(See attached PDF for exact problem). Show the Hamiltonian for a freely-falling body of mass m. Show...

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(See attached PDF for exact problem). Show the Hamiltonian for a freely-falling body of mass m. Show the generating function yields a canonical transformation to coordinates (P,Q). Show one of these coordinates is cyclic, and then solve the equations of motion.

Robert · Accepted Answer

1.  
a) Show that the Hamiltonian for a freely-falling body of mass m i s 
  
  
  
     
Sol: 
Kinetic energy of a freely – falling body = T 
 
 
    
If, p represents the momentum of such a body, then       
Using the definition of p to transform the kinetic energy equation, we get,

(See attached PDF for exact problem). Show the Hamiltonian for a freely-falling body of mass m. Show the generating function yields a canonical transformation to coordinates (P,Q). Show one of these...

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