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1 Conjugate Variables and Hamiltonian Dynamics Write the Hamiltonian function and find Hamilton canonical equat ions for the three-dimensional motion of a projectile in a uniform gravitational fi...
3. (10 points) The Hamiltonian for a particle moving in a vertical uniform gravitational field g is 2 Hmgq where q is the altitude above the ground. We want to find any canonical transformation from old variables (q,p) to new variables (Q,P) which provides a cyclic coordinate. To do this, define new variables as where a, b are constants. a) Determine any combination of constants a and b, which provides a canonical transformation b) Find the type 1 generating function,...