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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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