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Analytical Mechanics for Relativity and Quantum Mechanics$
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Oliver Johns

Print publication date: 2011

Print ISBN-13: 9780191001628

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780191001628.001.0001

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Lagrangian Theory of Constraints

Lagrangian Theory of Constraints

Chapter:
(p.46) 3 Lagrangian Theory of Constraints
Source:
Analytical Mechanics for Relativity and Quantum Mechanics
Author(s):

Oliver Davis Johns

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780191001628.003.0003

This chapter discusses how easy the Lagrangian method solves so-called constraint problems. Presented here are different methods of solving such problems, with corresponding examples. Constraints can be incorporated into the Lagrangian method in a particularly convenient way; if the constraints are idealised – such as frictionless surfaces or perfectly rigid bodies – then the equations of motion can be solved without knowing the forces of constraint. Also, the number of degrees of freedom of the Lagrangian system can be reduced by one for each constraint applied. The chapter also defines constraints, beginning with holonomic ones, which are the simplest class of constraints. A constraint is holonomic if it can be represented by a single function of the generalised coordinates, equated to zero.

Keywords:   constraint problems, Lagrangian method, frictionless surfaces, perfectly rigid bodies, forces of constraint

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