L.EIC008 – Physics I

I taught this course between 2007 and 2022. When the Masters Program in Informatics and Computing Engineering started in 2006 this course had the code "EIC0010 – Physics I". When the Masters Program was replaced by a Bachelors Program in 2021, the code was changed to "L.EIC008 – Physics I" but the program and methodology remained the same.

Objective

Basic knowledge on mechanics and computational methods are taught in this course, using the Computer Algebra System (Maxima). After taking this course you should be able to solve simple equations of motion using the method of separation of variables, identify the forces and torques acting on a mechanical system translating them into the equations of motion and analyze dynamical systems describing its type, its state variables, evolution equations and equilibrium points.

Program

1. Kinematics with one degree of freedom. Vector kinematics. Curvilinear motion. Centripetal acceleration. Kinematics of rigid bodies.
2. Vector mechanics. Work and energy. Conservative and dissipative forces. Rigid-body dynamics. Torque. Moment of inertia.
3. Lagrangian mechanics. Generalized coordinates, velocities and forces. Lagrange equations. Lagrange multipliers.
4. Dynamical systems. Phase portraits. Conservative systems. Linear and non-linear systems.
5. Limit cycles. Two-species systems. Predator-prey models. Strange attractors and chaotic systems.

Bibliography

• Villate, J. E. (2019). Dynamics and Dynamical Systems. Porto, Portugal: Author's edition.
• Villate, J. E. (2021). Exercícios resolvidos de dinâmica e sistemas dinâmicos. Porto, Portugal: Author's edition. ISBN: 9789727522736. DOI: 10.24840/978-972-752-273-6. Available (in Portuguese) in Web version and printable version.

Additional Material

1. Videos and summaries of the lectures (in Portuguese).
2. Exams and tests with their solutions (in Portuguese).
3. Chaotic systems (in Portuguese).