 | American Academy of Arts and Sciences - 1913 - 1034 страница
...combined into the operational equation /</»()= - //(<*SV)(), (61) where the operators may be applied to f in either inner or outer multiplication. In three...with proper regard to sign. The ordinary statement is which in our notation becomes and may be transformed by (35) into fdt-t = - ff(d*' V)-f. (62) In like... | |
 | American Academy of Arts and Sciences - 1913 - 1092 страница
...into the operational equation </•() = -• (rfs-vM), (6i) / where the operators may be applied to f in either inner or outer multiplication. In three...with proper regard to sign. The ordinary statement is f da-t = f jdS(curlf)«, which in our notation becomes Jrfs-f = j /rfS-(Vi); and may be transformed... | |
 | Robert Alexander Houstoun - 1912 - 222 страница
...52. Stokes' theorem. The line integral of the tangential component of a vector taken round any closed curve is equal to the surface integral of the normal component of the curl of the same vector taken over any surface bounded by the curve, or Let P(x, y, z) be the centre of a rectangle... | |
 | Heinz Lettau, Charles R. Stearns - 1969 - 214 страница
...that "The line integral of the tangential component of a vector A taken around a simple closed curve S is equal to the surface integral of the normal component of the curl of A taken over any surface A having S as its boundary. The vertical velocity determination is based on... | |
 | Robert H. Nunn - 1989 - 366 страница
...Kelvin*s relation and indicates that the circulation associated with a velocity field bounded by a closed curve is equal to the surface integral of the normal component of the vorticity over any surface bounded by that curve. Because the surface bounded by the curve may be warped... | |
 | Akhlesh Lakhtakia - 1994 - 570 страница
...sca (r)xH sca *(r)]}. (2.43a) In a similar vein, the time-averaged power absorbed in the scatterer is equal to the surface integral of the normal component of the time-averaged Poynting vector of the total field; thus, abs' = -(l/2)Re SCil 3Ds {jJSdru n (r).([E... | |
 | Martin Weik - 1997 - 1254 страница
...total integral of the divergence (dot product) of the field within the volume enclosed by the surface is equal to the surface integral of the normal component of the field over the entire enclosing surface. Note: Gauss' theorem is convenient in dealing with electromagnetic... | |
 | Arthur P. Boresi, Ken Pin Chong - 2000 - 640 страница
...Accordingly, we have Stokes's theorem: The line integral of a vector Iield ahout any closed curve equals (he surface integral of the normal component of the curl of the vector over anv capping surface. IF q is a velocity field, curl q is called the vorticity vector. Consequently,... | |
 | Neil Gershenfeld - 2000 - 390 страница
...(or Gauss' Theorem) I Jv V • E dV = E • dA . (5.22) v Js The volume integral of the divergence is equal to the surface integral of the normal component of the field. V is an arbitrary volume, 5 is its surface, dV is a volume element, and dA is a surface area... | |
 | Constantine Pozrikidis - 2001 - 692 страница
...closed loop in three-dimensional flow, L, enclosing an open area, D. The circulation around the loop is equal to the surface integral of the normal component of the vorticity, iJ • n, over D. where dS is the differential surface area of D. The orientation of the... | |
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Stokes's theorem states that the line integral of a vector around a curve is equal to the surface integral of the normal component of the curl of the vector over any surface spanning the curve, with proper regard to sign. The ordinary statement is which... 
