01770cam a22002055i 4500008004100000020001800041100003200059245015500091250000600246260003400252300002300286440003700309520104900346650002601395650002401421650001501445650002601460650002101486650005701507180704s2018    gw |||| o    |||| 0|eng    a97830300629891 aRakotomanana, RLalaonirina,10aCovariance and Gauge Invariance in Continuum Physics :bApplication to Mechanics, Gravitation, and Electromagnetism /cby Lalaonirina R. Rakotomanana.  a.  aSwitzerlandbBirkhauserc2020  axi, 325 p.;bill.;  aProgress in mathematical Physics  aThis book presents a Lagrangian approach model to formulate various fields of continuum physics, ranging from gradient continuum elasticity to relativistic gravito-electromagnetism. It extends the classical theories based on Riemann geometry to Riemann-Cartan geometry, and then describes non-homogeneous continuum and spacetime with torsion in Einstein-Cartan relativistic gravitation. It investigates two aspects of invariance of the Lagrangian: covariance of formulation following the method of Lovelock and Rund, and gauge invariance where the active diffeomorphism invariance is considered by using local Poincaré gauge theory according to the Utiyama method. Further, it develops various extensions of strain gradient continuum elasticity, relativistic 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. 0aMathematical physics. 0aMechanics, Applied. 0aMechanics.14aMathematical Physics.24aSolid Mechanics.24aTheoretical, Mathematical and Computational Physics.