Identifying Data 2019/20
Subject (*) Mechanics Code 730G03026
Study programme
 Grao en Enxeñaría Mecánica
Descriptors Cycle Period Year Type Credits
Second Obligatory 6
Language
 Spanish Galician
Teaching method Face-to-face
Prerequisites
Department Enxeñaría Naval e Industrial
 Ramil Rego, Alberto
E-mail
 alberto.ramil@udc.es
Lecturers
 Ramil Rego, Alberto
E-mail
 alberto.ramil@udc.es
Web
General description O obxectivo xeral é o desenvolvemento das destrezas e actitudes necesarias para a aplicación dos principios fundamentais da mecánica á resolución de problemas de interese na enxeñaría. Abórdase a estática, cinemática e dinámica do punto material, dos sistemas e do sólido ríxido dende a formulación newtoniana e dende a formulación lagrangiana. Esta materia contribuirá á mellora da capacidade de análise e de construción de modelos matemáticos que describen os efectos das forzas e os movementos sobre unha gran variedade de estruturas e máquinas incorporando as hipóteses físicas e as aproximacións matemáticas axeitadas.
Contingency plan

 Study programme competencies

 Learning aims
 Learning outcomes Study programme competences Know and understand the method of virtual works and the potential for their application in the resolution of static problems. A13 B1B2B3B6B7B8B9 C1C5 Know and understand the kinematics of the solid, being able to apply the composition of movements. A13 B1B2B3B6B7B8B9 C1C5 Know and understand the laws of dynamics, both in its vector and analytical formulation. A13 B1B2B3B6B7B8B9 C1C5

 Contents
 Topic Sub-topic NOTE. The following blocks or themes develop the contents established in the Verification Report card => Kinematics of the rigid solid. Static Dynamic of systems. 1. Introduction to kinematics. 1.1. Change of orthonormal reference. Transformation of the components of a vector. 1.2. Matrix form of a rotation. 1.3. Second order Cartesian Tensors. 1.4. Rate of change of a vector. 1.5. Frenet frame. Frenet formulas. 1.6. Speed and acceleration. Intrinsic components 2. Kinematics of the rigid body. 2.1. Rigid body definition. 2.2. Translation and rotation movements. 2.3. Helical speed distribution. Chasles Theorem. 2.4. Kinematic group. Invariants. 2.5. Instantaneous axis of rotation. Minimum sliding speed. 2.6. Axoid Surfaces. 2.7. Acceleration distribution. 2.8. Angles and rotations of Euler. 3. Relative Motion 3.1. Relative velocity. 3.2. Addition theorem for angular velocity. 3.3. Relative acceleration. 3.4. Addition theorem for angular acceleration. 3.5. Inverse movements. 3.6. Movement of two solids in contact. 4. Plane Motion 4.1. Instantaneous centre of rotation. Base and rolling curve. 4.2. Speed of succession of the instantaneous centre of rotation. 4.3. Distribution of accelerations in the plane movement 5. Distributed forces. 5.1. Centre of mass. 5.2. Inertia tensor. 5.3. Steiner's theorem or parallel axes. 5.4. Diagonalization of the inertial tensor. 5.5 Symmetries in mass distributions. 5.6. Inertia Ellipsoid 6. Rigid body equilibrium 6.1 Rigid body equilibrium. Free-Body Diagrams 6.2. Principle of virtual work. 6.3. Potential energy and equilibrium conditions. Stability 7. Cable equilibrium 7.1. Equilibrium of the ideal cable. 7.2. Equilibrium under a system of parallel forces. 7.3. Cable under the action of its own weight. Catenary 8. Principles of dynamics. 8.1. Principles and laws of Newtonian mechanics. 8.2. D'Alembert's principle. 8.3. Hamilton's principle 9. Basic elements of Analytical Mechanics. 9.1. Constraints in physical systems. Definition, properties and classification. 9.2. Equilibrium conditions and equations of movement in generalized coordinates. 9.3. D'Alembert's principle. 9.4. General equation of the dynamics for a system with constraints without friction. 9.5. Forces, work and energy in generalized coordinates. 10. Lagrange formulation. 10.1. Lagrange equations. 10.2. Generalized potentials and dissipation function. 10.3. Simple applications of the Lagrange formulation. 10.4. Constants of movement. Conservation theorems. 10.5. Variational principle of Hamilton. Application to the derivation of the Lagrange equations. 10.6. Hamiltonian function. 10.7. Elimination of cyclical coordinates. Routh function. 11. Dynamics of Rotational Motion about a Fixed Axis 11.1. Equations of movement 11.2. Reactions in the supports. Static and dynamic equilibrium 12. Dynamic of the rigid body with one fixed point 12.1. Equations of motion of a rigid body with one fixed point. Linear moment, angular moment and kinetic energy. 12.2. Application of the angular moment theorem. Euler equations. 12.3. Integration of Euler equations in the absence of pairs. Cases of ellipsoid of revolution and asymmetric ellipsoid. 12.4. Stability of the rotation around the principal axes. 12.5. Movement of a heavy solid around a fixed point. The Lagrange top. 13. Small oscillations about equilibrium 13.1. Small oscillations around stable equilibrium. 13.2. Determination of natural frequencies and normal modes. 13.3. Characterization of the movement according to the different modes of oscillation. Stability of motion. 13.4. Temporal response of the system to applied forces. Machine vibrations like forced oscillations.

 Planning
 Methodologies / tests Competencies Ordinary class hours Student’s personal work hours Total hours Guest lecture / keynote speech A13 B1 B2 B3 C5 27 36 63 Problem solving A13 B1 B2 B3 C1 27 36 63 Supervised projects A13 B1 B2 B3 B6 B7 B8 B9 C1 C5 0 12 12 Mixed objective/subjective test A13 B1 B2 4 6 10 Personalized attention 2 0 2 (*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

 Methodologies
 Methodologies Description Guest lecture / keynote speech Oral presentation complemented with the use of audio-visual media to develop the syllabus of the subject and make explanations and examples that allow the understanding of the principles of the subject to be able to apply them to practical examples. Problem solving Resolution of problems corresponding to the different subjects of the syllabus in order to understand the theoretical principles and know their practical application, comparing different methods highlighting the advantages of each. Supervised projects Individual student work designed to promote autonomous learning under the tutelage of the teacher. The theme is chosen to apply the knowledge developed in the subject but also includes aspects not addressed in the lectures to develop the capacity for research and self-learning. Mixed objective/subjective test It is a written test consisting of 2 parts (theory and problems) of approximately 1.5 and 2.5 hours, with a maximum total duration of 4 hours. The theory test will have about 5 questions of diverse amplitude and degree of concretion on the contents of the subject. The practical type test will consist of the resolution of 1 to 3 problems of varying complexity on the contents of the subject.

 Personalized attention
 Methodologies Mixed objective/subjective test Guest lecture / keynote speech Problem solving Supervised projects
 Description It is recommended that all students attend tutorials to clarify issues related to both theory and problem classes. In the case of problems, it is also recommended that they analyse in detail the problems solved in class and that they try to solve those that are left unresolved, consulting any doubt or difficulty. Once this is done with the problems of each subject, the problems of the mixed tests of previous courses will be similarly dealt with, consulting any doubt or difficulty. It is also recommended to consult any doubt about the contents, extension and detail with which the theory questions should be answered. In the supervised work there is a duty to attend a minimum of interviews with the teacher. These interviews aim to define its content and scope, as well as to check its progress. Students with academic dispensation may request the realization of tutorials in a different time from the one published on the UDC website.

 Assessment
 Methodologies Competencies Description Qualification Mixed objective/subjective test A13 B1 B2 The mixed test consists of two parts: theory (40%) and problems (60% of the test score). In the theory part the knowledge of the program of the subject is valued as well as the reasoned exposition of the theoretical developments. In the part of problems will be assessed both the formulation and the development applied to the specific case to obtain the solution. The qualification of this test in the first opportunity will be the average of two partial tests: the first one (subjects 1-7) in the middle of the semester and the second (subjects 8-13) at the end of the semester. Students who do not pass the subject at the first opportunity may perform a final test (topics 1-13) on the second opportunity period. The dates of these tests will be those that appear in the exam calendar and course planning published by the school. 80 Supervised projects A13 B1 B2 B3 B6 B7 B8 B9 C1 C5 The work is of an individual nature, so the originality will be rewarded and the copy of results or the method used will be penalized. Each student must submit their report within the deadline and attend mandatory tutoring. In case of not fulfilling these conditions the work will be scored as 0. The delivery will be made through Moodle, in digital format without the need to print it. 20 Assessment comments Only students who do not attend any of the mixed tests will be rated as NOT PRESENTED.Academic dispensation is allowed in the terms established in point 5 of article 7 of the "Standard that regulates the regime of dedication to study and the permanence and progression of undergraduate and master's degree students at the University of A Coruña", approved by the Social Council of 04/05/2017 Therefore, students with academic dispensation will be evaluated using the same system as the rest of the students, that is, supervised work 20% + mixed test 80%.The evaluation criteria of the 2nd opportunity are the same as those of the 1st opportunity.

 Sources of information
 Basic J.M. Bastero; J. Casellas (1991). Curso de Mecánica (4ª Ed.). EUNSA C.F. González (2003). Mecánica del sólido rígido. Ariel

 Recommendations
Subjects that it is recommended to have taken before
 Calculus /730G03001 Physics I /730G03003 Linear Algebra/730G03006 Physics II/730G03009

Subjects that are recommended to be taken simultaneously
 Diferential Equations/730G03011 Fundamentals of Electricity/730G03012 Thermodynamics /730G03014

Subjects that continue the syllabus
 Strength of Materials/730G03013 Theory of Machines/730G03019 Machine Components/730G03029