Least action Definition and 58 Threads

Are the principle of least action(http://astro.berkeley.edu/~converse/Lagrange/Kepler%27sFirstLaw.htm) and the hamilton principle 'exactly' the same? As far as I know, yes. How do I go from one to the other

In Volume II Chapter 19 of his Lectures on Physics, Feynman discusses the principle of least action and its role in quantum mechanics. He says the following on page 19-9: "The complete quantum mechanics (for the nonrelativistic case and neglecting electron spin) works as follows: The...

How do we know that it is true? Most people don't give me a very straightforward answer, but I don't like that. Lagrange must have gotten it from somwhere.

Could someone explain why the principle of least action is true?

I'll just throw down some definitions and then ask my question on this one. In a conservative system, the Lagrangian, in generalised coordinates, is defined as the kinetic energy minus the potential energy. L=L(q_i,\dot{q}_i,t) = K(q_i,\dot{q}_i,t) - P(q_i,t). All q_i here being functions...

Homework Statement The Lagrangian of a mass in a uniform gravitational field can be written as follows: L = \frac{1}{2}m\dot{y}^2 + mgy Consider all differentiale functions y(t) such that y(t1) = y1 and y(t2) = y2 where y1 and y2 are fixed values. Show that the action is a minimum for...

I'm not sure whether this question belongs in the quantum section or here, since it kind of involves both areas. I'm not even sure I can ask the question sensibly since I'm not a professional physicist, but I'll try: Suppose we look at a particle, say a photon, moving along in space time...

Have some people tried to find a meaning to the principle of least action that apparently underlies the whole physics? I know of one attempt, but not convincing to me (°). A convincing attempt, even modest, should suggest why it occurs, what is/could be behind the scene and how it might lead us...