By J.M. Honig (Auth.)
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Integration system because system P B 0. (dB- - dH) Again, the integration may now be restricted to the volume of the system since in free space M - 0. The fifth and sixth terms vanish automatically since in free space B 0 - H 0 and D O - E 0. When the integration is carried out each of the last four terms vanishes on account of a vector theorem derived by Stratton 3 (1941). Thus it follows that + fvd3rB0 9d~. The reader (i. 8) are taken over all space, whereas the remaining integrals on the right extend solely over the volume of the system.
Intersection - to a ft in hyperspace. the situation where Geometrically, of of namely f the geometric figure representing the function f - horizontal three is generalizable class a Eqs. E, Px, Py on an equal footing. 32) for a circle. representative to two Note space (Px, Py); the are further now reduced 'surface' of constant energy E0, relative that the from representing to a reference value E I for a particle of mass m, is given by the circle drawn in the plane E - 0 (the Px, Py plane). 33). , and ~.
35) PxdPx + pydpy + pzdpz - 0, the initial point is displaced infinitesimally location on the same spherical surface. 35) the i (i, ,k) space; these must A lie on the fixed sphere. A quantity VE - iPxdpx + ~pydpy + kpzdpz_ is proportional gradient coincident of in (px2 + p~ direction in The + p~)/2mwith the m - radius E I and of the is to the everywhere sphere. 32 I. FUNDAMENTALS Again, the ideas illustrated in the above example may be generalized. Constraints placed on a given set of variables are depicted as hypersurfaces in the hyperspace independent variables These constrained variables alone.
