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A history of non-holonomic constraints

JESPER LÜTZEN

in Mechanistic Images in Geometric Form: Heinrich Hertz's 'Principles of Mechanics'

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567370
eISBN:
9780191717925
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567370.003.0022
Subject:
Physics, History of Physics

Heinrich Hertz was not the first to introduce non-holonomic constraints into mechanics, but his careful distinction between holonomic and non-holonomic constraints in his book Principles of Mechanics ... More


Lagrangian Theory of Constraints

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0003
Subject:
Physics, Atomic, Laser, and Optical Physics

One attractive feature of the Lagrangian method is the ease with which it solves so-called constraint problems. This chapter presents several different ways of solving such problems, with examples of ... More


Topics in Mechanics

David J. N. Limebeer and Matteo Massaro

in Dynamics and Optimal Control of Road Vehicles

Published in print:
2018
Published Online:
April 2019
ISBN:
9780198825715
eISBN:
9780191864636
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198825715.003.0002
Subject:
Physics, Condensed Matter Physics / Materials

Chapter 2 provides a comprehensive review of the classical mechanics required when building vehicle models. Both vector-based methods and the variational approach to classical mechanics are reviewed, ... More


Constrained Lagrangian Mechanics

Peter Mann

in Lagrangian and Hamiltonian Dynamics

Published in print:
2018
Published Online:
August 2018
ISBN:
9780198822370
eISBN:
9780191861253
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822370.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter builds on the previous two chapters to tackle constrained systems, using Lagrangian mechanics and constrained variations. The first section deals with holonomic constraint equations ... More


Virtual Work & d’Alembert’s Principle

Peter Mann

in Lagrangian and Hamiltonian Dynamics

Published in print:
2018
Published Online:
August 2018
ISBN:
9780198822370
eISBN:
9780191861253
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822370.003.0013
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses virtual work, returning to the Newtonian framework to derive the central Lagrange equation, using d’Alembert’s principle. It starts off with a discussion of generalised force, ... More


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