Mathematical Methods in Mechanics
| Code: | M323 | Acronym: | M323 |
| Keywords | |
|---|---|
| Classification | Keyword |
| OFICIAL | Mathematics |
Instance: 2012/2013 - 2S
| Active? | Yes |
| Responsible unit: | Department of Mathematics |
| Course/CS Responsible: | Bachelor in Mathematics |
Cycles of Study/Courses
| Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
|---|---|---|---|---|---|---|---|
| L:AST | 3 | Plano de Estudos a partir de 2008 | 3 | - | 7,5 | - | |
| L:CC | 0 | Plano de estudos de 2008 até 2013/14 | 3 | - | 7,5 | - | |
| L:F | 2 | Plano de estudos a partir de 2008 | 3 | - | 7,5 | - | |
| L:M | 9 | Plano de estudos a partir de 2009 | 1 | - | 7,5 | - | |
| 2 | |||||||
| 3 |
Fields changed: Objectives, Métodos de ensino e atividades de aprendizagem, Fórmula de cálculo da classificação final, Componentes de Avaliação e Ocupação, Avaliação especial, Melhoria de classificação, Programa, Provas e trabalhos especiais
Teaching language
PortugueseObjectives
We intend to analyse, from a qualitative point of view, the motion of a particles system under the action of conservative forces.
Our approach will be of two types:
- for systems without restrictions on the movement, we will use the formalism of Newtonian mechanics;
- for systems with restrictions on the movement, the formalism of Lagrangian mechanics will be used instead.
Learning outcomes and competences
It is expected that students acquire the knowledge to solve problems on the motion of a system of particles under the action of conservative forces using both the formalism of Newtonian mechanics and that of Lagrangian mechanics.
Working method
PresencialProgram
Part I - Newtonian Mechanics
- Principle of newtonian determinism
- Study of equations of motion
- Systems with one degree of freedom
- Systems with two degrees of freedom; potential, or conservative force fields
- Study of motion in a central force field; the two-bodies problem
- Movement of an n particles system
Part II - Lagrangian Mechanics
- The calculus of variations; Euler-Lagrange equations, Legendre transform and Hamilton's equations; Liouville Theorem
- Introduction to the study of manifolds; charts and atlas; lagrangian dynamical system; symmetries of a system and conservation laws; Emmy Noether theorem
- Linearization around equilibrium points; stability and period of small oscillations
- Movement in a mobile coordinates system; forces of inertia; centrifugal and Coriolis forces
- Study of the rigid body; principal axes and principal moments of inertia; the inertia tensor and kinetic energy
- Euler angles and Lagrange gyroscope
Mandatory literature
000002963. ISBN: 0-387-90314-3000040314. ISBN: 0-201-65702-3
Teaching methods and learning activities
The contents of the syllabus are presented in theoretical lectures, which are accompaniedby the resolution of some illustrative exercises. There are also tutorial lessons to discuss and solve previously proposed exercises; where appropriate, the solutions found are checked with the aid of a computer algebra system (for example Maxima, Maple or Mathematica).
Software
Um qualquer sistema de computação algébrica (Maxima, Maple, Mathematica,...)keywords
Physical sciences > MathematicsPhysical sciences > Physics > Classical mechanics
Evaluation Type
Distributed evaluation without final examAssessment Components
| Description | Type | Time (hours) | Weight (%) | End date |
|---|---|---|---|---|
| Attendance (estimated) | Participação presencial | 76,50 | ||
| Teste | 3,00 | 22,00 | ||
| Teste | 3,00 | 22,00 | ||
| Teste | 3,00 | 22,00 | ||
| Prova oral | 1,50 | 34,00 | ||
| Total: | - | 100,00 |
Calculation formula of final grade
- three written tests; the average of the tests has a weight of 65% in the calculation of the final grade;
- oral presentations on topics identified in advance; this component has a weight of 35% in the calculation of the final grade.
CF = 0,65x(T1+T2+T3)/3 + 0.35xAO
T1 - score (0-20), in the 1st test
T2 - score (0-20), in the 2nd test
T3 - score (0-20), in the 3rd test
AO - score (0-20), in the oral presentations
To pass the course, a minimum score of 7 points in each of the written tests and oral presentations, is needed, that is:
T1 ≥ 7 and T2 ≥ 7 and T3 ≥ 7 and AO ≥ 7
Note: for approval in the Appeal Season, a minimum score of 9.5 in the exam is required, and the final grade (CF) is the score in the exam.
Examinations or Special Assignments
The normal components of the evaluation, as described above, may be supplemented by any student through an optional presentation of a computational work on a subject to be decided with the teacher. These additional works, being optional, can only serve as adequate information to enable the student to adjust the classification in cases where it is justified.
For ratings greater than or equal to 17 (in the scale 0-20), an additional written or oral examination, may be required.
Special assessment (TE, DA, ...)
Students in a special attendance regime are free of oral presentations, but, if they wish, they can make the presentations. Otherwise, their evaluation will be based only on the 3 written tests, and their classification will be the corresponding average, i.e., the final grade (CF) is calculated using the following formula:
CF = (T1+T2+T3)/3
T1 - score (0-20), in the 1st test
T2 - score (0-20), in the 2nd test
T3 - score (0-20), in the 3rd test
For ratings greater than or equal to 17 (in the scale 0-20), an additional written or oral examination, may be required.
Classification improvement
In accordance with the regulations of FCUP.
For ratings greater than or equal to 17 (in the scale 0-20), an additional written or oral examination, may be required.
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