| Code |
14903
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| Year |
2
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| Semester |
S1
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
Physics
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Entry requirements |
None
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Learning outcomes |
To gain a solid knowledge basis of the fundamentals and applications of classical mechanics, including topics of oscillator motion, Lagrangian formalism, rigid body dynamics, small oscillations, and Hamiltonian formalism.
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Syllabus |
1. Foundations of classical mechanics
Constants of motion. Energy conservation
2. Oscillations
Free harmonic oscillations
Damped oscillations
Forced oscillations
Ressonance
3. Kepler’s problem
Two body system: center of mass and relative coordinates
Gravitational interaction and central forces
Properties of motion under a central potential
The potential 1/r
Orbits and Kepler’s laws
4. Introduction to the Lagrangian formalism
Constraints and generalized coordinates
Lagrangian and Euler-Lagrange equation
Symmetries and conservation laws
5. Rigid Body Motion
The Inertia Tensor
Angular Momentum
Principal axes of inertia
Euler Angles
Euler's theorem on rigid body motion
Coriolis effect
6. Small oscillations and normal modes
Coupled oscillators
Normal modes
7. Hamiltonian formalism
Legendre transformations
Canonical transformations
Poisson Parentheses
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Main Bibliography |
1. Goldstein H, Poole Jr CP and Safko JL (2002). Classical Mechanics, 3rd ed. Reading, MA: Addison-Wesley
2. Kibble TWB and Berkshire FH (2004). Classical Mechanics, 5th ed. London: Imperial College Press
3. Maia NMM (2008). Introdução à Dinâmica Analítica. Lisboa: IST Press
4. Taylor J (2005). Classical Mechanics. University Science Books
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Teaching Methodologies and Assessment Criteria |
Mixed theory and problem solving sessions – the theoretical contents are presented and immediately illustrated by means of examples, allowing the clarification of concepts, methods and results. Besides two written tests, evaluation is based on small projects developed by the students.
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Language |
Portuguese. Tutorial support is available in English.
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