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## Main Question or Discussion Point

While I understand the use of the Lagrangian in Hamilton's principle, I have the gut feeling that there is more to it than meets the eye.

For instance, while the hamiltonian is conceptually easy to understand and even I could have thought about it, the Lagrangian is something else. I would never have thought about subtracting the potential energy from the kinetic energy. How was this found? was it just by accident? Did a monkey erase a plus sign in the Hamiltonian and put a minus? or were there some physical reasons that justified attempting to use the difference of T and V as opposite to their sum?. Or maybe someone Lagrange? Hamilton? was kind of bored and decided to have some fun by trying something different?

The way the subject is usually presented more or less along these lines:

Let there be a function which we call Lagrangian (L) defined by L=T-V. If we do this and that with this function, we obtain some very useful results.

It appears to me that the expression for the Lagrangian is so simple, that there should be some simple explanation of it's significance, which we could understand even before we start writing any equations.

If such an explanation exists, and you know it, I'll appreciate your sharing it with us.

-Alex-

For instance, while the hamiltonian is conceptually easy to understand and even I could have thought about it, the Lagrangian is something else. I would never have thought about subtracting the potential energy from the kinetic energy. How was this found? was it just by accident? Did a monkey erase a plus sign in the Hamiltonian and put a minus? or were there some physical reasons that justified attempting to use the difference of T and V as opposite to their sum?. Or maybe someone Lagrange? Hamilton? was kind of bored and decided to have some fun by trying something different?

The way the subject is usually presented more or less along these lines:

Let there be a function which we call Lagrangian (L) defined by L=T-V. If we do this and that with this function, we obtain some very useful results.

It appears to me that the expression for the Lagrangian is so simple, that there should be some simple explanation of it's significance, which we could understand even before we start writing any equations.

If such an explanation exists, and you know it, I'll appreciate your sharing it with us.

-Alex-

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