Hamiltonian for flight?

["Dr. Robert J. Meier" <robert.meier@fanucrobotics.com>]

Aeronautical physicists,

	I am looking for the physics formula that demonstrates that
unpowered aerodynamic flight is characterized by a constant glide
ratio (as opposed to the parabolic curve of ballistic flight).

	After too many years, I don't remember the detailed derivation
and have been unable to find it either on the web or in my old
textbooks.  I vaguelly remember that it involved evaluating a
Hamiltonian.  I vaguelly remember showing that for some sets of
constants (air density, mass, drag coefficient, moment of inertia,
???) the Hamiltonian was stable and minimized for a path that dropped
a proportionate distance for a given curve length (i.e. constant
glide ratio).  I vaguelly remember not worrying about the sets of
constants where the Hamiltonian was unstable.

	The equivalent of this would be to prove that the vertical
component of lift and drag is constant.  I seem to remember that
proving the contancy of lift and drag forces was much more
complicated than evaluating the Hamiltonian.  I further remember
that completely solving the Hamiltonian was too complicated, but
that proving a constant glide ratio was straightforward.

	I think my basic problem is that I am missing one of the
Hamiltonain components.

	o Gravitational Potential (m g z) <= altitude energy
	o Kinetic Energy (- m v^2 /2) <= energy of motion
	o Atmospheric compression (Cp p S v^2) <= wing loading
	o ??? = what am I forgetting?

Thank you,

Bob


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