History of Hamilton's principle

[Darkmisc]

How did Hamilton work out that action is the stationary quantity for a mechanical system?

I've seen proofs that action is stationary, but it's unclear to me how Hamilton worked out that action as opposed to some other quantity should be stationary.

 

[ardie]

he attempted to generalise the Newton's laws of motion to arbitrary coordinates. bearing in mind that virtual displacements from the true path of the particle should do no work. i.e. if you throw a stone down a tower, and it takes route A, some other route B infinitesimally close to route A should not be very much different in energy to route A, and in fact changing the particles route should not interfere with the energies of the particle, and can be regarded as an External energy.
right so if you throw a tennis ball straight, you expect it to go straight, if it doesn't then there is some other force acting on it that changes its path. which basically Newton's law. Hamilton wrote this down in an abstract world, where he sought the variations of the path to be related to the energies put upon the system.