The inertial positioning problem in Hamiltonian mechanics

The general inertial positioning problem—to determine the actual coordinates of a vehicle, moving with respect to the inertial frame, from its measured inertial accelerations—is discussed in Hamiltonian mechanics. The use of the Hamiltonian formalism allows the avoidance of sophisticated geometrical considerations. Starting from the canonical equations of motion for the general problem, the navigation equations of some special problems (motion on a rotating sphere, motion on a rotating ellipsoid) are derived in linearized form. Using the simplicity of the linearized form, the solutions can be easily computed in analytical form. This is done for the above problems.