENCH, A. P. (1971). Newtonian Mechanics. W. W. Norton.
GOLDSTEIN, H. (1980). Classical Mechanics. 2. ed. Addison-Wesley.
LANDAU, L. & LIFCHITZ, E. (1976). Mechanics. Pergammon.