Evaluation of geopotential and luni-solar perturbations by a recursive algorithm

The disturbing functions due to the geopotential and Luni-solar attractions are linear and bilinear forms in spherical harmonics. Making use of recurrence relations for the solid spherical harmonics and their derivatives, recurrence formulas are obtained for high degree terms as function of lower degree for any term of those disturbing functions and their derivative with respect to any element. The equations obtained are effective when a numerical integration of the equations of motion is appropriate. In analytical theories, they provide a fast way of obtaining high degree terms starting from initial very simple functions

The equations of motion of an artificial satellite in nonsingular variables

The equations of motion of an artificial satellite are given in nonsingular variables. Any term in the geopotential is considered as well as luni-solar perturbations up to an arbitrary power of r/r prime; r prime being the geocentric distance of the disturbing body. Resonances with tesseral harmonics and with the moon or sun are also considered. By neglecting the shadow effect, the disturbing function for solar radiation is also developed in nonsingular variables for the long periodic perturbations. Formulas are developed for implementation of the theory in actual computations

Use of altimetry data in a sampling-function approach to the geoid

Problems associated with using an altimetry sampling function approach to the geoid are examined. They include: (1) conventent mathematical representation of short-wavelength (eventually approximately 1 deg) features of the geoid or geopotential, (2) utilization of detailed data from only part of the globe (i.e., the oceans) (3) application of appropriate formalism to relate the sea-level equipotential below the atmospheric mass to the external potential above the atmosphere, (4) mathematical applicability of an adopted geopotential representation on the surface of the physical geoid

Notes on von zeipel's method

Canonical problems and von zeipel method - theory and applicatio

Possible geopotential improvement from satellite altimetry

Possible geopotential improvement from satellite altimetr

The motion of a satellite of the moon

Analytical solution for motion of lunar orbital satellit

Quantum Averaging I: Poincar\'e--von Zeipel is Rayleigh--Schr\"odinger

An exact analogue of the method of averaging in classical mechanics is constructed for self--adjoint operators. It is shown to be completely equivalent to the usual Rayleigh--Schr\"odinger perturbation theory but gives the sums over intermediate states in closed form expressions. The anharmonic oscillator and the Henon--Heiles system are treated as examples to illustrate the quantum averaging method.Comment: 12 pages, LaTeX, to appear in Journ. Phys.

Notes on Newton-Euler formulation of robotic manipulators

The equations corresponding to Newton-Euler iterative method for the determination of forces and moments acting on the rigid links of a robotic manipulator are given a new treatment using composed vectors for the representation of both kinematical and dynamical quantities. It is shown that Lagrange equations for the motion of a holonomic system are easily found from the composed vectors defined in this note. Application to a simple model of an industrial robot shows that the method developed in these notes is efficient in solving the dynamics of a robotic manipulator. An example is developed, where it is seen that with the application of appropriate control moments applied to each arm of the robot, starting from a given initial position, it is possible to reach equilibrium in a final pre-assigned position