New insights into the classical mechanics of particle systems

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December 2010, 28(4): 1469-1504. doi: 10.3934/dcds.2010.28.1469

New insights into the classical mechanics of particle systems

1.	Department of Mechanical Engineering, McGill University, Montréal, Québec H3A 2K6, Canada

Received October 2009 Revised February 2010 Published June 2010

Abstract
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The classical mechanics of particle systems is developed on the basis of the precept that, kinematics and the notion of force aside, power expenditures are of the foremost importance. The essential properties of forces between particles follow from requiring that the net power expended within any subsystem of particles be frame-indifferent. Furthermore, requiring that the net power expended on any subsystem of particles by external agencies be frame-indifferent yields force, moment, and power balances. These balances account for inertia but hold relative to any frame-of-reference, inertial or noninertial. Assuming that each particle possesses an interaction energy that embodies the extent to which it is attracted or repelled by other particles leads to the proposition of an interaction-energy inequality that serves as a purely mechanical statement of the second law of thermodynamics. In combination with the power balance, this inequality provides an avenue to ensure that constitutive equations do not permit a violation of thermodynamics. This inequality is used to develop the simplest class of constitutive equations that account for both conservative and dissipative particle-particle interactions.

Keywords: frame-indifference, Particle mechanics, balance laws, power, constitutive equations..

Mathematics Subject Classification: Primary: 70A05, 70F25; Secondary: 37J6.

Citation: Eliot Fried. New insights into the classical mechanics of particle systems. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1469-1504. doi: 10.3934/dcds.2010.28.1469

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