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Research Papers

Analysis of Discrete Mechanical Systems With Blockable Directions

[+] Author and Article Information
Kerim Yunt

P.O. Box 1070,
Zurich, Switzerland 8021
e-mail: kerimyunt@web.de

1Corresponding author.

Manuscript received July 17, 2012; final manuscript received November 25, 2012; accepted manuscript posted November 28, 2012; published online May 23, 2013. Assoc. Editor: Wei-Chau Xie.

J. Appl. Mech 80(4), 041030 (May 23, 2013) (9 pages) Paper No: JAM-12-1331; doi: 10.1115/1.4023106 History: Received July 17, 2012; Revised November 25, 2012; Accepted November 28, 2012

The classification of constraints in mechanics and the various mechanical principles that apply to different types of constraints constitute a major area of research in the field of theoretical and applied mechanics. The sudden introduction of bilateral constraints into a mechanical process is blocking and its sudden removal is releasing. The sudden introduction and removal of bilateral constraints, which exist in a subset of the whole process time span, may induce impacts. An impulsive action integral is proposed for such mechanical processes. The projectors of the tangent space of the submanifold and the cotangent space are derived and the equations of motion in different constrained submanifolds are obtained by making use of the projectors. The questions of the uniqueness and the existence of the post-transition velocity are addressed.

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References

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Figures

Grahic Jump Location
Fig. 1

The subdifferential of a Lipschitz function f at its minimum

Grahic Jump Location
Fig. 2

Planar double link with one impactively blockable DOF

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