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::[[E1. | ::[[E1. Work-Energy Theorem: differential form#E1.2 Power of an action-reaction pair|E1.2 Power of an action-reaction pair]] | ||
::[[E1. | ::[[E1. Work-Energy Theorem: differential form#E1.3 Power of a system of forces on a rigid body|E1.3 Power of a system of forces on a rigid body]] | ||
::[[E1. | ::[[E1. Work-Energy Theorem: differential form#E1.4 Power balance in a multibody system: direct and indirect calculation|E1.4 Power balance in a multibody system: direct and indirect calculation]] | ||
Latest revision as of 07:09, 13 May 2025
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
Vector calculus
KINEMATICS
C1. Configuration of a mechanical system
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
- 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
- C2.E General examples
C3. Composition of movements
C4. Rigid body kinematics
C5. Rigid body kinematics: planar motion
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
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
D6. Examples of 2D dynamics
D7. Examples of 3D dynamics
D8. Conservation of dynamic magnitudes
ENERGETICS
E1. Work-Energy Theorem: differential form
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)
