%\begin{filecontents}{leer.eps}
%\end{filecontents}
%
\documentclass[a4paper,12pt]{book}
\linespread{1.3}
\usepackage[T1]{fontenc} % Encodare
\usepackage[romanian]{babel}
\usepackage[latin1]{inputenc} % Utilizare accente
\usepackage{graphics}
\usepackage{textcomp} % Pentru a avea grade Celsius
\usepackage{carte} % Fisierul stil
%\usepackage{shading} % Nu il gaseste
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\begin{document}
%1
\[R_1  = \frac{{U_V }}{{2I_d }}\]

%2
\[R_1  = \frac{3}{2}\frac{{U_V }}{{I_d }}\]

%3
\[I_1  \simeq I_{01} \]

%4
\[Z_m  = \sqrt {R_m^2  + X_m^2 }  = \frac{{U_1 }}{{\sqrt 3 I_1 }}\]

%5
\[P_{Fe}  = P_{10}  - 3R_1 I_1^2  - P_{mec}\]

%6
\[R_m  = \frac{{P_{Fe} }}{{3I_1^2 }}\]

%7
\[X_m  = \sqrt {Z_m^2  - R_m^2 } \]

%8
\[L_m  = \frac{{X_m }}{{2\pi f}}\]

%9
\[I_1  \equiv I_{01} \]

%10
\[U_1  = f\left( {I_1 } \right)\]

%11
\[\Psi _1  = \left( {\frac{{U_1 }}{{\sqrt 3 }} - R_1 I_1 } \right)\frac{1}{{\omega _0 }}\]

%12
\[L_m  = \frac{{\Psi _1 }}{{I_1 }} = f\left( {I_{01}  \equiv I_1 } \right)\]

%13
\[P_{10}  = 3R_1 I_1^2  + P_{Fe}  + P_{mec}\]

%14
\[P_{Fe}  + P_{mec}  = P_{10}  - 3R_1 I_1^2\]

%15
\[P_{Fe}  + P_{mec}  = f\left( {U_1 } \right)\]

%16 
\[I_1  \simeq I_2^{'} \]

%17
\[I_c  \simeq I_N \]

%18
\[P_{Fe}  \simeq 0\]

%19
\[R_1  + R_2^{'}  = \frac{{P_c }}{{3I_c^2 }}\]

%20
\[R_2^{'}  = \frac{{P_c }}{{3I_c^2 }} - R_1 \]

%21
\[\sqrt {\left( {R_1  + R_2^{'} } \right)^2  + \left( {X_{1\sigma }  + X_{2\sigma }^{'} } \right)^2 }  = \frac{{U_c }}{{\sqrt 3 I_c }}\]

%22
\[L_{1\sigma }  = L_{2\sigma }^{'}  = \frac{1}{{4\pi f}}\sqrt {\frac{{U_c^2 }}{{3I_c^2 }} - \left( {R_1  + R_2^{'} } \right)^2 } \]

%23
\[L_1  = L_{1\sigma }  + L_m\]

%24
\[L_2^{'}  = L_{2\sigma }^{'}  + L_m\]

%25
\[0 = T_{s0}  + J\frac{{d\Omega }}{{dt}}\]

%26
\[J\frac{{d\Omega }}{{dt}} + k_v \Omega  + T_f  = 0\]

%27
\[J =  - T_{s0} \frac{{dt}}{{d\Omega }}\]

%28
\[T_{s0}  = \frac{{P_{mec} }}{{\Omega _0 }}\]

%29
\[\frac{{dt}}{{d\Omega }} =  - \frac{{t_1 }}{{\Omega _0 }}\]

%30
\[J = P_{mec} \frac{{t_1 }}{{\Omega _0^2 }} = P_{mec} \frac{\tau }{{\Omega _0 \left( {\Omega _0  + \frac{{T_f }}{{k_v }}} \right)}}\]

%31
\[\frac{{t_1 }}{\tau } = \frac{{\Omega _0 }}{{\Omega _0  + \frac{{T_f }}{{k_v }}}}\]

%32
\[T_{s0}  = k_v \Omega _0  + T_f \]

%33
\[J =  - T_{s0} \frac{{\Delta t}}{{\Delta \Omega }} = \left( {k_v \Omega _0  + T_f } \right)\frac{{t_1 }}{{\Omega _0 }}\]

%34
\[J = \left( {k_v  + \frac{{T_f }}{{\Omega _0 }}} \right)t_1 \]

%35
\[
\Omega  = \left( {\Omega _0  + \frac{{T_f }}{{k_v }}} \right)e^{ - \frac{t}{\tau }}  - \frac{{T_f }}{{k_v }}
\]

%36
\[
\tau  = \frac{J}{{k_v }}
\]

%37
\[
\left( {\Omega _0  + \frac{{T_f }}{{k_v }}} \right)e^{ - \frac{{t_s }}{\tau }}  = \frac{{T_f }}{{k_v }}
\]

%38
\[
\left( {k_v \Omega _0  + T_f } \right)e^{ - \frac{{t_s }}{\tau }}  = T_f 
\]

%39
\[
T_f  = \left( {\frac{J}{{t_1 }} - k_v } \right)\Omega _0 
\]

%40
\[
\left( {k_v \Omega _0  + T_f } \right)e^{ - \frac{{t_s }}{\tau }}  = \left( {\frac{J}{{t_1 }} - k_v } \right)\Omega _0 
\]

%41
\[\frac{J}{{t_1 }}\Omega _0 e^{ - \frac{{t_s }}{\tau }}  = \left( {\frac{J}{{t_1 }} - k_v } \right)\Omega _0 \]

%42
\[k_v  = \frac{J}{{t_1 }}\left( {1 - e^{ - \frac{{t_s }}{\tau }} } \right)\]

%43
\[k_v  = \frac{J}{{t_1 }}\left( {1 - e^{ - \frac{{t_s }}{{J/k_v }}} } \right)\]

%44
\[k_v  = \left[ {W\left( { - e^{ - \frac{{t_s }}{{t_1 }}}  \cdot \frac{{t_s }}{{t_1 }}} \right) + \frac{{t_s }}{{t_1 }}} \right] \cdot \frac{J}{{t_s }}\]

%45
\[x \cdot e^x \]

%46
\[a =  - e^{ - \frac{{t_s }}{{t_1 }}}  \cdot \frac{{t_s }}{{t_1 }}\]

%47
\[x \cdot e^x  = a\]


% Inserare documente slave 
%\tableofcontents
%\input Chap1.tex
%\input Chap2.tex
%\input Chap3.tex
%\input Cuprins.tex

\end{document}