A Geometric Approach to Thermomechanics of Dissipating - download pdf or read online

By Lalao Rakotomanana

ISBN-10: 0817642838

ISBN-13: 9780817642839

ISBN-10: 1461264111

ISBN-13: 9781461264118

around the centuries, the advance and progress of mathematical thoughts were strongly influenced through the desires of mechanics. Vector algebra used to be constructed to explain the equilibrium of strength platforms and originated from Stevin's experiments (1548-1620). Vector research used to be then brought to review speed fields and strength fields. Classical dynamics required the differential calculus constructed via Newton (1687). however, the concept that of particle acceleration used to be the place to begin for introducing a dependent spacetime. on the spot speed concerned the set of particle positions in house. Vector algebra idea was once no longer enough to check the various 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 right 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 single connection utilized in mechanics for over centuries. Then, significant steps within the evolution of spacetime recommendations have been made via Einstein in 1905 (special relativity) and 1915 (general relativity) through the use of Riemannian connection. a bit of later, nonrelativistic spacetime together with the most good points of normal relativity I It took approximately one and a part centuries for connection conception to be approved as an self sustaining thought in arithmetic. significant steps for the relationship idea 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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