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Necessary conditions for optimal fixed-time powered transfers with multiple coasts and thrusts between circular orbits
Time function analysis for optimal control of satellite attitude and control jet fuel consumption in circular orbits
Necessary conditions for optimal fixed-time powered transfers with multiple coasts and thrusts between circular orbits
The minimum velocity-change rendezvous solutions, when the motion may be linearized about a circular orbit, fall into two separate regions; the phase-for-free region and the general region. Phase-for-free solutions are derived from the optimum transfer solutions, require the same velocity-change expenditure, but may not be unique. Analytic solutions are presented in two of the three subregions. An algorithm is presented for determining the unique solutions in the general region. Various sources of initial conditions are discussed and three examples are presented.
By means of simple geometric construction compact expressions for the maximum and minimum eclipse durations of a circular orbit, whose semimajor axis and inclination are specified, can be obtained. The method outlined in this note provides the designer with the necessary envelope of eclipse durations that a spacecraft will experience throughout its lifetime, and, therefore, provides a quick method of estimating necessary thermal constraints. Moreover, the closed form method presented eliminates the need for extensive machine time expenditure previously required for this type of analysis. Some numerical data to aid in the design of the spacecraft is provided.
A closed form solution is presented for the coplanar transfer between nearby circular orbits for spacecraft using their own blow down propulsion system. The decaying thrust is applied along the local horizontal and the linearized equation of motion in the orbital elements formulation are used to describe the transfer which consists of a thrust-coast-relight program. Sensitivity partials are also presented analytically in order to study the effect of maneuver execution errors and various other parameters affecting the blow down propulsion system characteristics on the transfer. This strategy is applied to study the transfer of the TOPEX spacecraft from the Shuttle parking orbit to its final operational orbit.
Refinements for 150 and 190 n.mi. circular target orbits were examined along with the potential advantages of ground-hold as a means of reducing the phasing times associated with low orbit rendezvous.
Determination of optimum 3-dimensional trajectories to inject a saturn c-5 rocket into a space-fixed circular orbit
Simple control reference as aid to thrust axis orientation during ascent of lunar module from lunar surface to circular orbit and rendezvous with command and service module
A simple solution has been developed for the long term behavior of a near-circular orbit in a zonal gravity field. The solution is obtained by linearizing the singly averaged variational equations of motion and eliminating a degree of freedom with an integral of motion. The resulting solution is expressed in semiequinoctial elements (h and k), and has either an exponential or periodic form. The type of solution is dependent upon a stability factor determined by the inclination and the values of the gravity field coefficients. Frozen orbits correspond to the equilibrium solutions of the set of simplified variational equations. An approximate expression for the location of these orbits has been developed and can be useful for certain mission design applications.
Analytic solution for minumum impulse transfer between two neighboring low eccentricity orbits
A method is presented for devising a covariance matrix that either remains constant or grows in keeping with the presence of a period error in a rotating local-vertical coordinate system. The solution presented may prove useful in the initialization of simulation covariance matrices for near-circular-orbit problems. Use is made of the Clohessy-Wiltshire equations and the travelling-ellipse formulation.
Analytic solution obtained for minimum impulse transfer between two neighboring low eccentricity orbits
A nonlinear analysis is carried out for the optimal transfer between close near-circular noncoplanar orbits with no limit on time. The degeneracy of the linear analyses of Marec and Edelbaum is, thereby, removed and with the aid of a generalized Jacobi test, it is established that the minimum-impulse transfer requires, at most, three impulses. A field of extremals is generated in an orbit element space starting with the initial state and anticipated adjoint variables and integrating these variables by using the optimal thrust control law that maximizes the variational Hamiltonian. The nonoptimality of any four-impulse strategy is determined numerically by observing the reflection of every extremal from either an envelope (conjugate point test) or a switching surface on or before the application of the fourth impulse. This test is carried out in Regions I, II, and III of Marec, as well as the special transition region of Breakwell near the boundary of Region III.
Aerodynamic and gravity gradient torque effects on attitude control of Apollo/S-4B configuration in circular earth orbit
Differential equations of motion of spacecraft in planetocentric orbit solved cylindrical shell coordinate system
First-order perturbation solution to problem of minimum-fuel orbit transfer in form of equal slope guidance constraint
Attitude continuous instability regions in parameter space and resonance frequency of spinning unsymmetrical satellite noting periodic processes