I got my hands on Landau, Course of Theoretical Physics. I want to challenge my understanding of the book by writing a physics engine that provide a computational layer for the book chapter by chapter.
>>> Just another Physics Engine
Out there you can find any sort of stuff if you are interested in physics engines, from general computation frameworks like Mathematica to game engines like Unreal. A good textbook on physics engines is Structure and Interpretation of Classical Mechanics, an unusual physics textbook that approach the subject from computational perspective.
>>> The double-pendulum
Landau starts off describing Lagrangian mechanics and leaves as a exercise to the reader to find the equation of motions for a double pendulum, e.g. a pendulum attached at the end of another pendulum (see the double-pendulum on ScienceWorld for a good treatment of the problem).