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

By Lalao Rakotomanana

around the centuries, the improvement and development of mathematical suggestions were strongly prompted through the desires of mechanics. Vector algebra was once constructed to explain the equilibrium of strength structures and originated from Stevin's experiments (1548-1620). Vector research was once then brought to review 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 start line for introducing a established spacetime. prompt pace concerned the set of particle positions in house. Vector algebra idea used to be no longer adequate to check the several velocities of a particle during time. there has been a necessity to (parallel) delivery those velocities at a unmarried element prior to any vector algebraic operation. the ideal mathematical constitution for this shipping used to be 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 through Einstein in 1905 (special relativity) and 1915 (general relativity) through the use of Riemannian connection. a bit of later, nonrelativistic spacetime such as 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 thought in arithmetic. significant steps for the relationship thought are attributed to a chain 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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