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Analytical Mechanics for Relativity and Quantum Mechanics$
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Oliver Johns

Print publication date: 2005

Print ISBN-13: 9780198567264

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198567264.001.0001

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Lagrangian Theory of Constraints

Lagrangian Theory of Constraints

(p.46) 3 Lagrangian Theory of Constraints
Analytical Mechanics for Relativity and Quantum Mechanics

Oliver Johns

Oxford University Press

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 each. In the previous chapter, the generalised coordinates were assumed to be independent variables. However, there are problems of interest in which these coordinates are not independent, but rather are forced into particular relations by constraints. In this chapter, constraints are defined and virtual displacement is discussed, along with virtual work, form of the forces of constraint, general Lagrange equations with constraints, alternate notation for holonomic constraints, reduction of degrees of freedom, recovery of the forces of constraint, generalised energy theorem with constraints, and tractable non-holonomic constraints.

Keywords:   constraints, Lagrangian method, virtual displacement, virtual work, Lagrange equations, degrees of freedom, holonomic constraints, generalised energy theorem

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