# Course Details for A.Y. 2014/2015

#### Name:

**Meccanica Razionale / Rational Mechanics**

### Basic information

##### Credits:

*:* Bachelor Degree in Mathematics 9 CFU (b)

##### Degree(s):

Bachelor Degree in Mathematics 2^{nd} anno curriculum Generale Compulsory

##### Language:

Italian

### Course Objectives

The course presents the Newtonian Mechanic as an axiomatic-deductive theory formulated in a precise mathematical language.
The learning objectives of this presentation are 1) to clarify the connection between the description of physical phenomena and
their mathematical formalization, 2) to accustom the student to use different mathematical tools (analysis, geometry, etc)
to solve a specific problem 3) to develop the ability describe concrete phenomenological situations formalizing them into
mathematical models simple, but rigorous that allow predictions controllable. 4) Stimulate a critical understanding of
the arguments developed and a the use of a mathematical language.
Exercises are essential to achieve these goals.

### Course Content

- Space-time reference point material and Newton's laws.
- One-dimensional systems.
- Central forces, two-body problem, Kepler's laws.
- Constrained systems and Lagrange equations.
- Variational principles.
- Rigid bodies
- Equilibrium, stability and small oscillatuions
- Formulation of the equations of Hamilton
- Integrable systems
- Action-angles variables.
- Perturbation theory

### Learning Outcomes (Dublin Descriptors)

On successful completion of this course, the student should

- on classical mechanics and mathematical tools.
- and developpping skill in facing different novel problems with similar mathematical formalization.
- on the suitability of models and approximations
- the results of their studies in the course.
- autonomously. on related fields and topics

### Prerequisites and Learning Activities

A good background in Analysis and Geometry contained in the examas of Analysis 1 and Geoemtry 1 is essential and also is would
be good a good backgroud in Physic I and Algebra 1

### Assessment Methods and Criteria

Oral and written (exercises) exam.

### Textbooks

- E. Presutti, Appunti di Meccanica Analitica 2012. disponibile sul sito tra il materiale on-line https:
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- docs.google.com/viewer?a=v&pid=sites&srcid=bWF0LXVuaXZhcS5jb218bXJ8Z3g6NjRjYzEzMzdkZGJiZmJlN
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- A. Teta, APPUNTI DI MECCANICA RAZIONALE disponibile sul sito tra il materiale on-line https:
* *
- docs.google.com/viewer?a=v&pid=sites&srcid=bWF0LXVuaXZhcS5jb218bXJ8Z3g6NGUyMGU0M2Q2Mjc4MWQ3O
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- R. Esposito, Meccanica Razionale , ed. Aracne. 1998. disponibile sul sito tra il materiale on-line
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### Course page updates

This course page is available (with possible updates) also for the following academic years:

** To read the *** current * information on this course, if it is still available, go to the university course catalogue .
*Course information last updated on: 11 marzo 2015, 15:16*