What does it mean for momentum to be a constant of motion?

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Momentum being a constant of motion indicates that it is conserved within a system, meaning the total momentum remains unchanged in a specific direction or angle. This conservation implies that the time derivative of momentum is zero (\dot{p}=0), signifying that while motion may still occur, the evolution of that motion does not change over time. Understanding this concept is crucial for grasping the principles of classical mechanics and Hamiltonian dynamics.

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what does it mean for momentum to be constant of motion.
i know that if it is it will commute with the hamiltonian but what does it mean in words?
 
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If momentum is a constant of motion, there's a couple of things it means:

(1) momentum is conserved--the total momentum of the system (at least in the particular direction/angle) is constant
(2) the time derivative of momentum is zero ([itex]\dot{p}=0[/itex])--this does not mean there is no motion, just that the time-evolution of the motion is non-existent.

You should look at "[URL Theorem[/url] and http://en.wikipedia.org/wiki/Constant_of_motion" . These wiki articles might help you understand more.
 
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