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This book pursues a twofold objective: to introduce the methodologies of Italian Rational Mechanics to an international audience hoping they may prove valuable to teachers and students in Engineering, Physics, and Mathematics and to offer essential material for engineering students in Italy whose courses are taught in English. Readers are expected to have a background in Calculus and Linear Algebra, along with a basic familiarity with the fundamental principles of Newtonian Mechanics. Rational Mechanics is a mathematical discipline that spans from Newtonian to analytical and applied mechanics. It follows a rigorous deductive approach and has traditionally provided a foundational framework that bridges mathematics, physics, and engineering. This book builds on the long-standing Italian tradition of teaching Rational Mechanics at the undergraduate level. It is particularly well suited for courses that guide students from first principles to progressively more advanced topics, culminating in the sophisticated modeling of real-world phenomena. Historically, Rational Mechanics has often been the first course in which students of Engineering, Physics, or Mathematics encounter a rigorous and comprehensive framework for mathematical modeling, making its educational value especially significant. The presentation of fundamental concepts is consistently oriented toward applications, with the aim of fostering synergies in teaching, particularly in interdisciplinary contexts. The structure of the book reflects this approach, with special emphasis on sections that are often treated in a more abstract way such as constraints, the Principle of Virtual Work, d Alembert s Principle, and Analytical Mechanics.
List of contents
1 Point kinematics.- 2 Rigid body kinematics.- 3 Relative motions.- 4 Constraints.- 5 Geometry of masses.- 6 Kinematics of masses.- 7 Forces, work, power.- 8 The laws of Mechanics.- 9 Statics.- 10 Particle dynamics.- 11 Dynamics of systems.- 12 Dynamics of rigid bodies.- 13 Non-inertial reference frames.- 14 Lagrangian Mechanics.- 15 Equilibrium of one-dimensional continua.- Appendix A: A reminder of vectors, curves and differential equations.
About the author
Paolo Biscari
is Full Professor of Condensed Matter Physics at the Physics Department of the Politecnico di Milano. His research interests lie in Statistical Mechanics and Continuum Mechanics, with a focus on Complex Systems.
Tommaso Ruggeri
is an Emeritus Professor at the University of Bologna and former Full Professor of Mathematical Physics. He carries out his work at the Mathematical Department of the University of Bologna. His research concerns nonlinear propagation and non-equilibrium thermodynamics in both classical and relativistic continuous media.
Giuseppe Saccomandi
is a Full Professor of Mathematical Physics at the University of Perugia and is part of the Department of Engineering. His main scientific interest concerns elastomeric materials and biomechanics.
Maurizio Vianello
, now retired, was a full professor of Mathematical Physics at the Politecnico di Milano, where he taught Rational Mechanics for many years. His scientific research focused on continuum mechanics.
Summary
This book pursues a twofold objective: to introduce the methodologies of Italian Rational Mechanics to an international audience—hoping they may prove valuable to teachers and students in Engineering, Physics, and Mathematics—and to offer essential material for engineering students in Italy whose courses are taught in English.
Readers are expected to have a background in Calculus and Linear Algebra, along with a basic familiarity with the fundamental principles of Newtonian Mechanics.
Rational Mechanics is a mathematical discipline that spans from Newtonian to analytical and applied mechanics. It follows a rigorous deductive approach and has traditionally provided a foundational framework that bridges mathematics, physics, and engineering.
This book builds on the long-standing Italian tradition of teaching Rational Mechanics at the undergraduate level. It is particularly well suited for courses that guide students from first principles to progressively more advanced topics, culminating in the sophisticated modeling of real-world phenomena. Historically, Rational Mechanics has often been the first course in which students of Engineering, Physics, or Mathematics encounter a rigorous and comprehensive framework for mathematical modeling, making its educational value especially significant.
The presentation of fundamental concepts is consistently oriented toward applications, with the aim of fostering synergies in teaching, particularly in interdisciplinary contexts. The structure of the book reflects this approach, with special emphasis on sections that are often treated in a more abstract way—such as constraints, the Principle of Virtual Work, d’Alembert’s Principle, and Analytical Mechanics.
