By Roger Blanford, Kip Thorne
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Extra info for Applications of Classical Physics (web draft april 2013)
23) ij Here δki is the Kronecker delta. Examine the 4-index delta function δkl carefully; it says that either the indices above and below each other must be the same (i = k and j = l) with a + sign, or the diagonally related indices must be the same (i = l and j = k) with a − ij sign. [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.
E. + Tjk;k = 0 . 36) ∂t ∂t This is the differential law of momentum conservation. It has the standard form for any local conservation law: the time derivative of the density of some quantity (here momentum), plus the divergence of the flux of that quantity (here the momentum flux is the stress tensor), is zero. We shall make extensive use of this Newtonian law of momentum conservation in Part IV (elasticity theory), Part V (fluid mechanics) and Part VI (plasma physics). 13 **Example: Equations of Motion for a Perfect Fluid (a) Consider a perfect fluid with density ρ, pressure P , and velocity v that vary in time and space.
2 The Principle of Relativity and Constancy of Light Speed . . . 3 The Interval and its Invariance . . . . . . . . . . . 3 Tensor Algebra Without a Coordinate System . . . . . . . . . 4 Particle Kinetics and Lorentz Force Without a Reference Frame . . . .
Applications of Classical Physics (web draft april 2013) by Roger Blanford, Kip Thorne