Download PDF by Lalao Rakotomanana: A Geometric Approach to Thermomechanics of Dissipating

By Lalao Rakotomanana

around the centuries, the advance and development of mathematical recommendations were strongly influenced by way of the desires of mechanics. Vector algebra used to be constructed to explain the equilibrium of strength structures and originated from Stevin's experiments (1548-1620). Vector research was once then brought to check speed fields and strength fields. Classical dynamics required the differential calculus built through Newton (1687). however, the concept that of particle acceleration used to be the place to begin for introducing a established spacetime. immediate speed concerned the set of particle positions in house. Vector algebra idea used to be now not adequate to match the various velocities of a particle during time. there has been a necessity to (parallel) shipping those velocities at a unmarried aspect sooner than any vector algebraic operation. the best mathematical constitution for this shipping was once the relationship. I The Euclidean connection derived from the metric tensor of the referential physique used to be the one connection utilized in mechanics for over centuries. Then, significant steps within the evolution of spacetime strategies have been made by way of Einstein in 1905 (special relativity) and 1915 (general relativity) by utilizing Riemannian connection. a little bit later, nonrelativistic spacetime together with the most beneficial properties of normal relativity I It took approximately one and a part centuries for connection idea to be approved as an self sufficient conception in arithmetic. significant steps for the relationship inspiration 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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