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The principle of least action is that the integral of the Lagrangian is minimized - but, as this is intimately connected with total energy in most investigations.
But I'm trying to pin down what the equations MEAN in terms of the ontology and dynamics of the physical world.
alancalverd,This is a miscommunication. I meant to use the phrase "evolve in time", and I was not referring to biology.
We all know what velocity means.
Which one of these sentences best depicts the Principle of Least Action? And are any of these completely false?
A system that is under stress or strain will evolve in such a way as to relieve that stress.
Physical systems attempt to convert potential energy into kinetic energy as fast as possible.
The total energy of a system is conserved.
Physical systems tend to maximize potential energy.
A physical system evolves in such a way as to keep the the kinetic energy nearly equal to the potential energy, if it can.