Elasticity of Space-Time: Basis of Newton’s 2nd Law of Motion
Publication: Journal of Engineering Mechanics
Volume 129, Issue 9
Abstract
In this paper we derive Newton’s 2nd Law of Motion from the constitutive equation of elasticity of a space-time continuum in four dimensions. This we do by introducing a four-dimensional material continuum with a Minkowskian metric, in analogy with Einstein’s general theory of relativity. The four-continuum is deformable in both space and time. The physics of the deformation is embedded in a variational principle, which is a form-invariant extension of its classical mechanical counterpart in three dimensions, but with the acceleration term absent. General dynamic equations of elasticity in four dimensions are thereby derived. When the constraint of temporal inextensibility (universal time) is introduced, these equations yield readily the dynamic equations of elasticity in three dimensions. The presence of the inertia term in these equations, is a direct consequence of the temporal curvature induced by the deformation of the four-continuum. Newton’s law of motion for rigid bodies follows when the additional constraint of spatial inextensibility is introduced.
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Copyright © 2003 American Society of Civil Engineers.
History
Received: Jul 10, 2002
Accepted: Feb 3, 2003
Published online: Aug 15, 2003
Published in print: Sep 2003
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