New PDF release: Collisions Engineering: Theory and Applications

By Michel Frémond (auth.)

ISBN-10: 3662526948

ISBN-13: 9783662526941

ISBN-10: 3662526964

ISBN-13: 9783662526965

This booklet investigates collisions happening within the movement of solids, within the movement of fluids but in addition within the movement of pedestrians in crowds. The length of those provided collisions is brief in comparison to the full length of the movement: they're assumed prompt. The cutting edge thought confirmed during this ebook is approach made from solids, is deformable simply because their relative place alterations. The definition of the velocities of deformation of the process brought within the classical advancements of mechanics, the primary of the digital paintings and the legislation of thermodynamics, permits a wide range of purposes resembling crowd motions, particles stream motions, and form reminiscence alloys motions. The set of the purposes is even better: social sciences and mechanics are unified to foretell the movement of crowds with program to move administration and to evacuation of theaters management.

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Example text

No functional relationship may be founded. 17 approximatively. 2. Moreover it appears a relationship between collisions with the Coulomb law and smooth sliding on the plane with Coulomb friction law. It may be proved that smooth sliding is the limit of periodic small jumps (Coulomb collisions with rebounds) when the amplitude of the jumps tends to zero, [19]. Thus experimental and theoretical results suggest to have for both smooth friction and non smooth collisions, the Coulomb’s law with the same coefficient.

Pseudo-potential φ(UT ) = μ UT where UT is the tangential velocity, is often chosen. , position or distance d. It can depend on UT . 128) + 0 . 129) RNe ReT ∈ Tangential force is given by relationships UT , if UT = 0, UT ≤ −RN μ, if UT = 0. 131) 28 2 The Theory: Mechanics. 2 The Coulomb’s Collision Law For collisions, internal percussion is split in the same way Pint = PN N + PT , PN = Pint · N. 133) and Φ(X, χ ) = 0, if d > 0, Φ(X, χ ) = U + +U − ΦN ( N 2 N ) U + +U − + I+ ( N 2 N + U +U− −PN φ( T 2 T ) − UN− ) 2 , if d = 0.

But if we consider the system made of the two points, its form changes because the distance of the two points may change. Thus it is wise to consider that the system is deformable. 1) where U = (U1 , U2 ) is the set of the two actual velocities of the points. A rigid system set of velocities is such that the form of the system does not change: it is easy to see that they are characterized by D(U ) = U1 − U2 = 0, © Springer-Verlag Berlin Heidelberg 2017 M. 2) 33 34 3 The Theory: Mechanics and Thermics … U1 U2 Fig.

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Collisions Engineering: Theory and Applications by Michel Frémond (auth.)

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