the constant of a motion is also
knowns as
Answers
Explanation:
What is a constant of motion and what is its physical significance?
Swayang Priya Mahanta
Answered 1 year ago
-CONSTANT OF MOTION-
Considering a closed system (which do not involve time explicitly) of s degrees of freedom, there exists 2s quantities which vary with time. But there exists function of these quantities whose values remain constant during the motion. Such functions are called constants of motion.
-Depends only on initial condition.
-Not explicitly depends on time.
-Functions of generalised position and velocities.
-Ex:-Energy, Momentum, Angular momentum (Depends on homogeneity and isotropy of space and time)
Now come to the most important part. For s DOF we are having s 2nd order differential equations. So we need 2s arbitrary constants to solve completely. So in general there are 2s constants of motion for any system. However not all constants of motion are having equal importance. Only some are having profound significance,which are derived from the fundamental homogeneity and isotropy of space and time.