Exercise 1.9: Lagrange's equations

This exercise asks us to derive Lagrange's equations in steps for three different systems. Is this conscionable, given that we have the computer available to do the algebra for us? I think that this exercise is good practice for understanding the syntax, and maybe for refreshing your memory of how to symbolically manipulate derivatives.

But I'm feeling more and more that we're in the middle of a thicket of exercises that are smugly attempting to show us how bad life is with pencil and paper, and how nice a computer algebra system can be. These paper-and-pencil problems are going to get harder and harder, while they stay trivial in Clojure.

Decide for yourself. Exercise 1.12 solves implements each Lagrangian in Clojure and demonstrates the steps required to get to Lagrange's equations; I do buy that it would be difficult to do this without a good handle on the syntax.

Give it a try, then go examine exercise 1.12.