Titlebook: Covariance and Gauge Invariance in Continuum Physics; Application to Mecha Lalaonirina R. Rakotomanana Book 2018 Springer International Pub

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involves some steps. First of all, physical measurable quantities should be identified with geometrical variables (metric, torsion, and curvature on the material manifold) and other additional variables if any. Second point, the spacetime is generally a dynamical background with its metric, torsion

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Book 2018elativistic gravitation and electromagnetism when the torsion field of the Riemann-Cartan continuum is not equal to zero. Lastly, it derives heterogeneous wave propagation equations within twisted and curved manifolds and proposes a relation between electromagnetic potential and torsion tensor..

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Covariance and Gauge Invariance in Continuum PhysicsApplication to Mecha

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Covariance of Lagrangian Density Function,heory may thus be proposed to include metric and affine connection, not necessarily associated to metric (metric affine-manifold). Lagrangian we are interested in are function defined on such a manifold.

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Basic Concepts on Manifolds, Spacetimes, and Calculus of Variations,d equations governing theoretical physics are deduced from a variational principle after defining a suitable Lagrangian density . and its arguments. Three steps are considered for deriving the field equations governing their evolution and mutual interaction. The first focus on the continuum geometry

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Gauge Invariance for Gravitation and Gradient Continuum, involves some steps. First of all, physical measurable quantities should be identified with geometrical variables (metric, torsion, and curvature on the material manifold) and other additional variables if any. Second point, the spacetime is generally a dynamical background with its metric, torsion