# Classical Mech problems help

Does anyone know how to solves these, hints anything??? I was able to do #1,2 and got lost at 3 and without 3 I couldnt do 4 and then i couldnt do 5 :(

#3 in special relativity the dynamics are different. In particular, the momentum p is no longer mv. Failure to remeber this causes a lot of trouble. THe lagrangian of one dimensional speical relativity is
L(x, x(dot))= -mc^2 (sqroot of (1-(xdot/c)^2)-V(x)
where c is the speed of light. Use the definition of hte momentum p= partial derviatives of (L/xdot) to express the relativistic momentum in terms of velocity.

#4 use the lagrangian of #3 to find the hamiltonian of relativistic particle. Remember that H must be expressed as a function of p and x only. This hamiltonian is the energy of a relativistic particle.

#5 Use the hamiltonian of problem 4 and hamilton's equations of motion to express the velocity of a relativistic particle in terms of its momentum.