- #1

- 65

- 0

## Main Question or Discussion Point

I've recently read in this article http://www.en.uni-muenchen.de/news/newsarchiv/2013/f-m-77-13.html that "In the world of classical mechanics, the state of a physical system and its future evolution is fully determined by the instantaneous locations and velocities of its constituent particles"

Can someone provide me a pratical exemple that shows how we can derive everything from a physical system given the position and velocity of every particle?

I've got into this topic recently when i heard about "jerk", the derivative of acceleration, and wondered why we usually define equations using the second derivative, an exemple F=ma.

Why didnt Newton use jerk in his equations? Is jerk useless? Or is it that if we ignore jerk we can still have a good approximation of reality? I really need some answers here :(

I've also read here http://physics.stackexchange.com/questions/4102/why-are-there-only-derivatives-to-the-first-order-in-the-lagrangian the following

"To put it in simple terms, since Newton's second law relates functions which are two orders of derivative apart, you only need the 0th and 1st derivatives, position and velocity, to "bootstrap" the process, after which you can compute any higher derivative you want, and from that any physical quantity. This is analogous to (and in fact closely related to) the fact that to solve a second-order differential equation, you only need two initial conditions, one for the value of the function and one for its derivative."

Can someone better explain this to me? I can't understand why F = ma plus the position and velocity of all particles in a system are enough th know everything!

Thanks in advance

**Question 1.**Can someone provide me a pratical exemple that shows how we can derive everything from a physical system given the position and velocity of every particle?

I've got into this topic recently when i heard about "jerk", the derivative of acceleration, and wondered why we usually define equations using the second derivative, an exemple F=ma.

**Question 2.**Why didnt Newton use jerk in his equations? Is jerk useless? Or is it that if we ignore jerk we can still have a good approximation of reality? I really need some answers here :(

I've also read here http://physics.stackexchange.com/questions/4102/why-are-there-only-derivatives-to-the-first-order-in-the-lagrangian the following

"To put it in simple terms, since Newton's second law relates functions which are two orders of derivative apart, you only need the 0th and 1st derivatives, position and velocity, to "bootstrap" the process, after which you can compute any higher derivative you want, and from that any physical quantity. This is analogous to (and in fact closely related to) the fact that to solve a second-order differential equation, you only need two initial conditions, one for the value of the function and one for its derivative."

Can someone better explain this to me? I can't understand why F = ma plus the position and velocity of all particles in a system are enough th know everything!

Thanks in advance