The discussion focuses on demonstrating the rotation transformation equations x' = x cos Θ - y sin Θ and y' = x sin Θ + y cos Θ using Poisson brackets. Participants reference the infinite series expansion involving Poisson brackets, specifically ω → ω + a{ω,p} + a²/2!{{ω,p},p} + ... as a method to approach the problem. The challenge lies in effectively substituting variables to derive the transformation, with one participant expressing difficulty in finding a suitable substitution method. The forum emphasizes the importance of showing work before receiving assistance.
PREREQUISITESStudents of classical mechanics, physicists working with Hamiltonian systems, and anyone interested in the mathematical foundations of rotation transformations.
Please define all the symbols here.shinobi20 said:Homework Equations
ω→ω+a{ω,p}+a^2/2!{{ω,p},p}+...
3. The Attempt at a Solution
Rules of the forum require showing work before receiving help. Indicate the type of substitution you tried.Sorry, I just can’t think of any way, substituting doesn’t work.