[jeffreyH (OP)]

If we are at rest in an inertial frame and observing an object in motion in a moving frame, how do we calculate the action of the object to make it the least possible?

[opportunity]

If we are at rest in an inertial frame and observing an object in motion in a moving frame, how do we calculate the action of the object to make it the least possible?

You have to consider the basics of Newtonian physics "first"; why for instance planets revolve in an counter-weight manner around the sun as a good example. The sun was considered as it was at rest, observing objects revolving around it, yet the gravitational pull between the planets and the sun created a counter-weight. I'm just using basics here. You're asking to make the calculation of the moving object the least possible.....that has to involve considering the reference. In making it the least possible reference, and correct me if I am wrong, it's asking to translate the dynamics of that objects motion back to the initial reference. Then we give birth to relativity from Newtonian physics, how light plays into that equation, observer and observed, field forces, and how gravity and inertia could play a hand.

Then....we do those mathematical transformations in the context of "G" equations with light........

"Light"? Einstein gave light a process/propagation/limit because technically a wave at the time then couldn't be everywhere at once, according to Maxwell. Correct me if I am wrong again. It was all modelled on the idea of trains (well, sort of). So to resolve two objects in space the "reality" of their existence had to be resolved with light. Hence relativity. It's simple to work out if you know what the status quo was in terms of scientific theory, one step to the next.

Thus.....mathematical modelling with equations for gravity and light as transformations creating unique references had to become apparent.

To answer your question, plug in the details of your simulated ideas, reference mass, object velocity and mass, distance, etc etc etc, according to how we've officially got thus far with theory.

[Bill S]

Is that an answer to the OP, or just verbal salmagundi?

[opportunity]

Is that an answer to the OP, or just verbal salmagundi?

Well, the "pronciple" wording gave me a chance, right? I thought the meaning of "principle" was in order.....right?

I looked at "proncible" and thought, "wow....there's no principles here.....lets go back to Newton".

[Bill S]

I suppose a typo can always be pounced upon as an opportunity for a spot of "rabbit", in the absence of anything more constructive.

[opportunity]

I suppose a typo can always be pounced upon as an opportunity for a spot of "rabbit", in the absence of anything more constructive.

Such is the sport of Kings

[jeffreyH (OP)]

Typo corrected. Now you look silly.

[Colin2B]

You have to consider the basics of Newtonian physics "first";

No, wrong way round. You can derive Newton's laws of motion from least action.

@jeffreyH have a look here http://www.eftaylor.com/pub/energy_to_action.html section VII

[jeffreyH (OP)]

Thanks Colin that page has just what I have been looking for. The fact that the treatment is one dimensional helps a lot.

[Colin2B]

The fact that the treatment is one dimensional helps a lot.

thought it might, let me know when you've done the 4D version 

[jeffreyH (OP)]

Euler never ceases to amaze me.