455 B
455 B
PROBLEM Find the law of transformation of the action S from one inertial frame to another. SOLUTION. The Lagrangian is equal to the difference of the kinetic and potential energies, and is evidently transformed in accordance with a formula analogous to (8.5): Integrating this with respect to time, we obtain the required law of transformation of the action: S=S'tuV.R'+1uV2t, where R' is the radius vector of the centre of mass in the frame K'.