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RATIONAL MECHANICS

ADA AMENDOLA RATIONAL MECHANICS

0612500007
DEPARTMENT OF CIVIL ENGINEERING
EQF6
CIVIL AND ENVIRONMENTAL ENGINEERING
2024/2025

OBBLIGATORIO
YEAR OF COURSE 2
YEAR OF DIDACTIC SYSTEM 2022
AUTUMN SEMESTER
CFUHOURSACTIVITY
990LESSONS
ADA AMENDOLA T Curriculum
Objectives
EXPECTED LEARNING OUTCOMES AND SKILLS TO BE ACQUIRED:
KNOWLEDGE OF THE BASIC ELEMENTS OF MECHANICS ADDRESSED FROM A RATIONAL POINT OF VIEW, I.E
KINEMATICS AND DYNAMICS OF THE MATERIAL POINT AND OF POINT SYSTEMS, IN PARTICULAR RIGID ONES. KNOWLEDGE
OF THE FORMULATION OF MECHANICAL PROBLEMS IN THE LAGRANGIAN FORMALISM (II MODULE). ABILITY TO
ACQUIRE METHODS FOR SOLVING RATIONAL MECHANICAL PROBLEMS, BUT ABOVE ALL THE RELATIONSHIP BETWEEN
PROPERTIES OF A PHYSICAL SYSTEM AND THE MATHEMATICAL STRUCTURES FOR THEIR REPRESENTATION.
KNOWLEDGE AND UNDERSTANDING:
ACQUISITION OF THE METHODS NECESSARY TO SET UP AND ADDRESS PROBLEMS OF MECHANICS OF FREE SYSTEMS E
BOUND. IN PARTICULAR, KNOW THE BASIC ELEMENTS OF MASS GEOMETRY AND VECTOR CALCULUS
FOR THE STUDY OF THE KINEMATICS AND DYNAMICS OF THE POINT, OF THE SYSTEMS OF POINTS AND OF RIGID BODIES, ALSO IN
LAGRANGIAN FORMALISM (II MODULE). UNDERSTAND AND SCHEMATIZE SYSTEMS USING MATHEMATICAL MODELS
MECHANICS WITH A FINITE DEGREE OF FREEDOM, MADE UP OF TWO OR MORE MATERIAL ELEMENTS AND/OR RIGID BODIES.
ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING:
APPLICATION OF THE KNOWLEDGE ACQUIRED TO SOLVE SIMPLE, BUT CONCRETE, MECHANICAL PROBLEMS
CONCERNING THE GEOMETRY OF THE MASSES (IN THE CASE OF FLAT SYSTEMS), THE DYNAMICS (FLAT SYSTEMS WITH ONE OR MORE DEGREES
OF FREEDOM) AND THE STATICS OF MECHANICAL SYSTEMS (FOR FLAT SYSTEMS, WITH THE CARDINAL EQUATIONS OF STATICS AND WITH THE
PRINCIPLE OF VIRTUAL JOBS). IN PARTICULAR, ABILITY TO MODEL CONSTRAINED AND UNCONSTRAINED MECHANICAL SYSTEMS,
THROUGH AN APPROPRIATE CHOICE OF COORDINATES IN THE CONFIGURATION SPACE FOR WRITING THE
EQUATIONS OF MOTION.
INDEPENDENT JUDGMENTS:
ABILITY TO INDEPENDENTLY DEEPEN WHAT HAS BEEN LEARNED, IN ORDER TO USE THE KNOWLEDGE ACQUIRED
AS A STARTING POINT THAT ALLOWS US TO TACKLE NEW PROBLEMS AND ACHIEVE FURTHER RESULTS
THROUGH EVER-INCREASING MATURITY AND EVER-INCREASING AUTONOMY OF JUDGEMENT.
COMMUNICATION SKILLS:
ABILITY TO EXPLAIN IN A CONSCIOUS AND RIGOROUS WAY THE METHODS AND TECHNIQUES ADOPTED TO SOLVE THE PROBLEM
A MECHANICAL PROBLEM AND WHAT PROCEDURES ARE USED TO ACHIEVE THE RESULTS OBTAINED. ABILITY TO
EXPLAIN, EVEN TO NON-EXPERT PEOPLE, TO WHICH PRACTICAL EXPERIENCES WHAT YOU HAVE LEARNED CAN BE APPLIED.
LEARNING ABILITY:
CONSOLIDATION OF THE KNOWLEDGE AND SKILLS ACQUIRED IN ORDER TO APPLY THE KNOWLEDGE ACQUIRED
ALSO TO CONTEXTS OTHER THAN THOSE PRESENTED DURING THE COURSE, AS WELL AS DELVING DEEPER INTO THE TOPICS COVERED
USING ALTERNATIVE APPROACHES AND/OR PROCEDURES.
Prerequisites
FOR THE PROFITABLE ACHIEVEMENT OF THE SET OBJECTIVES, THE STUDENT IS REQUIRED TO HAVE BASIC MATHEMATICAL KNOWLEDGE, WITH PARTICULAR REFERENCE TO THE CONCEPTS AND SOLUTION TECHNIQUES INHERENT IN THE THEORY OF INTEGRATION AND THE SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS. A DEEP KNOWLEDGE OF VECTOR ALGEBRA AND MATRIX THEORY IS ALSO REQUIRED.
REQUIREMENTS: HAVE ACHIEVED THE MATHEMATICS II EXAM.
Contents
VECTOR CALCULATION (3/1/-):
CARTESIAN REPRESENTATION OF VECTORS AND OPERATIONS. FUNCTIONS WITH VECTOR VALUES.

GEOMETRIC-DIFFERENTIAL APPLICATIONS TO CURVES (3/-/-):
FERNET FORMULAS.

APPLIED VECTORS (8/3/-):
RESULTANT AND RESULTING MOMENT OF A SYSTEM OF APPLIED VECTORS. CENTRAL AXIS. EQUIVALENT APPLIED VECTOR SYSTEM. SYSTEM OF PLANE AND PARALLEL VECTORS.

POINT KINEMATICS (4/2/-):
SPEED. ACCELERATION. PLANE MOTIONS. CENTRAL MOTIONS. HARMONIC MOTORCYCLE.

KINEMATICS OF MATERIAL SYSTEMS (8/1/-):
DEGREES OF FREEDOM AND LAGRANGIAN COORDINATES. HOLONOMIC SYSTEMS. KINEMATICS OF RIGID SYSTEMS. EULER'S ANGLES. PARTICULAR RIGID MOTIONS: TRANSLATIONAL MOTION, ROTARY MOTION AND ROTATIONAL TRANSLATIONAL MOTION. POISSON FORMULA. MOZZI THEOREM. INSTANTANEOUS AXIS OF ROTATIONAL TRANSLATION.

KINEMATICS OF RELATIVE MOTIONS (4/1/-).

RIGID PLANE MOTIONS AND CHASLES THEOREM (1/-/-)

STATIC AND DYNAMIC OF THE STITCH FREE MATERIAL (6/5/-):
WORK OF A FORCE. CONSERVATIVE FORCES. LIVE FORCE THEOREM FOR A FREE MATERIAL SYSTEM AND CONSERVATION OF MECHANICAL ENERGY. DIFFERENTIAL EQUATIONS OF MOTION OF A FREE POINT. DIFFERENTIAL EQUATIONS OF THE MOTION OF A POINT WITH RESPECT TO TWO NON-INERTIAL REFERENCES (APPARENT FORCES, WEIGHT). STATIC OF THE POINT FREE MATERIAL.

STATIC AND DYNAMIC OF THE BOUND MATERIAL POINT (4/2/-):
EQUATIONS OF MOTION OF A CONSTRAINED POINT. STATICS OF A CONSTRAINED POINT. FRICTION AND POSITIONS OF EQUILIBRIUM. DYNAMICS OF A POINT RELATED TO A SURFACE, SPONTANEOUS MOTION OF A POINT ON A SURFACE. DYNAMICS OF THE POINT RELATED TO A CURVE. SIMPLE PENDULUM.

MASS GEOMETRY (5/7/-):
CENTER OF GRAVITY AND OWNERSHIP. PLANE SYSTEMS: BARYCENTRES AND STATIC MOMENTS. RAYS OF INERTIA. MOMENTUM AND MOMENTUM OF MOMENTUM. KOENIG THEOREM. KINETIC ENERGY AND MOMENTS OF INERTIA. WAY OF VARIING THE MOMENT OF INERTIA AS THE LINE VARIES: HUYGENS THEOREM AND ELLIPSOID OF INERTIA. APPLICATIONS.

GENERAL THEOREMS OF THE MECHANICS OF MATERIAL SYSTEMS (8/2/-):
CARDINAL EQUATIONS OF DYNAMICS. THEOREM OF THE CENTER OF GRAVITY MOTION. WORK OF INTERNAL FORCES FOR A RIGID SYSTEM. LIVE FORCE THEOREM AND CONSERVATION OF MECHANICAL ENERGY FOR A CONSTRAINED MATERIAL SYSTEM.

STATIC OF THE RIGID BODY (4/4/-):
CARDINAL EQUATIONS OF STATICS. GENERAL CONDITIONS OF EQUILIBRIUM OF A RIGID BODY. APPLICATIONS FOR A FREE RIGID BODY, RIGID BODY WITH A FIXED POINT AND RIGID BODY WITH A FIXED AXIS. BINDING REACTIONS EXPLAINED ON A RIGID BODY IN EQUILIBRIUM. FRICTION AND POSITIONS OF EQUILIBRIUM. BINDING REACTIONS IN EQUILIBRIUM CONDITIONS.

RIGID BODY DYNAMICS (5/4/-):
MOTION OF A RIGID BODY WITH A FRICTION-FREE FIXED AXIS AND CONSTRAINTS. MOTION OF A RIGID BODY WITH A FIXED POINT. MOTION OF A FREE RIGID BODY. MOTORCYCLE AT POINSOT.

ELEMENTS OF ANALYTICAL MECHANICS (13/6/-):
VIRTUAL SHIFT FOR A HOLONOMOUS SYSTEM. VIRTUAL WORK. SYMBOLIC EQUATION OF DYNAMICS AND D'ALEMBERT'S PRINCIPLE. SYMBOLIC EQUATION OF STATICS AND PRINCIPLE OF VIRTUAL WORKS. EQUILIBRIUM CONDITIONS FOR A HOLONOMOUS SYSTEM. CALCULATION OF THE REACTIONS THROUGH THE PRINCIPLE OF VIRTUAL WORKS. HOLONOMIC SYSTEMS STRESSED BY CONSERVATIVE FORCES. LAGRANGE EQUATIONS AND APPLICATIONS. KINETIC ENERGY OF A HOLONOMOUS SYSTEM AND STUDY OF LAGRANGE'S EQUATIONS. LIVE FORCE THEOREM FOR A HOLONOMOUS SYSTEM WITH TIME-INDEPENDENT CONSTRAINTS. LAGRANGE EQUATIONS FOR A CONSERVATIVE SYSTEM. LAGRANGIAN SYSTEMS AND THEIR FIRST INTEGRALS.

STABILITY AND SMALL FLUCKS (4/2/-):
STABILITY, DEFINITION OF STABILITY FOR A HOLONOMOUS SYSTEM, SMALL OSCILLATIONS AROUND A STABLE EQUILIBRIUM POSITION.
Teaching Methods
THE COURSE CONTAINS THEORETICAL LESSONS, DURING WHICH THE TOPICS OF THE COURSE WILL BE PRESENTED THROUGH CLASSROOM EXERCISES AND EXERCISES, DURING WHICH THE MAIN TOOLS NECESSARY FOR THE SOLUTION OF EXERCISES RELATING TO THE THEORETICAL COURSE CONTENT WILL BE PROVIDED . IT IS COMPULSORY TO ATTEND AT LEAST 70% OF THE HOURS OF EDUCATIONAL ACTIVITY (AS PER THE EDUCATIONAL REGULATIONS OF THE CDS). THE TEACHER WILL BE ABLE TO VERIFY THE ACHIEVEMENT OF THE MINIMUM PERCENTAGE REQUIRED OF CLASSROOM ATTENDANCE THROUGH ELECTRONIC DETECTION.
Verification of learning
THE EXAM IS AIMED AT ASSESSING THE KNOWLEDGE AND THE ABILITY TO UNDERSTAND THE CONCEPTS EXPOSED DURING THE LESSONS AND THE ABILITY TO APPLY THIS KNOWLEDGE AND FORMULATE THE DIFFERENTIAL EQUATIONS THAT DESCRIBE THE KINEMATICS AND DYNAMICS OF MATERIAL SYSTEMS. THE EXAM IS CARRIED OUT AT THE END OF THE COURSE AND IS DIVIDED INTO A SELECTIVE WRITTEN TEST AND AN ORAL INTERVIEW. THE WRITTEN TEST LASTS 3 HOURS AND OFFERS EXERCISES AND OPEN ANSWER QUESTIONS. THE ORAL INTERVIEW ASSESSES THE KNOWLEDGE ACQUIRED. IN THE FINAL EVALUATION, EXPRESSED OUT OF THIRTY, THE EVALUATION OF THE WRITTEN TEST WEIGHTS FOR 40%, WHILE THE INTERVIEW WEIGHTS FOR THE REMAINING 60%.
THE MINIMUM GRADE (18) IS GIVEN WHEN THE STUDENT SHOWS UNCERTAINTIES IN THE APPLICATION OF THE CONCEPTS AND TOOLS COVERED BY THE COURSE, AND HAS A BASIC KNOWLEDGE OF THE CONCEPTS OF THE COURSE TOPICS.
THE MAXIMUM GRADE (30) IS GIVEN WHEN THE STUDENT SHOWS A FULL KNOWLEDGE OF THE CONCEPTS AND APPLICATIVE TOOLS COVERED BY THE COURSE, AND IS ABLE TO SOLVE THE ASSIGNED PROBLEMS THROUGH EFFECTIVE AND ACCURATE PROCEDURES.
IN THE ORAL EVALUATION, FOR THE PURPOSES OF LAUDE, THE FOLLOWING WILL BE TAKEN INTO ACCOUNT: 1. THE QUALITY OF THE PRESENTATION, IN TERMS OF THE USE OF APPROPRIATE SCIENTIFIC LANGUAGE; 2. THE CAPACITY OF CROSS-CORRELATION BETWEEN THE DIFFERENT TOPICS OF THE COURSE AND WITH OTHER DISCIPLINES; 3. AUTONOMY OF JUDGMENT.
Texts
-MECCANICA RAZIONALE, PAOLO BISCARI, MAURIZIO VIANELLO, TOMMASO RUGGERI, GIUSEPPE SACCOMANDI, EDITORE:
SPRINGER VERLAG
-M. FABRIZIO, ELEMENTI DI MECCANICA CLASSICA, ED. ZANICHELLI.
ESERCIZI: S. CHIRITA, M. CIARLETTA, V. TIBULLO, MECCANICA RAZIONALE, ED. LIGUORI.
APPROFONDIMENTI: F. STOPPELLI, APPUNTI DI MECCANICA RAZIONALE, LIGUORI ED
More Information
THE COURSE IS PROVIDED IN THE PRESENCE WITH MANDATORY ATTENDANCE. THE LANGUAGE OF TEACHING IS ITALIAN.
Lessons Timetable

  BETA VERSION Data source ESSE3 [Ultima Sincronizzazione: 2024-11-18]