Conservation Laws

A powerful idea in physics is that of invariants, that is, things that do not change as a system evolves in time. The existence of invariants and their use allows us to place contraints on the possible dynamics of a system eventhough we might be ignorant of various details; this is particulraly important in the case of complicated systems with many components whereby it might be too difficult to solve for and follow in detail the trajectory of each component as described by Newton's laws. Invariants by definition imply a conservation law. Below we discuss some of these conservation laws.