Proving Energy Conservation & Loss in Odd/Even Derivatives

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Homework Help Overview

The discussion revolves around proving a relationship between even and odd derivatives in the context of energy conservation and loss, specifically related to general forces acting on a system, such as drag force.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are exploring the definitions and implications of even and odd derivatives in relation to energy conservation. Questions about the context and specifics of the derivatives are raised, as well as suggestions to consider potential energy and closed loop integrations.

Discussion Status

The discussion is in an exploratory phase, with participants seeking clarification on the problem's context and attempting to connect concepts related to energy and derivatives. Some guidance on potential approaches has been suggested, but no consensus or formal proof has emerged yet.

Contextual Notes

There is a noted vagueness in the problem statement, particularly regarding the specific context of the derivatives and the forces involved. Participants are questioning the definitions and assumptions underlying the problem.

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Homework Statement


Prove:
Even derivatives conserve energy and that odd derivatives give an energy loss.

This is for general forces acting on a system of some sort. Like drag force, etc.

Homework Equations





The Attempt at a Solution


I have no clue. I need resources. Any clues on where to begin?
 
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Is there any other context given for this problem? It seems a bit vague. What are these derivatives with respect to?
 
The derivatives are rates of displacement. Taken with respect to time.
An example is:
[tex]\vec{F}=-b \frac{dx}{dt}[/tex] The force of drag on a particle creates an energy loss in the system.
 
I can't think of how to prove it formally but it will probably involve looking potential energy and closed loop integrations, are you familiar with those concepts?
 

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