ISSN:
1573-272X
Keywords:
analytical mechanics
;
constraints
;
d'Alembert's principle
;
orthogonal complements
;
chains
;
recursivity
;
induction
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
Abstract A method is described for the successive imposition of constraints on a free particle mechanism and the subsequent derivation of closed sets of differential equations for the evolution of the mechanism with time. Fundamental is the idea of ideal constraints as contained in d'Alembert's principle. In particular, it is shown how constraints may be added one or more at a time, thereby obtaining intermediate descriptions with more dynamic freedom than the final mechanism. As a simple example, it is shown that the rigid body is such an intermediate description. The method is also applied to the problem of a chain of n particles or n rigid rods. Both an inductive and a constructive approach are demonstrated in deriving the equations of motion for arbitrary n.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1009886606941
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