The notion of inertial reference frame is abandoned and replaced by a local reference frame on which the fundamental law of mechanics is expressed. The distant interactions of the cause and effect are modeled by the propagation of waves from one local reference frame to another. The derivation of the equation of motion on a straight segment serves to express the proper acceleration as the sum of the accelerations imposed on it, in the form of an orthogonal local Helmholtz–Hodge decomposition, in one divergence-free and another curl-free contribution. The inertia term is written in the form of a gradient of a scalar potential and a dual curl of a vector potential. The adopted formalism opens the way to a reformulation of the material derivative in terms of potentials and allows the removal of the fictitious forces from continuum mechanics. The discrete equation of motion, invariant by rotation at a constant angular velocity, is used to conserve the angular momentum per unit of mass, in addition to the conservation of energy per unit of mass and acceleration. All the variables in this equation are expressed only with two fundamental units, length and time.
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August 2020
Research Article|
August 06 2020
On Helmholtz–Hodge decomposition of inertia on a discrete local frame of reference
Jean-Paul Caltagirone
Jean-Paul Caltagirone
a)
Bordeaux INP - University of Bordeaux, I2M Institute, UMR CNRS 5295
, 16 Avenue Pey-Berland, 33607 Pessac Cedex, France
a)Author to whom correspondence should be addressed: [email protected]
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Jean-Paul Caltagirone
a)
Bordeaux INP - University of Bordeaux, I2M Institute, UMR CNRS 5295
, 16 Avenue Pey-Berland, 33607 Pessac Cedex, France
a)Author to whom correspondence should be addressed: [email protected]
Physics of Fluids 32, 083604 (2020)
Article history
Received:
June 02 2020
Accepted:
July 22 2020
Citation
Jean-Paul Caltagirone; On Helmholtz–Hodge decomposition of inertia on a discrete local frame of reference. Physics of Fluids 1 August 2020; 32 (8): 083604. https://doi.org/10.1063/5.0015837
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