GCM27: Projectile motion using the Hamilton-Jacobi Formalism скачать в хорошем качестве

GCM27: Projectile motion using the Hamilton-Jacobi Formalism

After briefly introducing the ideas behind the powerful formalism arising from canonical transformations known as Hamilton-Jacobi theory, I apply the algorithm for solving separable systems laid out systematically to re-solve the rather trivial and well-known example of projectile motion in a constant gravity field and no air resistance. Examining this freshman physics problem in the most advanced light has many advantages: it teaches us how the complex formalism works, and you can perform all calculations explicitly, including the rare step of obtaining a closed form solution for both the Hamilton Characteristic function and the Hamilton Principal function!