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## Main Question or Discussion Point

I've just encountered the terms Hamiltonian and Lagrangian. I've read that the Hamiltonian is the total energy [tex]H = T + U[/tex], while the Lagrangian [tex]L = T - U[/tex], where [tex]T[/tex] is kinetic energy, and [tex]U[/tex] potential energy. In the case of Newtonian gravitational potential energy,

[tex]U = -G\frac{Mm}{r}[/tex].

So am I right in thinking that, in this case,

[tex]H = \frac{1}{2}mv^{2} - G\frac{Mm}{r}[/tex]

and

[tex]L = \frac{1}{2}mv^{2} + G\frac{Mm}{r}[/tex] ?

That's to say, is the sign of the potential significant, rather than just the absolute value?

[tex]U = -G\frac{Mm}{r}[/tex].

So am I right in thinking that, in this case,

[tex]H = \frac{1}{2}mv^{2} - G\frac{Mm}{r}[/tex]

and

[tex]L = \frac{1}{2}mv^{2} + G\frac{Mm}{r}[/tex] ?

That's to say, is the sign of the potential significant, rather than just the absolute value?