Is canonical and find a generating function. Therefore, the given generating does in fact generate the given transformation.ĩ.8. Plugging the value of Q from eq(i) in the above equation, We are given the following generating function of the F 3type:įor a generating function of F 3 type, q is given as: (b) Show that the function that generates this transformation is (a) Show directly from these transformation equations that Q,P are canonical variables if q and p are. The transformation equations between two sets of coordinates are Is canonical, where α is an arbitrary constant of suitable dimensions.ĩ.6. Show directly that for a system of one degree of freedom, the transformation Therefore, in order for the given transformation to be canonical, the Poisson Bracket of Q,P with respect to q & p should be equal to 1.ĩ.5. In other words the fundamental Poisson Brackets are invariant under canonical transformation. We know that the fundamental Poisson Brackets of the transformed variables have the same value when evaluated with respect to any canonical coordinate set. We are given a transformation as follows, I have also embedded the pdf below as well as posted them in this blog post. You can download the pdf version here: Solutions Goldstein Chapter 9 So, I have tried solving some of the problems of the Chapter 9 of Goldstein Classical mechanics.
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