# Analytical Mechanics

## Objectives

Describe the equations of mechanics in general coordinates.

Understand what a Law of Physics is.

This is the first contact for a Mathematics student with the Mathematical techniques for mechanics, in an applied

setting.

## General characterization

##### Code

12918

##### Credits

9.0

##### Responsible teacher

Fábio Augusto da Costa Carvalho Chalub

##### Hours

Weekly - 4

Total - 56

##### Teaching language

Português

### Prerequisites

Good command of differential and integral calculus in one and more variables, ordinary differential equations and linear matrix algebra. Notions of partial differential equations.

### Bibliography

C. Fox — An Introduction to the Calculus of Variations, Dover, 1987

H. Goldstein, C.P. Poole and J.L. Safko, — Classical Mechanics, 3rd ed., Addison Wesley, 2001

L.N. Hand and J.D. Finch — Analytical Mechanics, Cambridge University Press, 1998

J.V. José and E.G. Saletan — Classical Dynamics, Cambridge University Press, 1998

J.B. Marion and S.T. Thornton — Classical Dynamics of Particles and Systems, 4th ed., Saunders College Publishing,

1995

M.C. Povoas, Métodos Matemáticos da Física – Uma Introdução, Colecção Textos de Matemática, 17, Departamento de

Matemática, FCUL, 2002

H. Sagan — Introduction to the Calculus of variations, McGraw-Hill, 1969

### Teaching method

The classes will have a theoretical and practical character. In addition to the presentation of the subject, which is

illustrated with examples of application, are proposed for resolution by students, exercises of application of the

methods and results presented.

Any questions are answered in the course of classes or sessions designed to attend students or in sessions arranged

directly between student and teacher.

The assessment consists in the evaluation of work reports written by the students.

### Evaluation method

The assessment consists of homework (50%), an exam (30%), and a written report followed by a short presentation (20%).

## Subject matter

Part I - Dynamics of Particles

Part II - Dynamics of Rigid Bodies

Part III - - Calculus of Variations

Part IV - Continuum mechanics

## Programs

Programs where the course is taught: