Show that the transformation for a system of one degree of freedom, Q = q cos α − p sin α, P = q sin α + p cos α, satisfies the symplectic condition for any value of the parameter α. Find a generating function for the transformation. What is the physical significance of the transformation for α = 0? For α = π/2? Does your generating function work for both of these cases

Show that the transformation for a system of one degree of freedom, Q = q cos α − p sin α, P = q sin α + p cos α, satisfies the symplectic condition for any value of the parameter α. Find a generating function for the transformation. What is the physical significance of the transformation for α = 0? For α = π/2? Does your generating function work for both of these cases

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Question

Show that the transformation for a system of one degree of freedom,
Q = q cos α − p sin α,
P = q sin α + p cos α,
satisfies the symplectic condition for any value of the parameter α. Find a
generating function for the transformation. What is the physical significance
of the transformation for α = 0? For α = π/2? Does your generating function
work for both of these cases

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