By Roger Blanford, Kip Thorne
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Additional resources for Applications of Classical Physics (web draft april 2013)
Explain why this Euler equation is Newton’s second law of motion, “F=ma”, written on a per unit volume basis. In Part V of this book, we shall use Eqs. 37) to study the dynamical behaviors of fluids. For many applications, the Euler equation will need to be augmented by the force per unit volume exerted by the fluid’s internal viscosity. 14 **Problem: Electromagnetic Stress Tensor (a) An electric field E exerts (in SI units) a pressure ǫo E2 /2 orthogonal to itself and a tension of this same magnitude along itself.
4 Particle Kinetics and Lorentz Force Without a Reference Frame . . . .
We have put the indices ij of δkl up solely to facilitate remembering this rule. Recall (first paragraph of Sec. ] With the aid of Eq. 8. 20) of a parallelopiped vanishes only if its legs are all linearly independent. (ii) Once the volume has been specified for one parallelopiped (one set of linearly independent legs), it is thereby determined for all parallelopipeds. (iii) Therefore, we require only one number plus antisymmetry to determine ǫ fully. (iv) Compatibility with the metric (the fact that orthonormal parallelopipeds have volume ±1) means that ǫ is fully determined by its antisymmetry and a single sign: the choice of which parallelopipeds have positive volume and which negative.