Ingegneria Edile-Architettura | RATIONAL MECHANICS

cod. 0660100018

RATIONAL MECHANICS

	0660100018
	DEPARTMENT OF CIVIL ENGINEERING
	EQF7
	BUILDING ENGINEERING - ARCHITECTURE
	2022/2023

PERCORSO COMMON

	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2017
	AUTUMN SEMESTER

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/07	6	60	LESSONS	OPTIONAL SUBJECTS

	Objectives
	-) KNOWLEDGE AND UNDERSTANDING. THE STUDENT SHOULD KNOW THE BASIC ELEMENTS OF THE VECTOR CALCULATION IN ORDER TO STUDY BOTH THE KINEMATICS AND THE DYNAMICS OF A MATERIAL POINT, OF SYSTEMS OF MATERIAL POINTS AND RIGID BODIES. THE STUDENT HAS ALSO TO BE ABLE TO UNDERSTAND SIMPLE PROBLEMS OF MASS GEOMETRY. -) APPLYING KNOWLEDGE AND UNDERSTANDING. THE STUDENT SHOULD BE ABLE TO SOLVE SIMPLE PROBLEMS OF MASS GEOMETRY (IN THE CASE OF FLAT SYSTEMS), OF DYNAMICS (IN THE CASE OF PLAN SYSTEMS WITH ONE OR MORE DEGREES OF FREEDOM) AND STATIC OF MECHANICAL SYSTEMS (FOR PLAN SYSTEMS, BY MEANS OF CARDINALS EQUATIONS OF THE STATIC, AND BY MEANS OF THE PRINCIPLE OF VIRTUAL WORKS). -) JUDGMENT AUTONOMY. THE STUDENT HAS TO BE ABLE TO DEEPEN INTO OWN KNOWLEDGE, IN ORDER TO USE IT AS A STARTING POINT TO REACH FURTHER NEW RESULTS WHICH MAY BE MORE COMPLEX. -) COMMUNICATION SKILLS. THE STUDENT HAS TO BE ABLE OF EXPLAINING IN A SIMPLE WAY, WITH DETAILS AND PRECISIONS, ALL THE METHODS AND TECHNIQUES ADOPTED TO SOLVE A PROBLEM OF MECHANICS, AS WELL AS THE PROCEDURE WHICH HAS BEEN USED TO GET THE AIMED RESULTS. HE MUST BE ALSO ABLE TO APPLY THE OBTAINED KNOWLEDGE TO PRACTICAL APPLICATIONS. -) LEARNING SKILLS. THE STUDENT HAS TO DEVELOP THE LEARNING SKILLS THAT WILL BE NECESSARY FOR INSERTING HIM IN THE FOLLOWING STUDIES WITH A HIGH AUTONOMY OF STUDY, AND CRITICALLY FACE MORE GENERAL PROBLEMS.

-) KNOWLEDGE AND UNDERSTANDING.
THE STUDENT SHOULD KNOW THE BASIC ELEMENTS OF THE VECTOR CALCULATION IN ORDER TO STUDY BOTH THE KINEMATICS AND THE DYNAMICS OF A MATERIAL POINT, OF SYSTEMS OF MATERIAL POINTS AND RIGID BODIES. THE STUDENT HAS ALSO TO BE ABLE TO UNDERSTAND SIMPLE PROBLEMS OF MASS GEOMETRY.
-) APPLYING KNOWLEDGE AND UNDERSTANDING.
THE STUDENT SHOULD BE ABLE TO SOLVE SIMPLE PROBLEMS OF MASS GEOMETRY (IN THE CASE OF FLAT SYSTEMS), OF DYNAMICS (IN THE CASE OF PLAN SYSTEMS WITH ONE OR MORE DEGREES OF FREEDOM) AND STATIC OF MECHANICAL SYSTEMS (FOR PLAN SYSTEMS, BY MEANS OF CARDINALS EQUATIONS OF THE STATIC, AND BY MEANS OF THE PRINCIPLE OF VIRTUAL WORKS).
-) JUDGMENT AUTONOMY.
THE STUDENT HAS TO BE ABLE TO DEEPEN INTO OWN KNOWLEDGE, IN ORDER TO USE IT AS A STARTING POINT TO REACH FURTHER NEW RESULTS WHICH MAY BE MORE COMPLEX.
-) COMMUNICATION SKILLS.
THE STUDENT HAS TO BE ABLE OF EXPLAINING IN A SIMPLE WAY, WITH DETAILS AND PRECISIONS, ALL THE METHODS AND TECHNIQUES ADOPTED TO SOLVE A PROBLEM OF MECHANICS, AS WELL AS THE PROCEDURE WHICH HAS BEEN USED TO GET THE AIMED RESULTS. HE MUST BE ALSO ABLE TO APPLY THE OBTAINED KNOWLEDGE TO PRACTICAL APPLICATIONS.
-) LEARNING SKILLS.
THE STUDENT HAS TO DEVELOP THE LEARNING SKILLS THAT WILL BE NECESSARY FOR INSERTING HIM IN THE FOLLOWING STUDIES WITH A HIGH AUTONOMY OF STUDY, AND CRITICALLY FACE MORE GENERAL PROBLEMS.

	Prerequisites
	FOR THE SUCCESSFUL ACHIEVEMENT OF THE GOALS OF THE COURSE, STUDENTS ARE REQUIRED TO HAVE THE FOLLOWING PREREQUISITES: -) BASIC KNOWLEDGE OF MATHEMATICAL ANALYSIS (I.E., FUNDAMENTAL THEORY BOTH OF DIFFERENTIAL CALCULATION, AND OF INTEGRALS); -) BASIC KNOWLEDGE OF ORDINARY DIFFERENTIAL EQUATIONS; -) BASIC KNOWLEDGE OF TENSORIAL CALCULATION; -) BASIC KNOWLEDGE OF PHYSICS. THE AFOREMENTIONED BASIC KNOWLEDGES ARE COMPULSORY: EACH PART OF THE EXAM WILL BE FORBIDDEN IF THE FOLLOWING EXAMS DON'T HAVE BEEN PREVIOUSLY PASSED: MATHEMATICS I AND GENERAL PHYSICS.

Prerequisites

FOR THE SUCCESSFUL ACHIEVEMENT OF THE GOALS OF THE COURSE, STUDENTS ARE REQUIRED TO HAVE THE FOLLOWING PREREQUISITES:
-) BASIC KNOWLEDGE OF MATHEMATICAL ANALYSIS (I.E., FUNDAMENTAL THEORY BOTH OF DIFFERENTIAL CALCULATION, AND OF INTEGRALS);
-) BASIC KNOWLEDGE OF ORDINARY DIFFERENTIAL EQUATIONS;
-) BASIC KNOWLEDGE OF TENSORIAL CALCULATION;
-) BASIC KNOWLEDGE OF PHYSICS.

THE AFOREMENTIONED BASIC KNOWLEDGES ARE COMPULSORY: EACH PART OF THE EXAM WILL BE FORBIDDEN IF THE FOLLOWING EXAMS DON'T HAVE BEEN PREVIOUSLY PASSED: MATHEMATICS I AND GENERAL PHYSICS.

	Contents
	VECTORIAL CALCULUS (4 HOURS): VECTORS AND BASIC OPERATIONS. APPLICATIONS TO DIFFERENTIAL GEOMETRY. APPLIED VECTORS (2 HOURS): SYSTEM OF APPLIED VECTORS. RESULTANT VECTOR AND RESULTANT TORQUE FOR A SYSTEM OF APPLIED VECTORS. CENTRAL AXIS. SYSTEMS OF APPLIED VECTORS. KINEMATICS OF A MATERIAL POINT (2 HOURS): SPEED. ACCELARATION. IN-PLANE MOTION. CENTRAL MOTION. HARMONIC MOTION. KINEMATICS OF A SYSTEM OF MATERIAL POINTS (8 HOURS): DEGREES OF FREEDOM AND LAGRANGIAN COORDINATES. HOLONOMIC SYSTEMS. KINEMATICS OF RIGID-BODY SYSTEMS. EULER DEGREE. PARTICULAR RIGID MOTIONS. POISSON FORMULAS. MOZZI THEOREM. KINEMATICS OF RELATIVE MOTIONS. IN-PLANE RIGID MOTION. STATICS AND DYNAMICS OF A FREE PARTICLE (10 HOURS). WORK OF A FORCE. CONSERVATIVE FORCES. MECHANICAL ENERGY AND RELATIVE THEOREMS. DIFFERENTIAL EQUATIONS OF THE MOTION OF A FREE PARTICLE BOTH IN AN INERTIAL REFERENCE FRAME, AND IN A NON-INERTIAL REFERENCE FRAME. STATICS OF A FREE PARTICLE. HARMONIC OSCILLATOR, DAMPED HARMONIC OSCILLATOR, RESONANCE. STATICS AND DYNAMICS OF A RESTRICTED PARTICLE (4 HOURS): EQUATIONS OF MOTION. STATICS. EQUILIBRIUM. DYNAMICS. SIMPLE GRAVITY PENDULUM. THE MASS GEOMETRY (10 HOURS): BARYCENTER AND ITS PROPERTIES. LINEAR AND ANGULAR MOMENTUM. KOENING THEOREM. KINETIC ENERGY AND MOMENT OF INERTIA. HUYGENS THEOREM AND INERTIA ELLIPSOID. GENERAL THEOREMS OF MATERIAL-SYSTEM MECHANICS (4 HOURS): CARDINAL EQUATIONS OF DYNAMICS. THEOREM OF THE MOTION OF BARYCENTER. THEOREMS ABOUT THE WORK OF INTERNAL AND EXTERNAL FORCES. THEOREM OF ENERGY CONSERVATION. STATICS OF RIGID BODIES (4 HOURS): CARDINAL EQUATIONS OF STATICS. GENERAL CONDITIONS FOR THE EQUILIBRIUM OF A RIGID BODY AND SOME APPLICATIONS. VINCULAR REACTIONS FOR A RIGID BODY IN EQUILIBRIUM. DYNAMICS OF A RIGID BODY (2 HOURS): THE MOTION OF A RIGID BODY. ANALYTICAL MECHANICS (10 HOURS): VIRTUAL DISPLACEMENTS OF A HOLONOMIC SYSTEM. VIRTUAL WORK. THE SYMBOLIC EQUATION OF DYNAMICS AND THE D'ALAMBERT PRINCIPLE. THE SYMBOLIC EQUATION OF STATICS AND THE PRINCIPLE OF VIRTUAL WORK. EQUILIBRIUM OF A HOLONOMIC SYSTEM. THE LAGRANGE EQUATIONS. THE KINETIC ENERGY OF HOLONOMIC SYSTEMS AND RELATIVE THEOREMS.

Contents

VECTORIAL CALCULUS (4 HOURS):
VECTORS AND BASIC OPERATIONS. APPLICATIONS TO DIFFERENTIAL GEOMETRY.
APPLIED VECTORS (2 HOURS):
SYSTEM OF APPLIED VECTORS. RESULTANT VECTOR AND RESULTANT TORQUE FOR A SYSTEM OF APPLIED VECTORS. CENTRAL AXIS. SYSTEMS OF APPLIED VECTORS.
KINEMATICS OF A MATERIAL POINT (2 HOURS):
SPEED. ACCELARATION. IN-PLANE MOTION. CENTRAL MOTION. HARMONIC MOTION.
KINEMATICS OF A SYSTEM OF MATERIAL POINTS (8 HOURS):
DEGREES OF FREEDOM AND LAGRANGIAN COORDINATES. HOLONOMIC SYSTEMS. KINEMATICS OF RIGID-BODY SYSTEMS. EULER DEGREE. PARTICULAR RIGID MOTIONS. POISSON FORMULAS. MOZZI THEOREM. KINEMATICS OF RELATIVE MOTIONS. IN-PLANE RIGID MOTION.
STATICS AND DYNAMICS OF A FREE PARTICLE (10 HOURS).
WORK OF A FORCE. CONSERVATIVE FORCES. MECHANICAL ENERGY AND RELATIVE THEOREMS. DIFFERENTIAL EQUATIONS OF THE MOTION OF A FREE PARTICLE BOTH IN AN INERTIAL REFERENCE FRAME, AND IN A NON-INERTIAL REFERENCE FRAME. STATICS OF A FREE PARTICLE. HARMONIC OSCILLATOR, DAMPED HARMONIC OSCILLATOR, RESONANCE.
STATICS AND DYNAMICS OF A RESTRICTED PARTICLE (4 HOURS):
EQUATIONS OF MOTION. STATICS. EQUILIBRIUM. DYNAMICS. SIMPLE GRAVITY PENDULUM.
THE MASS GEOMETRY (10 HOURS):
BARYCENTER AND ITS PROPERTIES. LINEAR AND ANGULAR MOMENTUM. KOENING THEOREM. KINETIC ENERGY AND MOMENT OF INERTIA. HUYGENS THEOREM AND INERTIA ELLIPSOID.
GENERAL THEOREMS OF MATERIAL-SYSTEM MECHANICS (4 HOURS):
CARDINAL EQUATIONS OF DYNAMICS. THEOREM OF THE MOTION OF BARYCENTER. THEOREMS ABOUT THE WORK OF INTERNAL AND EXTERNAL FORCES. THEOREM OF ENERGY CONSERVATION.
STATICS OF RIGID BODIES (4 HOURS):
CARDINAL EQUATIONS OF STATICS. GENERAL CONDITIONS FOR THE EQUILIBRIUM OF A RIGID BODY AND SOME APPLICATIONS. VINCULAR REACTIONS FOR A RIGID BODY IN EQUILIBRIUM.
DYNAMICS OF A RIGID BODY (2 HOURS):
THE MOTION OF A RIGID BODY.
ANALYTICAL MECHANICS (10 HOURS):
VIRTUAL DISPLACEMENTS OF A HOLONOMIC SYSTEM. VIRTUAL WORK. THE SYMBOLIC EQUATION OF DYNAMICS AND THE D'ALAMBERT PRINCIPLE. THE SYMBOLIC EQUATION OF STATICS AND THE PRINCIPLE OF VIRTUAL WORK. EQUILIBRIUM OF A HOLONOMIC SYSTEM. THE LAGRANGE EQUATIONS. THE KINETIC ENERGY OF HOLONOMIC SYSTEMS AND RELATIVE THEOREMS.

	Teaching Methods
	THE COURSE CONSISTS OF THEORETICAL LECTURES AND CLASSROOM PRACTICES, PROVIDING THE STUDENTS WITH THE MAIN TOOLS NEEDED TO PROBLEM-SOLVING ACTIVITIES. ATTENDANCE IS MANDATORY FOR 70%. LECTURES ARE IN ITALIAN.

	Verification of learning
	BOTH WRITTEN TESTS AND ORAL INTERVIEWS WILL BE PLANNED. THE WRITTEN TESTS WILL CONSIST IN SOLVING TYPICAL PROBLEMS. THE SCORES WILL BE EXPRESSED ON A SCALE FROM 1 TO 30. TO PASS TO THE ORAL INTERVIEWS A MINIMUM SCORE OF 18 WILL BE ALWAYS NEEDED. THE WRITTEN TESTS WILL BE NOT PRESERVATIVE. THE ORAL INTERVIEW IS SUBJECTED TO BEING SELECTED IN THE CORRESPONDING WRITTEN TEST, AND AIMS AT EVALUATING THE KNOWLEDGE OF ALL TOPICS, AND COVERS DEFINITIONS, ARGUMENTS AND PROOFS. THE FINAL MARK, EXPRESSED ON A SCALE FROM 18 TO 30 (POSSIBLY WITH LAUDEM), DEPENDS BOTH ON THE MARKS OF THE WRITTEN TESTS, AND ON THE ORAL INTERVIEWS.

Verification of learning

BOTH WRITTEN TESTS AND ORAL INTERVIEWS WILL BE PLANNED.

THE WRITTEN TESTS WILL CONSIST IN SOLVING TYPICAL PROBLEMS. THE SCORES WILL BE EXPRESSED ON A SCALE FROM 1 TO 30. TO PASS TO THE ORAL INTERVIEWS A MINIMUM SCORE OF 18 WILL BE ALWAYS NEEDED. THE WRITTEN TESTS WILL BE NOT PRESERVATIVE.

THE ORAL INTERVIEW IS SUBJECTED TO BEING SELECTED IN THE CORRESPONDING WRITTEN TEST, AND AIMS AT EVALUATING THE KNOWLEDGE OF ALL TOPICS, AND COVERS DEFINITIONS, ARGUMENTS AND PROOFS.

THE FINAL MARK, EXPRESSED ON A SCALE FROM 18 TO 30 (POSSIBLY WITH LAUDEM), DEPENDS BOTH ON THE MARKS OF THE WRITTEN TESTS, AND ON THE ORAL INTERVIEWS.

	Texts
	-) DISPENSE DEL CORSO. -) S. CHIRITA, M. CIARLETTA, V. TIBULLO, MECCANICA RAZIONALE, ED. LIGUORI. -) M. FABRIZIO, ELEMENTI DI MECCANICA CLASSICA, ED. ZANICHELLI. -) L. ASCIONE, ELEMENTI DI SCIENZA DELLE COSTRUZIONI, APOGEO EDUCATION 2015. -) C. COMI E L. CORRADI DELL’ACQUA, INTRODUZIONE ALLA MECCANICA STRUTTURALE, MCGRAW-HILL, 2016. -) L. ASCIONE, SULLA STATICA DELLE TRAVI E DEI SISTEMI DI TRAVI. VOL. 1, LIGUORI, 2001. -) L. ASCIONE, SULLA STATICA DELLE TRAVI E DEI SISTEMI DI TRAVI. VOL. 2, LIGUORI, 2001.

Texts

-) DISPENSE DEL CORSO.
-) S. CHIRITA, M. CIARLETTA, V. TIBULLO, MECCANICA RAZIONALE, ED. LIGUORI.
-) M. FABRIZIO, ELEMENTI DI MECCANICA CLASSICA, ED. ZANICHELLI.
-) L. ASCIONE, ELEMENTI DI SCIENZA DELLE COSTRUZIONI, APOGEO EDUCATION 2015.
-) C. COMI E L. CORRADI DELL’ACQUA, INTRODUZIONE ALLA MECCANICA STRUTTURALE, MCGRAW-HILL, 2016.
-) L. ASCIONE, SULLA STATICA DELLE TRAVI E DEI SISTEMI DI TRAVI. VOL. 1, LIGUORI, 2001.
-) L. ASCIONE, SULLA STATICA DELLE TRAVI E DEI SISTEMI DI TRAVI. VOL. 2, LIGUORI, 2001.

Lessons Timetable

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