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Correction.Least Action Principle Follows From F=ma,not Vicevers

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Posted by Alexander on January 21, 2002 18:20:36 UTC

Harvey, you can NOT derive F=ma from minima of action integral, it is mathematically ILLOGICAL.

Action (= time integral of energy) can not be defined BEFORE enegy is defined. Energy is defined as work, work is defined as force times distance.

So, force should be defined FIRST and then action can be.

By the way, F=ma as you like to write many times, is INCORRECT definition of force. Correct one is F=dp/dt.

So, minimum of action integral is NOT a fundamental principle, but is a mathematical consequence of the definition of force F=dp/dt.

No need to break a head thinking how nature selects one path out of all possible - it is simply the only one allowed by correct definition of force (and thus energy).

Very simple and beautiful.

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