Consider a particle in a plane with Lagrangian L(r.9, , 9) = r, m + -mi+mr4-1...

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Consider a particle in a plane with Lagrangian L(r.9, , 9) = r, m + -mi+mr4-1 - V(r). d dr (a) Give the Euler-Lagrange equations of the system. (b) The equation of motion for implies that the generalized momentum p, is constant. Use it to eliminate from the equation of motion for r and show that it can be brought into the form mi(t) (1) Ven (r(t)). (2) Consider a particle in a plane with Lagrangian L(r.9, , 9) = r, m + -mi+mr4-1 - V(r). d dr (a) Give the Euler-Lagrange equations of the system. (b) The equation of motion for implies that the generalized momentum p, is constant. Use it to eliminate from the equation of motion for r and show that it can be brought into the form mi(t) (1) Ven (r(t)). (2)

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