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ySEOtextz0.General Formulation,[2]Classical Hamiltonian Formulation@Discrete System(i)Velocity,If there exists a function VRn(Rn,Rn) that satisfies:x,yRn;yi=L(x,V*(x,y))/Vi(x,y),then let's call it velocity. I worry about confusion of velocity with potentials in [1]B.(ii)Hamiltonian,Hamiltonian is defined as a function HR(Rn,Rn) such that:H(x,y)=yiVi(x,y)-L(x,V*(x,y)),(iii)Canonical Equations,q,pRn(R);[0qi(t)=Vi(q*(t),p*(t)) and I(q)/qi(t)=0]{H(q*(t),p*(t))/pi(t)=0qi(t),H(q*(t),p*(t))/qi(t)=-0pi(t),(iv)Action Principle,The canonical equations ensures the following equivalence.{/qi(t)dt[pj(t)0qj(t)-H(q*(t),p*(t))]=0,/pi(t)dt[pj(t)0qj(t)-H(q*(t),p*(t))]=0[I(q)/qi(t)=0 and 0qi(t)=Vi(q*(t),p*(t))] |
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