This section is dedicated to the transition from the Lagrangian to Hamiltonian description of motion. Instead of taking coordinates and velocities as the arguments of the Lagrangian function, we take coordinates and momenta as the variables in the Hamiltonian function. We then derive the equations of motion in terms of coordinates and momenta, which is called the canonical Hamilton’s equation. We also introduce the important concept of the Poisson bracket, which will play a fundamental role in the following chapters on Hamiltonian mechanics.