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CAN-4-1-16
補足説明をここに書く予定です
【SEOテキスト】宇田雄一05.5.31,CAN-4-1-16-26～29,(与式)=∫b+⊿b,a+⊿a,dt[H(q(t;α);p(q(t;α);q(t;α)))+L(q(t;α);q(t;α))]-∫b,a,dt[H(q(t;0);p(q(t;0);q(t;0)))+L(q(t;0);q(t;0))]≒[[(b+⊿b)-(a+⊿a)]-(b-a)]H(q(a;0);p(q(a;0);q(a;0)))+⊿b・L(q(b;0);q(b;0))-⊿a・L(q(a;0);q(a;0))+α[∂/∂α∫b,a,dt・L(q(t;α);q(t;α))]α=0,∂/∂α∫b,a,dt・L(q(t;α);q(t;α))|α=0=∫b,a,dt[∂2ηl(t;0)・∂L(q(t;0);q(t;0))/∂ql(t;0)+∂2ηl(t;0)・∂L(q(t;0);q(t;0))/∂ql(t;0)]=∫b,a,dt・∂2ηl(t;0)[∂L(q(t);q(t))/∂ql(t)-d/dt・∂L(q(t);q(t))/∂ql(t)]+[∂2ηl(t;0)・∂L(q(t);q(t))/∂ql(t)]b,t=a=∂2ηl(b;0)・pl(q(b);q(b))-∂2ηl(a;0)・pl(q(a);q(a)),α∂2ηl(b;0)≒ηl(b+⊿b;α)=ql(b+⊿b;α)-ql(b+⊿b;0)=ql(b;0)-ql(b+⊿b;0)≒-⊿b・ql(b;0),α∂2ηl(a;0)-⊿a・ql(a;0)∴(与式)≒⊿b・[H(q(b);p(q(b);q(b)))+L(q(b);q(b))-ql(b)pl(q(b);q(b))]-⊿a・[H(q(a);p(q(a);q(a)))+L(q(a);q(a))-ql(a)・pl(q(a);q(a))]=0