(b) Consider Lagrangian L of an N particle system. Show that total momentum of this system will be conserved if the Lagrangian remains invariant under translation vec(r)_(i)longrightarrowvec(r)_(i)+vec(d) (Homogeneity of space), here vec(d) is an arbitrary small constant translation vector. (c) Hamiltonian H=H(q_(i),p_(i),t) and the canonical equat solutionspile.com

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(b) Consider Lagrangian L of an N particle system. Show that total momentum of this system will be conserved if the Lagrangian remains invariant under translation vec(r)_(i)longrightarrowvec(r)_(i)+vec(d) (Homogeneity of space), here vec(d) is an arbitrary small constant translation vector. (c) Hamiltonian H=H(q_(i),p_(i),t) and the canonical equations of motion : q_(i)^(?)=(delH)/(delp_(i)) and p_(i)^(?)=-(delH)/(delq_(i)). Using Legendre transformation find out Lagrangian L=L(q_(i),q_(i)^(?),t). (1+3)+3+3  solutionspile.com

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