 Q-19 Home > Q-19 Sitemap Next Page  Previous Page  Home ▲Top of This Page ▲Top of This Page www．GrammaticalPhysics．ac | Siteowner 【SEOtext】0. General Formulation,Notice that if ∂0qi(t)=Vi(q*(t),p*(t)) then:I(q)=∫dt[pi(t)∂0qi(t)-H(q*(t),p*(t))]=0.Then we know the equations before ‘⇔’ mean vanishing of variation of a functional which is connected to the action by:∂0qi(t)=Vi(q*(t),p*(t)).(v)Poisson bracket,Poisson bracket {}PB is defined as a mapping which maps an element of (R(Rn,Rn),R(Rn,Rn)) to an element of R(Rn,Rn) as follows.{F,G}PB(x,y)=∂F(x,y)/∂yi∂G(x,y)/∂xi-∂F(x,y)/∂xi∂G(x,y)/∂yi,Canonical equations can be written in terms of Poisson bracket as follows.(d/dt)F(q*(t),p*(t))={H,F}PB(q*(t),p*(t)),To know this equation contains the original canonical equations, we have only to consider the special cases:F=Qi,Pi where Qi,Pi∈R(Rn,Rn) are defined by the equations:Qi(x,y)=xi,Pi(x,y)=yi(i=1,2,・・・,n).The Poisson bracket between Qj and Pk is:{Qj,Pk}PB(x,y)=-δjk.(vi)Canonical Transformations,Prove that conserved quantities in Noether's theorem play a role of generators in canonical transformations.(vii)Treatment of Complex Variables(n=2) (C) Yuuichi Uda. All rights reserved.