By G. Fowles, G. Cassiday

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Additional info for Analytical Mechanics [SOLUTIONS MANUAL]

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Without magnetic effects, that is, if angular momentum is orbital angular momentum only and does not have a spin contribution, the stress tensor turns out to be symmetric. Locally, it can be diagonalized orthogonally. This defines three directions such that a corresponding surface element is exposed to normal stress or normal pressure, and no shear forces are encountered. The volumetric momentum production rate is the same as external force per unit volume. 6 Energy and the First Law of Thermodynamics In this section we shall discuss the balance equation for energy.

They are intimately coupled. Note that the shear viscosity Ás as well as the bulk viscosity Áb will depend on mass density and on temperature, they may become fields. %; T / have to be specified, if necessary. Aerodynamics is a vast field. Just think of airplane or automotive engineering, meteorology and climate models, or such simple things as Bernoulli’s law. We have just scratched the surface. 2 Solid Media 37 flows, chemical reactions such as combustion in a jet engine, and many, many more effects must be taken into account in real-world problems.

44) The heat current density is proportional to the temperature gradient. A positive value of guarantees that internal energy flows from warm to colder regions. 9 Per unit mass. 44 2 Material Equations This is in accordance with the second law of thermodynamics. 41) and find hc D 1 T2 Indeed, the matrix ij must be non-negative in order to warrant isotropic medium this boils down to 0. hc 0. 2 More on Heat Conduction We assume an isotropic medium in order to simplify the discussion. The heat conductivity coefficient must not be negative.