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Solve problems neatly and clearly. Determine or find everything that is asked of you and that we have underlined in bold and listed. Circle each answer in a box and put the corresponding number in parentheses next to or below it. A particle of mass m is subjected to a gravitational potential U (x, y, z) in an inertial frame. The position of the particle is determined by the Cartesian coordinates x, y and z with the orientation shown in the figure. Determine (1) the Lagrangian and (2) the Hamiltonian of the system using the Legendre transform. Determine (3) the Hamilton equation(s) of the system. Suppose now that the gravitational potential is that which corresponds to the one near the earth's surface; that is, a uniform field of module g and directed downwards. Determine for this case (4) the Hamiltonian, in any way you like, and (5) the Hamiltonian equation(s) of the system. Om Earth