Tartalomjegyzék

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Teljes Matlab script kiegészítő függvényekkel.

Coordinate transformation, feedback linearization and zero dynamics.

syms Ex Ey Ez Bx By Bz v c gamma beta real

% beta  = v/c;
gamma = 1/sqrt(1-beta^2);

E = @(F) F(2:4,1) * c;
B = @(F) [
    F(4,3)
    F(2,4)
    F(3,2)
    ];

F = [
    0    -Ex/c -Ey/c -Ez/c
    Ex/c  0    -Bz    By
    Ey/c  Bz    0    -Bx
    Ez/c -By    Bx    0
    ];

L = [
    gamma      -gamma*beta 0 0
   -gamma*beta  gamma      0 0
    0           0          1 0
    0           0          0 1
    ];
% L = eye(4);


F_ = simplify(L*F*L);

simplify(F_(1,2))

Output:

 
ans =
 
-Ex/c
 

The quantity $\frac{c}{4} \tilde F^{\mu \nu} F_{\mu \nu} = \vec E \dot \vec B$

ZERO = simplify(  E(F)' * B(F)  - E(F_).' * B(F_)  )

Output:

 
ZERO =
 
0
 

Published with MATLAB® R2020b, and sanitarized by BeautifulSoup (Python script using BSoup is written by Polcz).