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21 - From Metaphysical Principles to Dynamical Laws
from Part III - Problems and Controversies
- By Marius Stan
Edited by David Marshall Miller, Iowa State University, Dana Jalobeanu
Book:

The Cambridge History of Philosophy of the Scientific Revolution

Published online:

14 January 2022

Print publication:

06 January 2022, pp 387-405
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Summary

Through the 1600s, the fundamental laws of mechanics served as bridge principles to ontology and confirmation theory. By the mid-eighteenth century, the laws came to lose their former bridging function. As a result, the metaphysics and epistemology of classical mechanics became opaque. The chapter diagnoses several factors that catalyzed the changed status of basic laws.

6 - The Projection Method in Classical Mechanics
- By A. M. Perelomov
Edited by Ron Donagi, University of Pennsylvania, Tony Shaska, Oakland University, Michigan
Book:

Integrable Systems and Algebraic Geometry

Published online:

19 March 2020

Print publication:

02 April 2020, pp 109-132
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Summary

The new method of explicit integration of equations of motion of systems of classical mechanics (the projection method) is described. For Calogero, Sutherland and Toda systems the explicit solutions of equations of motion are given. These solutions are impossible to obtain by other known methods.

An Alternative View of Theoretical Reasoning in Physics
3rd edition
Malcolm S. Longair
Published online:

27 March 2020

Print publication:

16 April 2020
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In this original and integrated approach to theoretical reasoning in physics, Malcolm Longair illuminates the subject from the perspective of real physics as practised by research scientists. Concentrating on the basic insights, attitudes and techniques that are the tools of the modern physicist, this approach conveys the intellectual excitement and beauty of the subject. Through a series of seven case studies, an undergraduate course in classical physics and the discovery of quanta are reviewed from the point of the view of how the great discoveries and changes of perspective came about. This approach illuminates the intellectual struggles needed to attain understanding of some of the most difficult concepts in physics. Longair's highly acclaimed text has been fully revised and includes new studies on the physics of fluids, Maxwell's great paper on equations for the electromagnetic field and problems of contemporary cosmology and the very early universe.

1 - Short Review of Classical Mechanics
from Part I - General Properties of Fields; Scalars and Gauge Fields
Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
Book:

Classical Field Theory

Published online:

04 March 2019

Print publication:

14 March 2019, pp 3-13
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Summary

In the first chapter, the most important concepts of classical mechanics are quickly reviewed. The Lagrangian and Hamiltonian formalism are described. The way to deal with systems with constraints is described. Poisson brackets and the use of canonical transformations in the Hamiltonian formalism, as well as the basics of Hamilton–Jacobi theory complete this chapter.

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