Three particles of mass m in 1-dimension with coordinates x x2 X3, interact with a potential...

  

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Three particles of mass m in 1-dimension with coordinates x x2 X3, interact with a potential e1X2 + e*23 + ex3). V = g (e1- (a) Write its Lagrangian and Hamiltonian. Find the equations of motion for the three coordinates and their momenta using Hamilton's equations. (b)Identify at least one constant of motion, apart from the energy. Using this constant of motion, show that the number of degrees of freedom can be reduced, and write the Lagrangian in terms of the reduced set of generalized coordinates. Three particles of mass m in 1-dimension with coordinates x x2 X3, interact with a potential e1X2 + e*23 + ex3). V = g (e1- (a) Write its Lagrangian and Hamiltonian. Find the equations of motion for the three coordinates and their momenta using Hamilton's equations. (b)Identify at least one constant of motion, apart from the energy. Using this constant of motion, show that the number of degrees of freedom can be reduced, and write the Lagrangian in terms of the reduced set of generalized coordinates.