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85036264794
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As is usual for collision (e.g., 328), the two-particle problem is reduced to the scattering problem of a single-particle with an effective mass (Formula presented)
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As is usual for collision (e.g., 328), the two-particle problem is reduced to the scattering problem of a single-particle with an effective mass (Formula presented).
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38
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39
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85036322689
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Derivation of the dissipative force given in 2526 for colliding spheres may be straightforwardly generalized to obtain the relation (13) [or Eq. (A17) in 25 26] for colliding bodies of any shape, provided that displacement field in the bulk of the material of bodies in contact is a one-valued function of the compression (see also 39
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Derivation of the dissipative force given in 2526 for colliding spheres may be straightforwardly generalized to obtain the relation (13) [or Eq. (A17) in 2526] for colliding bodies of any shape, provided that displacement field in the bulk of the material of bodies in contact is a one-valued function of the compression (see also 39).
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41
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85036316040
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Obviously, the coefficients of the Padé approximation may be chosen up to an arbitrary factor to multiply numerator and denominator; we chose it to have unity as a leading term for both of these
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Obviously, the coefficients of the Padé approximation may be chosen up to an arbitrary factor to multiply numerator and denominator; we chose it to have unity as a leading term for both of these.
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42
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85036400888
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Note that, in difference to the calculations in the main part of the article the quantities x, (Formula presented), and (Formula presented) do have units, namely (Formula presented). The rescaled time is dimensionless. The purpose of this scaling was only to simplify the dependence of the problem on the material parameters, it was necessary to keep the explicit dependence of the problem on the initial velocity
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Note that, in difference to the calculations in the main part of the article the quantities x, (Formula presented), and (Formula presented) do have units, namely (Formula presented). The rescaled time is dimensionless. The purpose of this scaling was only to simplify the dependence of the problem on the material parameters, it was necessary to keep the explicit dependence of the problem on the initial velocity.
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43
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85036313743
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The maple-program is available at URL: http://summa.physik.hu-berlin.de/∼kies/papers/DimAnalysis/epsilon_simple.html
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The maple-program is available at URL: http://summa.physik.hu-berlin.de/∼kies/papers/DimAnalysis/epsilon_simple.html
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