Intrinsic variational equations for conservative dynamical systems withN degrees of freedom

For a conservative dynamical system withn deg. of freedom we show that the equations of variation along an orbit may be written with respect to an orthonormal moving frame (a generalized Frenet frame) in which the tangential variation is given by a quadrature and the normal andn-2 binormal variations are solutions ofn-1 coupled second order equations of the form of Hill's equation.