Provide the students with a solid background in the field of Rigid Body Dynamics, as well as an introduction to Tensor Analysis, aiming to allow the writing of the physical equations using index notation in a curvilinear coordinate system.
Introduction: Kinematics and Dynamics of Particles; Systems of Particles.
Plane Motion of Rigid Bodies: Equations of Motion; Angular Momentum; D'Alembert's Principle; Work and Energy; Systems of Rigid Bodies; Conservation of Energy and Angular Moment.
Dynamics of Rigid Bodies in Three Dimensions: Angular Momentum and Kinetic Energy of a Rigid Body in Three Dimensions; Motion of a Gyroscope; Eulerian angles; Motion of an Axisymmetrical Body under No Force.
Mechanical Vibrations: Free Vibrations of Particles and Rigid Bodies; Forced Vibrations; Damped Vibrations; Mass-Spring-DamperSystem.
Tensor Calculus: Index Notation; Summation Convention; Vector Operations; Transformation laws; Invariance with Coordinate Systems; Metric Tensor; Physical Components of Tensors; Covariant Derivative; Curvilinear Acceleration; Differential Operators.
The Final Grade consists of three independent assessment components:
- Laboratory work performed in group, evaluated based on a written report (15%)
- Individual tests in class (35%)
- Final written exam (50%)
The teaching methodologies aim to promote learning based on problem solving and laboratorial work, reinforcing the practical component, active learning, autonomous work and student accountability. The assessment model incorporates elements of continuous assessment in the context of active learning compatible with the significant reduction of assessment by exams.
Vector Mechanics for Engineers: Statics and Dynamics, F.P. Beer, E.R. Johnston Jr., D. Mazurek, P.J. Cornwell, B. Self, 2019,McGraw-Hill Education; Elementos de Análise Tensorial, F.J.P. Lau e P.J.S. Gil, 2020, Instituto Superior Técnico.
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