x'' = -x + h/x

h = k - (x^2 + x'^2)/2

?? .....

?? some interesting results from mathematica so far ... ?? ...

?? hamiltonian / poisson / symplectic structure here (...) ??? .....

?? bit about ... ?? extra info in symplectic (?? ...) system beyond (?? ...) "2th order dynamical system" ... ??? .... ?? energy .... ???? ..... ??? action ... ???? ...

?? "friction" ... ??? ...

?? "dispersion" ... ??? ....

?? energy function" ... "hamiltonian" ... "dynamics" ... ??? ....

?? fiberwise constant hamiltonian ??? .... ????? ......

?? some kind of symplectic /poisson reduction ?? .... ???? ....