miércoles, 29 de enero de 2020

vectors corrent-rotacionals de camps de variables separades

d_{t}[ F(x,y,z) ] = rot[ E(x,y,z) ]

F(x,y,z) = kq·(1/2)·( x_{k} )^{2} [o(t)o] ( x_{k} )^{[o(t)o](-1)} [o(t)o] ...
... ( ∫ [ f(y_{i}) ] d[t] + (-1)·∫ [ f(z_{j}) ] d[t] ).

d_{t}[ D(x,y,z) ] = rot[ B(x,y,z) ]

D(x,y,z) = (-1)·kq·(1/2)·( x_{k} )^{2} [o(t)o] ( x_{k} )^{[o(t)o](-1)} [o(t)o] ...
... ( ∫ [ f( d_{t}[y_{i}]·t ) ] d[t] + (-1)·∫ [ f( d_{t}[z_{j}]·t ) ] d[t] ).

div[ F(x,y,z) ] = kq·∑ ( x_{k}/d_{t}[x_{k}] )·( f(y_{i})+(-1)·f(z_{j}) ).

div[ D(x,y,z) ] = (-1)·kq·∑ ( x_{k}/d_{t}[x_{k}] )·( f( d_{t}[y_{i}]·t )+(-1)·f( d_{t}[z_{j}]·t ) ).

∯ [ F(x,y,z) ] d[(yz,zx,xy)] = ...
... kq·∑ ( x_{k} )^{2} [o(t)o] ( x_{k} )^{[o(x)o](-1)} [o(t)o] ... 
... ( ∫ [ ∫ [ f(y_{i}) ] d[t] ] d[y_{i}]·z_{j} + (-1)·∫ [ ∫ [ f(z_{j}) ] d[t] ] d[z_{j}]·y_{i} ).

∯ [ D(x,y,z) ] d[(yz,zx,xy)] = ...
... (-1)·kq·∑ ( x_{k} )^{2} [o(t)o] ( x_{k} )^{[o(x)o](-1)} [o(t)o] ... 
... ( ∫ [ ∫ [ f( d_{t}[y_{i}]·t ) ] d[t] ] d[y_{i}]·z_{j} + (-1)·∫ [ ∫ [ f( d_{t}[z_{j}]·t ) ] d[t] ] d[z_{j}]·y_{i} ).

m·d_{tt}^{2}[x_{k}] = p( F(x,y,z)+D(x,y,z) )

x_{k} = V_{k}·t

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