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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 🎯.

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

DYNAMICS

D1. Foundational laws of Newtonian dynamics

D1.1 Galilean reference frames

D1.2 Galileo’s Principle of Relativity

D1.3 Newton’s Principle of Determinacy

D1.4 Newton’s first law (inertia law)

D1.5 Newton’s second law (fundamental law of dynamics)

D1.6 Newton’s third law (action-reaction principle)

D1.7 Particle dynamics in non Galilean reference frames

D2. Interaction forces between particles

D2.1 Kinematic dependence of interaction forces

D2.2 Classification of interaction forces

D2.3 Gravitational attraction

D2.4 Interaction through springs

D2.5 Interaction through dampers

D2.6 Interaction through actuators

D2.7 Constraint interactions

D2.8 Friction

D3. Interactions between rigid bodies

D3.1 Torsor associated with a system of forces

D3.2 Gravitational attraction

D3.3 Interaction through linear and torsion springs and dampers

D3.4 Direct constraint interactions

D3.5 Indirect constraint interactions: Constraint Auxiliary Elements (CAE)

D3.6 Interaction through linear and rotatory actuators

D4. Vector theorems

D4.1 Linear Momentum Theorem (LMT) in Galilean reference frames

D4.2 LMT: application examples

D4.3 Linear Momentum Theorem (LMT) in non Galilean reference frames

D4.4 Angular Momentum Theorem (AMT): general formulation

D4.5 Angular Momentum Theorem (AMT): particular formulations

D4.6 AMT: application examples

D4.7 Dynamics of Constraint Auxiliary Elements

D4.8 Barycentric decomposition of the angular momentum

D5. Mass distribution

D5.1 Centre of masses

D5.2 Inertia tensor

D5.3 Some relevant properties of the inertia tensor

D5.4 Steiner’s Theorem

D5.5 Change of vector basis

D6. Examples of 2D dynamics

D6.12D kinematics and 2D dynamics

D6.2 Free-body diagram (FBD) and roadmap

D6.3 Examples with just one rigid body

D6.4 General diagram of interactions (GDI)

D6.5 Examples of multibody systems

D7. Examples of 3D dynamics

D7.1 Analysis of the equations of motion

D7.2 General examples

D8. Conservation of dynamic magnitudes

D8.1 Examples

ENERGETICS

E1. Work-Energy Theorem: differential form

E1.1 Power balance in a system of particles

E1.2 Power of an action-reaction pair

E1.3 Power of a system of forces on a rigid body

E1.4 Power balance in a multibody system: direct and indirect calculation

Authors

Ana Barjau Condomines
Lluís Ros Giralt
Ernest Bosch Soldevila

Ilustrations:

Joquim Agulló i Batlle

Collaborators:

Daniel Clos Costa
Rosa Pàmies Vilà
Albert Peiret Giménez
Javier Sistiaga Vidal-Ribas

Editing and interactive animations:

Arnau Marzábal Gatell
Berta Ros Blanco
Ana Pons Ferrer
Jana Bonet Fernández
Gemma Izquierdo Santamaria

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)