New Foundations for Classical Mechanics
Title | New Foundations for Classical Mechanics PDF eBook |
Author | D. Hestenes |
Publisher | Springer Science & Business Media |
Total Pages | 716 |
Release | 2005-12-17 |
Genre | Science |
ISBN | 0306471221 |
(revised) This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applications matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.
New Foundations for Classical Mechanics
Title | New Foundations for Classical Mechanics PDF eBook |
Author | D. Hestenes |
Publisher | Springer Science & Business Media |
Total Pages | 655 |
Release | 2012-12-06 |
Genre | Science |
ISBN | 9400948026 |
This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applica tions matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.
New Foundations for Classical Mechanics
Title | New Foundations for Classical Mechanics PDF eBook |
Author | David Hestenes |
Publisher | Springer |
Total Pages | 662 |
Release | 1986-06-30 |
Genre | Mathematics |
ISBN |
This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applica tions matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.
Foundations of Classical Mechanics
Title | Foundations of Classical Mechanics PDF eBook |
Author | P. C. Deshmukh |
Publisher | Cambridge University Press |
Total Pages | 591 |
Release | 2019-12-12 |
Genre | Mathematics |
ISBN | 110848056X |
The book aims at speeding up undergraduates to attain interest in advanced concepts and methods in science and engineering.
Foundations Of Mechanics
Title | Foundations Of Mechanics PDF eBook |
Author | Ralph Abraham |
Publisher | CRC Press |
Total Pages | 849 |
Release | 2019-04-24 |
Genre | Science |
ISBN | 0429689047 |
Foundations of Mechanics is a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the two-body problem and three-body problem.
Mathematical Methods of Classical Mechanics
Title | Mathematical Methods of Classical Mechanics PDF eBook |
Author | V.I. Arnol'd |
Publisher | Springer Science & Business Media |
Total Pages | 530 |
Release | 2013-04-09 |
Genre | Mathematics |
ISBN | 1475720637 |
This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
Classical Mechanics
Title | Classical Mechanics PDF eBook |
Author | Emmanuele DiBenedetto |
Publisher | Springer Science & Business Media |
Total Pages | 364 |
Release | 2010-10-17 |
Genre | Mathematics |
ISBN | 0817646485 |
* Offers a rigorous mathematical treatment of mechanics as a text or reference * Revisits beautiful classical material, including gyroscopes, precessions, spinning tops, effects of rotation of the Earth on gravity motions, and variational principles * Employs mathematics not only as a "unifying" language, but also to exemplify its role as a catalyst behind new concepts and discoveries