Analytical Mechanics

Code:

FIS2011

Acronym:

FIS2011

Keywords
Classification	Keyword
OFICIAL	Physics

Instance: 2021/2022 - 2S

Active?	Yes
Responsible unit:	Department of Physics and Astronomy
Course/CS Responsible:	Bachelor in Physics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:F	66	Official Study Plan	2	-	6	56	162

Teaching language

Suitable for English-speaking students

Objectives

To master classical formalisms of analytical mechanics and its application to problems of classical mechanics. In this line the student is exposed to the notions of symmetry and algebrization in the description of movement, as an introductory path to the concepts to be developed in chairs on Quantum Mechanics.

Learning outcomes and competences

This course develops skills to solve more advanced problems in more complex mechanical systems, using more sophisticated mathematical techniques.

In addition, the student will learn several concepts that play an important role in modern theoretical physics, including the principles of symmetry and the geometric structure of mechanics.

Upon completion of the course the student should be able to use the formalisms of Lagrange and Hamilton in specific examples, solve a greater variety of problems using methods of Analytical Mechanics, and apply the mathematical tools that were developed during the course.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Program

1. Review the basic concepts of Newtonian mechanics. Principle of d'Alembert. Generalized forces.

2. Review of variational methods. Variational formulation of the equations of Lagrange. Case of generalized potentials. Case of dissipative forces. Symmetries and conservation laws. Noether's theorem.

3. The problem of two bodies (point like) with a central potential.

4. Movement of a solid. Euler angles. Euler equations. The symmetrical top.

5. The formulation of Hamilton. Hamilton equations.

6. Canonical transformations. The generating function of a canonical transformation. The Poincaré invariants. Poisson brackets.  Infinitesimal canonical transformations, symmetries and constants of motion.

7. Hamilton-Jacobi theory. Separation of variables in Hamilton-Jacobi equation.

8. Action-angle variables. Adiabatic invariants. Brief presentation of the canonical theory of perturbations.

Mandatory literature

H. Goldstein, C.P. Poole, J.L. Safko; Classical Mechanics (3rd ed.), Addison Wesley, 2001

Complementary Bibliography

Woodhouse, N.; Introduction to Analytical Dynamics, Springer, 2009

Comments from the literature

From the adopted work it will be taught subjects addressed in the sections: 1.3 to 1.6; 2.1 to 2.7; 3.1 to 3.3; 3.7 to 3.9; 4.1 to 4.4; 4.7 to 4.9; 5.1 to 5.8; 8.1 to 8.3; 8.5 to 8.6; 9.1-9.9; 10.1 to 10.7; 11.1 to 11.6; 12.1 to 12.5.

Punctually it will be provided slides and notes of the materials presented in class.

Teaching methods and learning activities

Lectures: exposition.
Practical lectures: problem solving.

Evaluation Type

Evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	100,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

Calculation formula of final grade

Observations

The jury of the curricular unit includes:
- José Miguel Nunes da Silva
- Miguel Sousa da Costa
- Orfeu Bertolami Neto