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Classical Mechanics and Relativity: Lecture 13
Theoretical physicist Dr Andrew Mitchell presents an undergraduate lecture course on Classical Mechanics and Relativity at University College Dublin. This is a complete, self-contained, and standalone course in which everything is derived from scratch.
In this lecture I discuss the time-dependence of dynamical variables in classical mechanics, and how they can be obtained from so-called Poisson Brackets. We will see how Hamilton's equations of motion can themselves be cast in terms of Poisson Brackets, and we will study their general properties. Canonical transformations constitute a more general class of coordinate transformation that involve all canonical coordinates (positions and momenta). A canonical transformation is one that preserves the fundamental Poisson Bracket relations. Poisson Brackets are canonical invariants, as are Hamilton's equation's.
Full lecture course playlist: • Classical Mechanics an...
Course textbooks:
"Classical Mechanics" by Goldstein, Safko, and Poole
"Classical Mechanics" by Morin
"Relativity" by Rindler