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ySEOtextz0. General Formulation, [1] Classical Lagrangian Formulation, (1) Discrete System, Consider the special case: I(q)=dtL(q1(t),EEE,qn(t);0q1(t),EEE,0qn(t)), qRn(R), LR(R2n) The function L is called Lagrangian of the system. (i) Euler-Lagrange Equation I(q)/qi(t)=0L(q*(t);0q*(t))/qi(t)-d/dtL(q*(t);0q*(t))/[0qi(t)]=0 (ii) Noether's Theorem for Discrete System, Assumption, If I(q)/qj(t)=0 then: t1,t2R; (/݃)I(q'*(*;q,);t'(t1;),t'(t2;))|=0=0 where: I(q;t1,t2)=t(2)t(1)dtL(q*(t),0q*(t)), q'Rn(R;Rn(R),R), t'R(R;R), q'j(t;q,0)=qj(t), t'(t;0)=t, Conclusion, If I(q)/qj(t)=0 then: (d/dt)Q(t;q)=0 where: QR(R;Rn(R)), Q(t;q)=t'(t;)/݃|=0L(q*(t);0q*(t))+q'j(t;q,)/݃|=0L(q*(t);0q*(t))/[0qj(t)]

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