Download e-book for kindle: A Geometric Approach to Thermomechanics of Dissipating by Lalao Rakotomanana

By Lalao Rakotomanana

around the centuries, the improvement and progress of mathematical techniques were strongly prompted through the desires of mechanics. Vector algebra was once built to explain the equilibrium of strength platforms and originated from Stevin's experiments (1548-1620). Vector research used to be then brought to check speed fields and strength fields. Classical dynamics required the differential calculus constructed by means of Newton (1687). however, the concept that of particle acceleration used to be the place to begin for introducing a dependent spacetime. on the spot pace concerned the set of particle positions in house. Vector algebra idea used to be no longer enough to check different velocities of a particle during time. there has been a necessity to (parallel) delivery those velocities at a unmarried aspect earlier than any vector algebraic operation. the precise mathematical constitution for this shipping was once the relationship. I The Euclidean connection derived from the metric tensor of the referential physique was once the one connection utilized in mechanics for over centuries. Then, significant steps within the evolution of spacetime innovations have been made through Einstein in 1905 (special relativity) and 1915 (general relativity) through the use of Riemannian connection. a little later, nonrelativistic spacetime including the most beneficial properties of basic relativity I It took approximately one and a part centuries for connection concept to be authorised as an self sustaining concept in arithmetic. significant steps for the relationship idea are attributed to a sequence of findings: Riemann 1854, Christoffel 1869, Ricci 1888, Levi-Civita 1917, WeyJ 1918, Cartan 1923, Eshermann 1950.

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A Geometric Approach to Thermomechanics of Dissipating Continua (Progress in Mathematical Physics) by Lalao Rakotomanana

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