Classical Mechanics

Recommended Prerequisites

Not applicable.

Teaching Methods

Partition of contact hours: Lectures 45h, Theoretical-Practical 15 h, Laboratory Practice 0h, Field Work 0h, Seminar 0h, Tutorial 15h, Other 0h.

Evaluation components and corresponding weights (as percentage) in the final grade

Problem solving 30, Exam 70.

Presentation of different topics illustrated with practical applications.

Students will solve problems independently.

Whenever necessary, a brief introduction to the mathematical techniques necessary to understand the issues and to solve physical problems will be given: the second-order tensor, calculus of variations, etc.

Learning Outcomes

Theoretical understanding of physical phenomena, namely:

Using the conservation laws to study the motion of a mechanical system, identify the possible orbits of a particle in a central force field, determine the orbit of a particle in a central force field, choose the coordinate system appropriate to the resolution of various problems, identify the links in a dynamic system, know how to write the Lagrangian in terms of the different types of generalized coordinates and how to get the equations of motion; Know the degrees of freedom of a rigid body, know how to calculate moments of inertia of a rigid body; know how to solve problems involving fluids in equilibrium. Understand the characteristics of the possible flows of fluids.

Ability to solve problems; Mathematical skills to solve problems; General knowledge in physics;

Ability to learn; Ability to search for and use bibliography.

Work Placement(s)

No

Syllabus

1 - Newtonian mechanics.

2 - Field of central forces: the orbit of a particle, equations of motion, the Kepler problem, binary systems, dispersion of particles.

3 - System of particles, conservation laws.

4 - Lagrangian Formalism: links, generalized coordinates, the principle of d'Alembert and Hamilton's variational principle, calculus of variations, Lagrange's equations, conservation laws, equations of Hamilton.

5 - Movement of the rigid body: orthogonal transformations, Euler angles, Euler's theorem, the Coriolis force, movement on the Earth, angular momentum, kinetic energy and equations of motion of a body with a fixed point, and moment of inertia tensor of inertia, gyroscope.

6 - Fluid Mechanics: fundamental equation of hydrostatics, applications, ideal fluids, fundamental equation of hydrodynamics, the equations of continuity and Bernoulli; viscous fluids: Newton's law of viscosity, laminar flow, Reynolds number and turbulent flow.

Head Lecturer(s)

Fernando Davide de Sousa Caldeira Sampaio dos Aidos

Assessment Methods

Assessment
Resolution Problems: 30.0%
Exam: 70.0%

Bibliography

A. P. French, ``Newtonian Mechanics'', W. W. Norton, 1971.

H. Goldstein, ``Classical Mechanics'', 2. ed., Addison-Wesley, 1980.

J. B. Marion e S. T. Thornton, ``Classical Dynamics of Particles and Systems'', 4. ed. Academic Press, 1995.

L. Landau e E. Lifchitz, ``Mechanics'', Pergammon, 1976. Este livro é um clássico.