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===[[C2. Movement of a mechanical system]]===
===[[C2. Movement of a mechanical system]]===
:: [[C2. Movement of a mechanical system#C2.1 Velocitat d’una partícula|C2.1 Velocitat d’una partícula]]
:: [[C2. Movement of a mechanical system#C2.1 Velocity of a particle|C2.1 Velocity of a particle]]
:: [[C2. Movement of a mechanical system#C2.2 Acceleració d’una partícula|C2.2 Acceleració d’una partícula]]
:: [[C2. Movement of a mechanical system#C2.2 Acceleration of a particle|C2.2 Acceleration of a particle]]
:: [[C2. Movement of a mechanical system#C2.3 Direccions intrínseques. Components intrínseques de l’acceleració|C2.3 Direccions intrínseques. Components intrínseques de l’acceleració]]
:: [[C2. Movement of a mechanical system#C2.3 Intrinsic components of the acceleration|C2.3 Intrinsic components of the acceleration]]
:: [[C2. Movement of a mechanical system#C2.4 Velocitat angular d’un sòlid rígid|C2.4 Velocitat angular d’un sòlid rígid]]
:: [[C2. Movement of a mechanical system#C2.4 Angular velocity of a rigid body|C2.4 Angular velocity of a rigid body]]
::::<small>[[C2. Movement of a mechanical system#Rotació simple|Rotació simple]]</small>
::::<small>[[C2. Movement of a mechanical system#Simple rotation|Simple rotation]]</small>
::::<small>[[C2. Movement of a mechanical system#Rotació a l’espai|Rotació a l’espai (Rotacions d'Euler)]]</small>
::::<small>[[C2. Movement of a mechanical system#Rotation in space|Rotation in space (Rotacions d'Euler)]]</small>
:: [[C2. Movement of a mechanical system#C2.5 Acceleració angular d’un sòlid rígid|C2.5 Acceleració angular d’un sòlid rígid]]
:: [[C2. Movement of a mechanical system#C2.5 Angular acceleration of a rigid body|C2.5 Angular acceleration of a rigid body]]
:: [[C2. Movement of a mechanical system#C2.6 Cinemàtica de partícula VS cinemàtica de sòlid rígid|C2.6 Cinemàtica de partícula VS cinemàtica de sòlid rígid]]
:: [[C2. Movement of a mechanical system#C2.6 Particle kinematics versus rigid body kinematicsrígid|C2.6 Particle kinematics versus rigid body kinematics]]
:: [[C2. Movement of a mechanical system#C2.7 Graus de llibertat d’un sistema mecànic|C2.7 Graus de llibertat d’un sistema mecànic]]
:: [[C2. Movement of a mechanical system#C2.7 Degrees of freedom of a mechanical system|C2.7 Degrees of freedom of a mechanical system]]
:: [[C2. Movement of a mechanical system#C2.8 Enllaços habituals en els sistemes mecànics|C2.8 Enllaços habituals en els sistemes mecànics]]
:: [[C2. Movement of a mechanical system#C2.8 Usual constraints in mechanical systems|C2.8 Usual constraints in mechanical systems]]


===[[C3. Composition of movements]]===
===[[C3. Composition of movements]]===

Revision as of 13:49, 17 July 2023

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This website is specially built to complement the learning of the Mechanics course in the bachelor's degrees of Barcelona School of Industrial Engineering (ETSEIB) of the Polytechnic University of Catalonia (UPC) · BarcelonaTech.

This aims to be an accessible and interactive open tool. It's development started on 2022 and it gathers more than 50 years of teaching experience. It's content is organized in brief units which contain the fundamental concepts and some fully worked-out examples. Some simple mathematical proofs are included, but the longer or complex ones are refered to biblography.

The contentent is focused on general space movement of rigid bodies and muli-body systems, but particles are also considered. Dynamics formulation is vectorial, due to the relevance of the force vector in mechanical engineering. The last units are an introduction to energetics.


About the status of the site:

This project has been developed with limited resources, both technical and human. Nowadays, the server presents some issues, so in case any error may appear, we kindly invite the users to refresh the page and continue enjoying the content 😊.

The best experience will be through a computer or a tablet 📵.

The site is still under construction and some interactive resources and videos are still to be uploaded. Also, the Dynamics and Energetics blocks are still to be published. Having said that, it already is a good tool to help in the process of learning Mechanics 🎯.

© Universitat Politècnica de Catalunya. All rights reserved



Introduction

I.1 What is mechanics?
I.2 Models for material objects
I.3 Limitations of Newtonian mechanics
I.4 Reference frame

Vector calculus

V.1 Geometric representation of a vector
V.2 Operations between vectors with geometric representation
Instantaneous operations: addition, scalar product, vector product
Operations along time: time derivative
V.3 Analytical representation of a vector
V.4 Operations between vectors with analytical representation
Instantaneous operations: addition, scalar product, vector product
Operations along time: time derivative

KINEMATICS

C1. Configuration of a mechanical system

C1.1 Position of a particle
C1.2 Configuration of a rigid body
C1.3 Orientation of a rigid body with planar motion
C1.4 Orientation of a rigid body moving in space
Rotations about fixed axes
Euler rotations
C1.5 Independent coordinates

C2. Movement of a mechanical system

C2.1 Velocity of a particle
C2.2 Acceleration of a particle
C2.3 Intrinsic components of the acceleration
C2.4 Angular velocity of a rigid body
Simple rotation
Rotation in space (Rotacions d'Euler)
C2.5 Angular acceleration of a rigid body
C2.6 Particle kinematics versus rigid body kinematics
C2.7 Degrees of freedom of a mechanical system
C2.8 Usual constraints in mechanical systems

C3. Composition of movements

C3.1 Composició de velocitats
C3.2 Composició d'acceleracions
C3.3 Composició de moviments VS derivació temporal

C4. Rigid body kinematics

C4.1 Distribució de velocitats
C4.2 Distribució d’acceleracions
C4.3 Geometria de la distribució de velocitats: Eix Instantani de Rotació i Lliscament (EIRL)
C4.4 Axoide fix i axoide mòbil

C5. Rigid body kinematics: planar motion

C5.1 Centre Instantani de Rotació (CIR)
C5.2 Introducció a la cinemàtica de vehicles


DYNAMICS

UNDER CONSTRUCTION


ENERGETICS

UNDER CONSTRUCTION




Authors

Ilustrations:
Editing and interactive animations:
Collaborators:


Mechanics Lab - Barcelona School of Industrial Engineering (ETSEIB)

Mechanical Engineering Department - Polytechic University of Catalonia (UPC) · BarcelonaTech




Bibliographic references

Batlle, J. A., Barjau, A. (2020) “Rigid Body Kinematics” Cambridge Univerity Press. ISBN: 978-1-108-47907-3

Batlle, J. A., Barjau, A. (2022) “Rigid Body Dynamics” Cambridge Univerity Press. ISBN: 978-1-108-84213-6

Agulló, J. (2002) “Mecànica de la partícula i del sòlid rígid" Publicacions OK Punt. ISBN: 84-920850-6-1 (Disponible en accés obert al web de l'autor)

Agulló, J. (2000) “Mecánica de la partícula i del sólido rígido" Publicacions OK Punt. ISBN: 84-920850-5-3 (Disponible en accés obert al web de l'autor)







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