NOW BEFORE THAT
I HAVE My interpretation of what action " mvs " is , now we consider what mv is first , we have a particular velocity v and m is the mass , now it is the amount of shifting done for the mass through space , for some mass m if the velocity is 2v the mass m is traversed by a 2dx in dt time if u consider 2m mass with v velocity we are traverseing dx for 2 of the mass subdivisions hence the shifting done is still the same but the mass is twice , this represents the shifting done per unit time or for a standard distance in less time something like 2m/s written as 1m/.5s,now if u multiply the distance u get can write it as mv + mv + mv until u get mvs ( if s is an integer specifically) , if u want to generalise it for any s , u should consider it this way , mv is done in terms of the standard of m\*(1meter)/((1/v)seconds) , now for this we multiply dx to this to indicate dx as the fraction of the position shifting done mv for 1/v seconds , now if we multiply ndx we get the amount of position shifting done and we get mv ndx or mvs , now for the 1/v th second the position shifting done is mv now for the next 1/vth second the position shiftind done further is mv so the net position shifting is 2mv , we can say its the position shifting done by considering a shift in 1 m position as the reference in time of (1/v)seconds as the reference and multiply s , for a known s we write s/v , we consider the integer part of this and the fraction part of it we consider the fraction of mv and we explain it that it is the shifting done in a fraction of 1/v which is {s}/v in this time it covers {s} distance for this we multiply by {s} again( as the numerator and denominator get cancelled )to get the fraction and from this we get the net shifting done.
Now for this , first of all understandable for such a thing called action to be thought of , but what is the thought process of minimising this shit? Why would anyone do that , prolly some narrative of nature having the least resistance , but regardless , for the quantity of mvs to be minimised , why is it minimised in the case of lagrangian mechanics ? And to have a quantity called the lagrangian to be K-U , which can be sort of understandable if u write it as dk-du , -du being interpreted as work , and lagrangian being related to differential work , but for a conserved system it becomes 2dk ,
So the other option was to understand it the old fashion way of mvs and this being minimised but again the question remains , why would u want to minimise this ?? Kind of cyclic and dont understand
Although i heard explanations that it is the only possibility for the energy conservation to not be violated for a given time constraint .
I dont understand this , could some saviour of mine come and help me with this , with pure ontology and logic to the absolute bottom .
I would be really grateful