This chapter introduces the Euler–Lagrange equations as a means to extend the concepts of conservation of energy used earlier in the book. This topic relies on the calculus of variations but in a small-enough dose that the reader does not have to be acquainted with the subject previously to gain access to the ideas presented here. The power of the Euler–Lagrange equations in deriving equations of motion provides an important and useful counterpoint to the Newtonian balance of momentum methods.