Educational guide
IDENTIFYING DATA 2024_25
Subject CLASSICAL MECHANICS Code 00708014
Study programme
0708 - GRADO EN INGENIERÍA MECÁNICA
Descriptors Credit. Type Year Period
6 Compulsory Second First
Language
Aleman
Castellano
Ingles
Prerequisites
Department QUIMICA Y FISICA APLICADAS
Coordinador
ZORITA CALVO , MIGUEL
E-mail mzorc@unileon.es
jlmarm@unileon.es
Lecturers
MARCOS MENÉNDEZ , JOSÉ LUIS
ZORITA CALVO , MIGUEL
Web http://www.youtube.com/@miguelzorita
General description This course deepens topics of classical Newtonian mechanics previously introduced in a first semester course. The focus is on dynamics of systems of particles and rigid bodies, non-inertial frames of reference, conservation of angular momentum, three-dimensional rotational kinematics and dynamics, mechanical vibrations, coupled oscillators and Lagrangian mechanics.
Tribunales de Revisión
Tribunal titular
Cargo Departamento Profesor
Presidente QUIMICA Y FISICA APLICADAS FRAILE LAIZ , ROBERTO
Secretario QUIMICA Y FISICA APLICADAS GARCIA ORTEGA , EDUARDO
Vocal QUIMICA Y FISICA APLICADAS BURDALO SALCEDO , GABRIEL
Tribunal suplente
Cargo Departamento Profesor
Presidente QUIMICA Y FISICA APLICADAS CALVO GORDALIZA , ANA ISABEL
Secretario QUIMICA Y FISICA APLICADAS CEPEDA RIAÑO , JESUS RAMIRO
Vocal QUIMICA Y FISICA APLICADAS LOPEZ CAMPANO , LAURA

Competencias
Code  
A18156
B5634
B5635
B5643
B5645
B5646
C1 CMECES1 That students have demonstrated possession and understanding of knowledge in an area of study that is based on general secondary education, and is usually found at a level that, although supported by advanced textbooks, also includes some aspects that involve knowledge from the cutting edge of their field of study
C2 CMECES2 That students know how to apply their knowledge to their work or vocation in a professional manner and possess the skills that are usually demonstrated through the development and defense of arguments and the resolution of problems within their area of study.
C5 CMECES5 That students have developed those learning skills necessary to undertake further studies with a high degree of autonomy

Learning aims
Competences
A18156
 B5634
B5645
B5646
 C1
C5
A18156
 B5635
B5643
B5645
B5646
 C2
A18156
 B5635
B5643
B5645
B5646
 C2

Contents
Topic Sub-topic
INTRODUCTION TO THE DYNAMICS OF MECHANICAL SYSTEMS Topic 1: Classical Mechanics. Newton's Laws. Inertial reference systems. Constraint forces and applied forces. Degrees of freedom and equations of motion. Linear and non-linear systems. Analytical and numerical solution of the equations of motion. Examples of chaotic systems.
PARTICLE DYNAMICS Topic 2: Particle dynamics. Newton's laws in polar coordinates. Intrinsic components of motion. Dynamics of rotation and curvilinear motion. Linear momentum and angular momentum. Central forces. Work-Kinetic Energy Theorem. Potential energy and mechanical energy.

Topic 3: Equilibrium, stability and oscillations. Linearization of the equations of motion. Harmonic oscillations. Potential barriers and wells. Damped and driven oscillations. Resonance.

Topic 4: Relative motion and composition of motions. Newton's laws and dynamics in non-inertial reference systems. Fictitious forces. Rotating reference systems. Centrifugal and Coriolis forces.
DYNAMICS OF PARTICLE SYSTEMS AND RIGID SOLIDS Topic 5: Dynamics of particle systems. Internal and external forces. Conservation of linear momentum and angular momentum. Center of mass. Orbital and spin angular momentum. Work and energy. Conservative forces and potential energy. Equilibrium and stability. Planar rotation of rigid bodies. Moment of inertia. Instantaneous axis of rotation Slip-free rolling.

Topic 6: Lagrangian mechanics. Constraints, holonomous systems and generalized coordinates. Displacements and virtual works. D'Alembert's Principle. Calculus of Variations and Hamilton's Principle. Euler-Lagrange equations. Generalized forces and moments. Invariances and conservation principles.

Topic 7: General dynamics of rigid bodies. Degrees of freedom and generalized coordinates. Tensor of inertia. Principal axes. Theorems of parallel and perpendicular axes. Euler equations and angles. Gyroscopes.

Topic 8: Systems formed by coupled oscillators. Normal modes of oscillation. Wave equation in elastic media.

Planning
Methodologies  ::  Tests
  Class hours Hours outside the classroom Total hours
Problem solving, classroom exercises 9 30 39
 
Practicals using information and communication technologies (ICTs) in computer rooms 21 30 51
 
Lecture 24 30 54
 
Mixed tests 6 0 6
 
(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies
Methodologies   ::  
  Description
Problem solving, classroom exercises The problem and exercise classes are oriented to the development of the students' ability to apply the knowledge obtained in the theoretical classes, promote their capacity for analysis, critical reasoning, exchange of information and communication of the results. Exercises will be proposed to be solved by the students during the classes.
Practicals using information and communication technologies (ICTs) in computer rooms The professor will train and guide the students in the application of simulation and visualization tools necessary for the practical resolution of problems, encouraging at all times critical reasoning and the exchange of information between working groups. Exercises will be proposed and students will try to solve them, thus acquiring skills in the use of the necessary tools for problem solving.
Lecture In the theoretical and practical work sessions in the classroom, the professor will introduce, by means of theoretical explanations and illustrative examples, the concepts, results and methods of the subject. Their relation with other branches of Physics, their development and their application to the resolution of concrete problems will be shown. The student will have to prepare the theoretical part with the help of the bibliography and resources indicated by the professor.

Personalized attention
 
Lecture
Problem solving, classroom exercises
Practicals using information and communication technologies (ICTs) in computer rooms
Description
The student can count on the teacher's help to resolve any doubts that may arise throughout the course through individual tutorials. The tutorials are voluntary and will take place preferably through the corresponding forum in the Moodle platform of the course or in person in the office indicated by the teacher within his tutoring schedule, in which case the student must request the teacher in advance and with sufficient time via e-mail.

Assessment
  Description Qualification
Lecture Evaluation by means of a written exam at the end of the semester.
(see other comments) 		35 %
Problem solving, classroom exercises Evaluation by means of a written exam at the end of the semester.
(see other comments) 		35 %
Practicals using information and communication technologies (ICTs) in computer rooms Evaluation by means of exercises carried out throughout the semester.
(see other comments) 		30 %
 
Other comments and second call
The assessment of the student's knowledge will be carried out as described in detail below:

There will be a written exam at the end of the semester, in each of the calls, which will consist of a clear and reasoned answer to different questions. In this exam the student will have to demonstrate the understanding of the fundamental concepts of the subject and his capacity to apply these concepts to the resolution of problems.

The student will be asked to solve different questions and exercises during any of the theoretical or practical classes throughout the semester. In them the student will have to show his capacity to reason and solve problems, especially by means of computer models and simulation. These exercises must be carried out in the classroom during the corresponding class.

In order to pass the course, it is required to obtain a minimum grade in the final written exam of 5 points out of 10. If the score of the written exam does not reach that minimum grade then the student will not have passed the exam and will obtain a numerical grade equal to the score of that exam.

If the grade of the final written exam is equal or higher than 5 points out of 10, then the student will have passed the course and will have at least a grade of 5 points in the global certification. The overall numerical grade of the call will be higher than 5 points if the weighting by 70% of the grade of the written exam and 30% of the grade of the exercises performed in class results in a score higher than 5.

The grade obtained in the exercises performed during the classes throughout the semester will be maintained and applied with the same criteria in the final evaluation of the second call, but not for subsequent courses.

During the development of the tests and exercises, only the material and aids explicitly permitted by the professor in advance may be used. In particular, during the course of the exams, the possession and use of unauthorized mobile and/or electronic devices is strictly forbidden. The simple possession of such devices, as well as unauthorized notes, books, folders or other materials during the evaluation tests, will result in the immediate withdrawal and expulsion from the exam and the grade of 0 in the subject, transferring the incident to the corresponding Academic Authority to carry out the appropriate regulatory actions provided for in the regulations of the University of León.

Sources of information
Access to Recommended Bibliography in the Catalog ULE

Basic John R. Taylor, Classical Mechanics, University Science Books, 2005
Goldstein, Poole & Safko, Classical Mechanics, Addison Wesley, 2013

– Wolfram Mathematica and Wolfram Language Resources: https://www.wolfram.com/support/learn

– Mecánica: https://www.youtube.com/user/miguelzorita/playlists

– MIT 2.003SC Engineering Dynamics: https://ocw.mit.edu/courses/mechanical-engineering/2-003sc-engineering-dynamics-fall-2011/

– MIT 2.003 Dynamics and Control I: https://ocw.mit.edu/courses/mechanical-engineering/2-003j-dynamics-and-control-i-spring-2007/

– MIT 8.03 Physics III: Vibrations and Waves – Fall 2004: http://videolectures.net/mit803f04_physics_vibrations/
Complementary R. C. Hibbeler, Engineering Mechanics. Dynamics, Pearson, 2017
David Morin, Introduction to Classical Mechanics, Cambridge University Press, 2023
Mary L. Boas, Mathematical Methods in the Physical Sciences, John Wiley & Sons, 2006
– MIT 8.03SC Physics III - Vibrations and Waves: https://ocw.mit.edu/courses/physics/8-03sc-physics-iii-vibrations-and-waves-fall-2016/
– MIT STEM Concept Videos: https://ocw.mit.edu/resources/res-tll-004-stem-concept-videos-fall-2013/videos/

Recommendations


Subjects that it is recommended to have taken before
LINEAR ALGEBRA AND GEOMETRY / 00708001
DIFFERENTIAL AND INTEGRAL CALCULUS / 00708002
PHYSICAL FUNDAMENTALS / 00708003
NUMERICAL AND STATISTICAL METHODS / 00708006
HEAT AND ELECTROMAGNETISM / 00708007
INFORMATICS / 00708010
 
Other comments
Previous computer skills is highly recommended. Regular attendance and active participation in the classes is essential. Equally important is the previous preparation of the classes and the study of the subject matter.