The constant of motion of a free fall body

AI Thread Summary
In the discussion on the constants of motion for a free-falling body, the key points revolve around identifying these constants in one-dimensional motion. Initial velocity and initial displacement are proposed as constants of motion, but their relationship to total energy is examined, indicating they are not independent. The conversation suggests that while initial velocity and displacement can be treated as constants, their connection to energy must be acknowledged. Additionally, the discussion raises the question of whether these constants correspond to any symmetry within the free-fall system. Overall, the exploration highlights the interplay between these variables in understanding motion in free fall.
jomoonrain
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1.what are the the constants of motion of a free fall body(treat this as a one-dimension motion,so there are two [independent] constants of motion )?

2.are they initial velocity and initial displacement？

3.and i know the total energy(T+V) is one,but they are not independent with the initial velocity and initial displacement, isn't it?

4.so i means can we just treat the initial velocity and initial displacement as constants of motion ?

5.if we can,do these constant of motin (initial velocity and initial displacement) correspond to some symmetry of the system (free fall body)?

thanks
 
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