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【SEOtext】0.General Formulation,[2]Classical Hamiltonian Formulation①Discrete System(i)Velocity,If there exists a function V∈Rn(Rn,Rn) that satisfies:∀x,y∈Rn;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]③.(ii)Hamiltonian,Hamiltonian is defined as a function H∈R(Rn,Rn) such that:H(x,y)=yiVi(x,y)-L(x,V*(x,y)),(iii)Canonical Equations,∀q,p∈Rn(R);[∂0qi(t)=Vi(q*(t),p*(t)) and δI(q)/δqi(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.{δ/δqi(t)∫dt[pj(t)∂0qj(t)-H(q*(t),p*(t))]=0,δ/δpi(t)∫dt[pj(t)∂0qj(t)-H(q*(t),p*(t))]=0⇔[δI(q)/δqi(t)=0 and ∂0qi(t)=Vi(q*(t),p*(t))]