Every mechanichal system is characterised by a definite function depending on the coordinates of each point of the system, the first time derivative of these coordinates, and time.
What is the proof of this statement? Why only the only first derivative is included not the higher derivatives?
Thank you

every mechanichal system is characterised by a definite function depending on the coordinates of each point of the system, the first time derivative of these coordinates, and time.
what is the proof of this statement?. why only the only first derivative is included not the higher derivatives?
thank you
Isn't that a homework question?
Think along the lines of "what else can characterize a mechanical system, other than the 4 known dimensions (height, width, length, and time) ?"
Aren't higher derivatives based on combinations of first derivatives?
;)

If higher derivatives based on combinations of first derivatives then no need to put first derivative in the formula because it is based on coordinates .I can not imagine that you believe it as soon as you see it I think that it needs a proof.Sure it is not a homework. This statement is the beginning of formulation of laws of motion using the least action principle in the book " acourse of theoretical physics vol. 1 by Landau and Lifz

Isn't that a homework question?
Think along the lines of "what else can characterize a mechanical system, other than the 4 known dimensions (height, width, length, and time) ?"
Aren't higher derivatives based on combinations of first derivatives?
;)

If higher derivatives based on combinations of first derivatives then no need to put first derivative in the formula because it is based on coordinates .I can not imagine that you believe it as soon as you see it I think that it needs a proof.Sure it is not a homework. This statement is the beginning of formulation of laws of motion using the least action principle in the book " acourse of theoretical physics vol. 1 by Landau and Lifz