Jean-Paul Caltagirone - Böcker

The discrete vision of mechanics is based on the founding ideas of Galileo and the principles of relativity and equivalence, which postulate the equality between gravitational mass and inertial mass. To these principles are added the Hodge–Helmholtz decomposition, the principle of accumulation of constraints and the hypothesis of the duality of physical actions. These principles make it possible to establish the equation of motion based on the conservation of acceleration considered as an absolute quantity in a local frame of reference, in the form of a sum of the gradient of the scalar potential and the curl of the vector potential. These potentials, which represent the constraints of compression and rotation, are updated from the discrete operators. Discrete Mechanics: Concepts and Applications shows that this equation of discrete motion is representative of the compressible or incompressible flows of viscous or perfect fluids, the state of stress in an elastic solid or complex fluid and the propagation of nonlinear waves.

The unification of the laws of physics – a legitimate and long-standing aspiration – is undertaken here using the framework of discrete mechanics. Towards a Unification of the Laws of Physics in Classical Fields Theory extends these concepts to classical field physics.This book examines and revisits the fundamental principles of physics to derive a unified law of motion capable of modeling the phenomena observed, which are currently described by disparate laws. The global reference frames of classical mechanics and relativity are abandoned: space is defined from a one-dimensional local reference frame, and time is considered discrete. Applying the principle of parsimony to the derivation of this single law leads to the rejection of many concepts from classical mechanics and relativity, retaining only proper acceleration as the sole absolute quantity.The construction of this unified law of motion paves the way for a rational resolution of phenomena relating to mechanics, special and general relativity, electromagnetism and, more broadly, physics as a whole

This book presents the fundamental principles of mechanics to re-establish the equations of Discrete Mechanics. It introduces physics and thermodynamics associated to the physical modeling. The development and the complementarity of sciences lead to review today the old concepts that were the basis for the development of continuum mechanics. The differential geometry is used to review the conservation laws of mechanics. For instance, this formalism requires a different location of vector and scalar quantities in space. The equations of Discrete Mechanics form a system of equations where the Helmholtz-Hodge decomposition plays an important role.