We derive conservation laws from symmetry operations using the principle of least action. These derivations, which are examples of Noether's theorem, require only elementary calculus and are suitable for introductory physics. We extend these arguments to the transformation of coordinates due to uniform motion to show that a symmetry argument applies more elegantly to the Lorentz transformation than to the Galilean transformation.

We outline a story line that introduces Newtonian mechanics by employing conservation of energy to predict the motion of a particle in a one-dimensional potential. We show that incorporating constraints and constants of the motion into the energy expression allows us to analyze more complicated systems. A heuristic transition embeds kinetic and potential energy into the still more powerful principle of least action.

We present a method for introducing students to the classical principle of least action, using a novel approach based on the ordinary calculus of one variable. We define the classical action for a path and draw the connection between it and Newton's laws for a free particle and for a particle in a conservative potential. The use of software to help students visualize the principle of least action and analyze rectilinear motion is discussed. We also briefly discuss the origin of the principle of least action in Feynman's sum over paths formulation of quantum mechanics.

We derive Lagrange's equations of motion from the principle of least action using elementary calculus rather than the calculus of variations. We also demonstrate the conditions under which energy and momentum are constants of the motion.

In the book Surely You Are Joking, Mr. Feynman! Richard Feynman tells a story of a Cornell cafeteria plate being tossed into the air. As the plate spun, it wobbled. Feynman noticed a relation between the two motions. He solved the motion of the plate by using the Lagrangian approach. This solution didn’t satisfy him. He wanted to understand the motion of the plate by analyzing the motion of its individual particles and the forces acting on them. He was successful, but he didn’t tell us how he did it. We provide an elementary explanation for the two-to-one ratio of wobble to spin frequencies, based on an analysis of the motion of the particles and the forces acting on them. We also demonstrate the power of numerical simulation and computer animation to provide insight into a physical phenomenon and guidance on how to do the analysis.