DEPARTAMENTO DE FÍSICA

Classical Mechanics II - F+mnrF

Ano letivo: 2016-2017

Specification sheet

Specific details

course code | cycle os studies | academic semester | credits ECTS | teaching language |

1002781 | 1 | 2 | 6 | pt |

Learning goals

Theoretical understanding of physical phenomena.

Mathematical skills to solve problems.

Deep general education in physics.

Ability to search and use bibliography.

Understand the phenomena of oscillation of systems with several degrees of freedom and their normal modes of oscillation;

Understand the theory of relativity and the dynamics of relativistic processes;

Understand key aspects of tensor calculus and the covariant formulation of physical laws;

Understand the phenomenology of deformable bodies , in particular the formulation of tensor fields of deformations and stress and the equations that govern them;

Know the phenomenology of fluid mechanics and learn how to apply its equations to inviscid and viscid fluids.

Generic skills :

analysis and synthesis;

organization and planning;

oral and written communication;

to solve problems;

critical thinking;

autonomous learning and adaptability to new situations.

Mathematical skills to solve problems.

Deep general education in physics.

Ability to search and use bibliography.

Understand the phenomena of oscillation of systems with several degrees of freedom and their normal modes of oscillation;

Understand the theory of relativity and the dynamics of relativistic processes;

Understand key aspects of tensor calculus and the covariant formulation of physical laws;

Understand the phenomenology of deformable bodies , in particular the formulation of tensor fields of deformations and stress and the equations that govern them;

Know the phenomenology of fluid mechanics and learn how to apply its equations to inviscid and viscid fluids.

Generic skills :

analysis and synthesis;

organization and planning;

oral and written communication;

to solve problems;

critical thinking;

autonomous learning and adaptability to new situations.

Syllabus

1 - Small oscillations of systems with N degrees of freedom. Normal modes of oscillation; the system of principal axes and normal coordinates. Forced and damped oscillations of systems. Resonance.

2 - Covariant formulation of special relativity: the Einstein's postulates, covariant formulation of the theory, invariance and conservation, center of mass system, threshold energy, elastic and inelastic collisions.

3 - Elements of tensor calculus: general transformations, tensors, the fundamental metric tensor.

4 - Deformable bodies/elasticity: tensor fields of deformations and stresses, the Cauchy equation, elastic energy and elastic hysteresis; observables of the theory of elasticity; the Navier equation, propagation of elastic waves , s and p waves.

5 - Deformable bodies/fluid mechanics: ideal fluids, the Euler and Bernoulli equations; real fluids, the Navier-Stokes equation, vorticity, the Reynolds number, boundary layer of Prandt; drag force, lift force, the D' Alembert paradox.

2 - Covariant formulation of special relativity: the Einstein's postulates, covariant formulation of the theory, invariance and conservation, center of mass system, threshold energy, elastic and inelastic collisions.

3 - Elements of tensor calculus: general transformations, tensors, the fundamental metric tensor.

4 - Deformable bodies/elasticity: tensor fields of deformations and stresses, the Cauchy equation, elastic energy and elastic hysteresis; observables of the theory of elasticity; the Navier equation, propagation of elastic waves , s and p waves.

5 - Deformable bodies/fluid mechanics: ideal fluids, the Euler and Bernoulli equations; real fluids, the Navier-Stokes equation, vorticity, the Reynolds number, boundary layer of Prandt; drag force, lift force, the D' Alembert paradox.

Prerequisites

Mathematical Analysis Linear Algebra and Analytical Geometry General Physics I and II Classical Mechanics I

Generic skills to reach

. Competence in analysis and synthesis;. Competence to solve problems;

. Critical thinking;

. Competence in autonomous learning;

. Competence in applying theoretical knowledge in practice;

. Competence in organization and planning;

. Competence in oral and written communication;

. Competence to communicate with people who are not experts in the field;

. Adaptability to new situations;

(by decreasing order of importance)

Teaching hours per semester

lectures | 45 |

theory-practical classes | 30 |

total of teaching hours | 75 |

Assessment

Assessment Tests | 100 % |

Exam | 100 % |

Bibliography of reference

GOLDSTEIN, H. (1980). Classical Mechanics. 2. ed. Addison-Wesley.

LANDAU & LIFSHITZ. Mechanics.

LANDAU & LIFSHITZ. Elasticity.

BHATIA A. B.; & SINGH, R. N. (1986). Mechanics of Deformable Media. Adam Hilger.

FEYNMAN, R. P.; SANDS, R. B. Leightonm M. (1977). The Feynmann Lectures on Physics. Addison-Wesley. vol. II.

JACKSON, J. D.. Classical Electrodynamics.

MATHEWS & WALKER. Mathematical Methods of Physics

MARION, J. B. & THORNTON, S. T. (1995). Classical Dynamics of Particles and Systems. 4. ed. Academic Press.

FRENCH, A. P. (1968). Special Relativity. W. W. Norton.

Mecânica clássica II, textos letivos (2013), J. Pinto da Cunha.

LANDAU & LIFSHITZ. Mechanics.

LANDAU & LIFSHITZ. Elasticity.

BHATIA A. B.; & SINGH, R. N. (1986). Mechanics of Deformable Media. Adam Hilger.

FEYNMAN, R. P.; SANDS, R. B. Leightonm M. (1977). The Feynmann Lectures on Physics. Addison-Wesley. vol. II.

JACKSON, J. D.. Classical Electrodynamics.

MATHEWS & WALKER. Mathematical Methods of Physics

MARION, J. B. & THORNTON, S. T. (1995). Classical Dynamics of Particles and Systems. 4. ed. Academic Press.

FRENCH, A. P. (1968). Special Relativity. W. W. Norton.

Mecânica clássica II, textos letivos (2013), J. Pinto da Cunha.

Teaching method

Introduction and discussion of the different theoretical topics, accompanied by its practical application. Introduction of mathematical methods and techniques needed to understand the matters and the resolution of physical problems.

Discussion of examples and case studies.

Discussion of examples and case studies.

Resources used

Acesso ao laboratório para estudar para vários materiais o diagrama

'deformação versus tensão' e o efeito de forças de torção e de flexão.

'deformação versus tensão' e o efeito de forças de torção e de flexão.