what is the use of principle of least action in classical mechanics?...in simple words......pls?

Question

principle of least action is a variational principle related with hamiltonian formulation

Answer 1

First, the non-simple words. This is one example of a principle of thermodynamics. The state of a system will be that with the lowest Gibbs Energy.

If you mix 2 parts hydrogen gas and one part oxygen gas and trigger the reaction with a spark, they will combust to form water, releasing energy in the process. That's because the water molecule has a lower energy level than the isolated atoms.

In classical mechanics, it started out as an empirical observation that nature is lazy. Light travelling from one point to another takes a specific path because any other path would be a longer one. Deducing the path this way is a minimization problem. You write a system of equations for all the ways the path could vary. Then you solve that system for a minimum of its energy function. The Hamilton and Lagrangian formulations are ways of specifying laws of physics (mechanics) so that these mathematical methods can be used for finding solutions.

Answer 2

It helps to say why among the many trajectories, a drop of water on a roof, a rolling ball on a tilted plane, a projectile influenced by a magnetic field will follow the path of least resistance, the one that will make it spend less energy than in other paths.
Mathematically, it means you can find equations of movement by deriving the potential energy

Answer 3

When a body "want" to go from the point A to point B, choose the path in which spend a more small (smaller) quantitie of energy.

Answer 4

it really is once you're saying, "Honey, as long as you're up besides, might want to you get me a tumbler of water?" it extremely works because Honey doesn't experience that is all that huge an imposition as long as he/she replaced into going that way besides. yet indirectly i don't believe of it really is what you meant.