Classical Mechanics
Code: 100148 ECTS Credits: 10| Degree | Type | Year | Semester |
|---|---|---|---|
| 2500097 Physics | OB | 2 | A |
Contact
- Name:
- José María Crespo Vicente
- Email:
- JoseMaria.Crespo@uab.cat
Use of Languages
- Principal working language:
- spanish (spa)
- Some groups entirely in English:
- No
- Some groups entirely in Catalan:
- No
- Some groups entirely in Spanish:
- Yes
Teachers
- José María Crespo Vicente
- María del Pilar Casado Lechuga
Prerequisites
No prerequisits are needed but following recommendations may be useful.
It is very important to have a deep knowledge of basic concepts of Mechanics and Relativity from first year.
It is important to master basic tools of differential and integral calculus (one variable), approximations with taylor series and to know elementary integrals.
It is also recommended to know basic principles of calculus in several variables for Analytical Mechanics and matrix diagonalisation for coupled oscillators and inertia tensor.
Objectives and Contextualisation
General goals are :
1. Learning more advanced subjects in Newtonian Mechanics;
2. Being able to deal with approximations, mainly by means of Taylor series.
3. Knowing and applying basic concepts of Analytical Mechanics.and recognize its importance for the whole of Physics.
Specific goals are :
. Resolving central forces problems using rotational symmetry.
. Dealing with particle systems and coupled oscillators.
. Studying rigid body rotations, inertia tensor and Euler equations.
. In Relativistic Dynamics, a deeper knowledge of relativistic linear momentum and energy and its applications.
. Knowing Lagragian and Hamiltonian formalisms.
Competences
- Develop strategies for analysis, synthesis and communication that allow the concepts of physics to be transmitted in educational and dissemination-based contexts
- Formulate and address physical problems identifying the most relevant principles and using approximations, if necessary, to reach a solution that must be presented, specifying assumptions and approximations
- Know the fundamentals of the main areas of physics and understand them
- Use critical reasoning, show analytical skills, correctly use technical language and develop logical arguments
- Use mathematics to describe the physical world, selecting appropriate tools, building appropriate models, interpreting and comparing results critically with experimentation and observation
- Work independently, have personal initiative and self-organisational skills in achieving results, in planning and in executing a project
Learning Outcomes
- Analytically and numerically solve the Newton’s equation.
- Describe conservative forces.
- Describe motion in one, two and three dimensions.
- Describe non-inertial reference systems.
- Describe relativistic kinematics.
- Describe shocks.
- Describe the fundamentals of analytical mechanics.
- Describe the fundamentals of classical mechanics.
- Describe the kinematics and dynamics of rigid bodies.
- Formulate and solve the motion of a system using Lagrange’s equations.
- Identify laws of conservation in a system of particles.
- Identify the concepts of linear and angular momentum and energy.
- Identify types of oscillators: simple harmonic, buffed and forced.
- Properly handle the developments in Taylor series, the chain rule, implicit equations, diagonalization, dimensional analysis and vector calculus.
- Solve movement in the event of variable force or mass.
- Solve the movement produced by a central force.
- Translate specific physical problems to a mathematical formulation that allows subsequent resolution, either exact or approximate.
- Transmit, orally and in written format, physical concepts of a certain complexity, making them understandable to non-specialist settings.
- Use critical reasoning, show analytical skills, correctly use technical language and develop logical arguments
- Work independently, take initiative itself, be able to organize to achieve results and to plan and execute a project.
Content
First Semester :
1. Motion in one dimension.
Potential diagram. Harmonic Simple, damped and forced oscillators.
2. Motion in 3 dimensions.
Kinematics. Vector differential operators. Conservative forces.
3. Central Forces.
Conservation Laws. Two bodies system. Motion and orbit equations. Effective potential diagram. Inverse square law central force. Kepler problem : elliptic orbits. Rutherford scattering : hyperbolic orbits. Cross section. Virial theorem. Laplace vector.
4. Particle Systems.
Conservation laws. Collisions in laboratory and center of mass. Application to Rutherford problem.
5. Coupled Oscillators.
Normal vibrating modes. Weak coupling. Limit of infinit oscillators. The vibrating string.
6. Rigid Body I
Moments of Inertia. Steiner theorem. Rotation around fix axis.
7. Rotating reference systems.
Coriolis theorem. Motion laws on Earth. Foucault pendulum.
Second Semester :
8. Rigid Body II
Rotation kinetic Energy. Inertia Tensor. Angular Momentum. Free rotation of symmetric top. Euler angles. Euler equations. Stability around principal axis.
9. Relativistic linear Momentum.
10. Invariants and four-vectors.
11. Relativistic Energy.
12. Collisions and Decays. Compton effect and other reactions.
13. Relativistic motion.
14. Constraints and generalized coordinates. Possible and virtual infinitesimal displacements. D'Alembert Principle.
15. Generalized forces. Lagrange equations. Lagrange equations for potential forces.
16. Generalized momenta. Cyclic coordinates and motion constants. Variation of total Energy.
17. Hamiltonian variables. Hamiltonian. Hamilton équations.
18. Hamilton Principle. Application to relativistic free particle.
19. Generalized potential. Example : electromagnetism.
20. Variations calculus. Example : brachystochron.
21. Poisson claudator.
Methodology
It has been decided in principle by Facultat de Ciències and Coordinació del Grau de Física that teaching will be semipresential in first semester and presential in second semester. If allowed by sanitary situation, the start of presential teaching will be advanced.
Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.
Activities
| Title | Hours | ECTS | Learning Outcomes |
|---|---|---|---|
| Type: Directed | |||
| magister lecture | 55 | 2.2 | 3, 7, 8, 4, 6, 9, 5, 2, 10, 12, 11, 15, 16 |
| problem teaching | 28 | 1.12 | 10, 14, 19, 15, 16, 1, 17, 18 |
| Type: Supervised | |||
| Supervised tests | 2 | 0.08 | 7, 8, 19, 16 |
| Type: Autonomous | |||
| Individual work | 138 | 5.52 | 3, 7, 8, 4, 6, 9, 5, 2, 10, 12, 11, 14, 19, 15, 16, 1, 17, 18 |
| problem resolution | 12 | 0.48 | 18 |
Assessment
The qualification is 50% each semester. The semester qualification is equal parts for the two partials. Problem delivery can be 10% of qualification only in case of improvement.
The evaluation is successful if the student has attended all four partials, if the qualification is at least 5 and each semester at least 3.
If not successful or if successful but willing to improve students can do the final recovery examination. This final examination has two parts, one for each semester and the qualification of each part replaces the previous semester qualification only in case of improvement. The student can do both parts or only one. The qualifications of the final examination do not take in account problem delivery.
A student is evaluated if he/she has attended at least 35% of the qualification.
Students will be previously informed if a self-made formular is authorized in the examinations.
Assessment Activities
| Title | Weighting | Hours | ECTS | Learning Outcomes |
|---|---|---|---|---|
| 1st partial 1st semester (recoverable) | 22.5-25% | 3 | 0.12 | 3, 8, 6, 2, 12, 13, 11, 19, 1, 18 |
| 1st partial 2nd semester (recoverable) | 22.5-25% | 3 | 0.12 | 4, 9, 5, 19, 17, 18 |
| 2nd partial 1st semester (recoverable) | 22.5-25% | 3 | 0.12 | 6, 11, 14, 19, 15, 16, 1, 17, 18 |
| 2nd partial 2nd semester (recoverable) | 22.5-25% | 3 | 0.12 | 7, 10, 19, 17, 18 |
| Problem delivery (recoverable in corresponding partial) | 10% | 0 | 0 | 19, 1, 17, 18, 20 |
| Recovery Examination (Optional if successful in partials) | 100% | 3 | 0.12 | 3, 7, 8, 4, 6, 9, 2, 10, 12, 11, 14, 19, 15, 16, 1, 17, 18 |
Bibliography
J.B. Marion Classical Dynamics of Particles and Systems Academic Press New York and London
T.W.B. Kibble Classical Mechanics McGraw-Hill
A.F. Rañada Dinámica Clásica Ed. Alianza Universidad
Software
No particular programary is used in this course.