On 6/7/2025 11:04 PM, Alan Grayson wrote:
Because there is so much slop in in the question. First, what does "a closed path" mean. If it means in the state space of an isolated system then it is trivially true that energy is conserved. And then J.C. refers to a system that obeys a least action principle. I think that's equivalent to a system without a dissipative term, like friction, so that would be sufficient. But applying a least action principle means knowing two points in state space. Noether's proved her theorem for a system defined by a Lagrangian which applies to both a least action and also to a problem in terms of initial state. Then it is sufficient that the Lagrangian be time-translation invariant in order for a conserved energy exist.On Saturday, June 7, 2025 at 10:45:36 PM UTC-6 Brent Meeker wrote: Lagrange (1736-1813) was born nine years after Newton (1642-1727) died. They weren't centuries apart. Hamilton was the next generation (1805-1865) just overlapping Lagrange. Brent On 6/7/2025 3:46 PM, Alan Grayson wrote:And their reformulations were discovered centuries after Newton discovered his way of doing thingsThat's what CLARK wrote! Why don't you comment on a substantive matter, such as can conservation of energy on a closed path be established without the principles Clark alleges, such as Least Action? AG
And that's why I didn't comment, because I hate to have to explain the question before answering it.
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