共查询到20条相似文献，搜索用时 15 毫秒
1.
The minimum-propellant deterministic guidance law for bounded-thrust, constant jetexhaust velocity, spacecrafts is developed using the neighboring extremal theory. Minimization of the first-order variation in cost between a multi-burn nominal extremal and the perturbed trajectory eliminates all correction strategies except small changes in the nominal thrust-on, thrust-off times and small rotations of the thrust vector. Optimal values of these corrective controls for fixed values of initial state deviations, x
0, are found by minimizing the second variation in cost subject to the variational state and adjoint equations — an accessory minimum problem. The solution takes the linear feedback form u=A
–1
22
A
21x
0, where the matricesA
22 andA
21 are functions only of transition matrices calculated along the nominal trajectory. The solution is applied to a three-burn Earth-Mars transfer. 相似文献
2.
An indirect optimization procedure is applied to find the mission opportunities for a manned or round-trip mission to Mars. Both the conjunction-class and opposition-class high-thrust trajectories are considered, taking into account simple legs (with only departure and arrival impulses), three-impulse legs (departure, midcourse and arrival impulses) and flyby legs, where the non-propelled flyby of the planet Venus is used instead of the midcourse impulse to reduce the propellant consumption. The absolute positions of all the relevant planets repeat almost perfectly after 32 years: therefore, only the mission opportunities in a 32-year syzygistic cycle are analyzed. The two-body problem formulation is sufficient for preliminary analyses of interplanetary missions and the trajectory is approximated by heliocentric conic orbits passing through the centres of the planets. The mission opportunities correspond to the local minima of the characteristic velocity, that is, the sum of the actual velocity changes obtained by expending the propellant. Numerical results are presented to show that the same mathematical approach can be applied to different classes of missions, to emphasize the indications suggested by Pontryagin's Maximum Principle, to point out some periodicities in the solutions and to discuss the problem of providing initial guesses at the solutions. 相似文献
3.
A new approach is presented for the problem of planar optimal impulsive rendezvous of a spacecraft in an inertial frame near
a circular orbit in a Newtonian gravitational field. The total characteristic velocity to be minimized is replaced by a related
characteristic-value function and this related optimization problem can be solved in closed form. The solution of this problem
is shown to approach the solution of the original problem in the limit as the boundary conditions approach those of a circular
orbit. Using a form of primer-vector theory the problem is formulated in a way that leads to relatively easy calculation of
the optimal velocity increments. A certain vector that can easily be calculated from the boundary conditions determines the
number of impulses required for solution of the optimization problem and also is useful in the computation of these velocity
increments. Necessary and sufficient conditions for boundary conditions to require exactly three nonsingular non-degenerate
impulses for solution of the related optimal rendezvous problem, and a means of calculating these velocity increments are
presented. A simple example of a three-impulse rendezvous problem is solved and the resulting trajectory is depicted. Optimal
non-degenerate nonsingular two-impulse rendezvous for the related problem is found to consist of four categories of solutions
depending on the four ways the primer vector locus intersects the unit circle. Necessary and sufficient conditions for each
category of solutions are presented. The region of the boundary values that admit each category of solutions of the related
problem are found, and in each case a closed-form solution of the optimal velocity increments is presented. Similar results
are presented for the simpler optimal rendezvous that require only one-impulse. For brevity degenerate and singular solutions
are not discussed in detail, but should be presented in a following study. Although this approach is thought to provide simpler
computations than existing methods, its main contribution may be in establishing a new approach to the more general problem. 相似文献
4.
Bruce A. Conway Christian M. Chilan Bradley J. Wall 《Celestial Mechanics and Dynamical Astronomy》2007,97(2):73-86
The space mission planning process is considered as a hybrid optimal control problem. Hybrid optimal control problems are
problems that include categorical variables in the problem formulation. For example, an interplanetary trajectory may consist
of a sequence of low thrust arcs, impulses and planetary flybys. However, for each choice of the structure of the mission,
for example, for a particular choice of the number of planetary flybys to be used, there is a corresponding optimal trajectory.
It is not a priori clear which structure will yield the most efficient mission. In this work we present a mathematical framework
for describing such problems and solution methods for the hybrid optimal control problem based on evolutionary principles
that have the potential for being a robust solver of such problems. As an example, the methods are used to find the optimal
choice of three asteroids to visit in sequence, out of a set of eight candidate asteroids, in order to minimize the fuel required. 相似文献
5.
A strategy is formulated to design optimal time-fixed impulsive transfers between three-dimensional libration-point orbits in the vicinity of the interiorL
1 libration point of the Sun-Earth/Moon barycenter system. The adjoint equation in terms of rotating coordinates in the elliptic restricted three-body problem is shown to be of a distinctly different form from that obtained in the analysis of trajectories in the two-body problem. Also, the necessary conditions for a time-fixed two-impulse transfer to be optimal are stated in terms of the primer vector. Primer vector theory is then extended to non-optimal impulsive trajectories in order to establish a criterion whereby the addition of an interior impulse reduces total fuel expenditure. The necessary conditions for the local optimality of a transfer containing additional impulses are satisfied by requiring continuity of the Hamiltonian and the derivative of the primer vector at all interior impulses. Determination of the location, orientation, and magnitude of each additional impulse is accomplished by the unconstrained minimization of the cost function using a multivariable search method. Results indicate that substantial savings in fuel can be achieved by the addition of interior impulsive maneuvers on transfers between libration-point orbits.An earlier version was presented as Paper AAS 92–126 at the AAS/AIAA Spaceflight Mechanics Meeting, Colorado Springs, Colorado, February 24–26, 1992. 相似文献
6.
M. Sabatini D. Izzo G. B. Palmerini 《Celestial Mechanics and Dynamical Astronomy》2009,105(1-3):141-157
Large ΔV amounts are often required to maintain the relative geometry which is needed to implement a formation flying concept. A wise use of the orbital environment makes the orbit keeping phase easier, reducing the overall propellant consumption. A first important step in this direction is the selection of formation configurations and orbits which, while still satisfying the mission requirements, are less subject to perturbations resulting naturally in closed relative motion. Within this frame, a number of studies have been recently carried out in order to identify possible sets of invariant relative orbits under the effects of the Earth oblateness, a conservative force commonly referred to as J2 which is also the most important perturbation for Low Earth Orbit. These efforts clearly marked the difficulties connected with achieving genuine periodic relative motion under J2 effect, but they also showed the existence of a set of conditions on the orbital parameters which allow for quasi-periodic J2 trajectories. This paper presents these particular trajectories, by means of deeper theoretical explanations, showing the dependency of the shape of the relative configurations on the orbital inclination. Since the quasi-periodic trajectories cannot be written analytically, and moreover, they are very sensitive with respect to the initial conditions, difficulties arise when trying to exploit these paths as reference for the control of a formation. This paper proposes a novel approach to find, from the actual quasi periodic natural trajectories, minimal control periodic reference trajectories. Next, it evaluates quantitatively the amount of propellant which is needed to control a spacecraft formation along these paths. The choice of Hill’s classical circular projected configuration as a nominal trajectory is considered as a comparison, showing the clear advantages of the proposed guidance design, which assumes low-perturbed periodic reference orbits as nominal trajectories. 相似文献
7.
M. Vetrisano W. Van der Weg M. Vasile 《Celestial Mechanics and Dynamical Astronomy》2012,114(1-2):25-53
This paper presents a navigation strategy to fly to the Moon along a Weak Stability Boundary transfer trajectory. A particular strategy is devised to ensure capture into an uncontrolled relatively stable orbit at the Moon. Both uncertainty in the orbit determination process and in the control of the thrust vector are included in the navigation analysis. The orbit determination process is based on the definition of an optimal filtering technique that is able to meet accuracy requirements at an acceptable computational cost. Three sequential filtering techniques are analysed: an extended Kalman filter, an unscented Kalman filter and a Kalman filter based on high order expansions. The analysis shows that only the unscented Kalman filter meets the accuracy requirements at an acceptable computational cost. This paper demonstrates lunar weak capture for all trajectories within a capture corridor defined by all the trajectories in the neighbourhood of the nominal one, in state space. A minimum Δv strategy is presented to extend the lifetime of the spacecraft around the Moon. The orbit determination and navigation strategies are applied to the case of the European Student Moon Orbiter. 相似文献
8.
Andrzej J. Maciejewski Maria Przybylska Wojciech Szumiński 《Celestial Mechanics and Dynamical Astronomy》2017,127(2):163-184
In this paper we show that the anisotropic Kepler problem is dynamically equivalent to a system of two point masses which move in perpendicular lines (or planes) and interact according to Newton’s law of universal gravitation. Moreover, we prove that generalised version of anisotropic Kepler problem as well as anisotropic two centres problem are non-integrable. This was achieved thanks to investigation of differential Galois groups of variational equations along certain particular solutions. Properties of these groups yield very strong necessary integrability conditions. 相似文献
9.
This paper discusses the Rayleigh-Taylor (RT) instability of an infinitely conducting medium having an exponential density distribution which includes the effects of finite ion Larmor-radius (FLR) corrections and suspended particles in the presence of a uniform horizontal magnetic field. The relevant equations of the problem are linearized and from the linearized perturbation equations a dispersion relation is obtained, using appropriate boundary conditions. It has been found that the criterion for the stable density stratification remains uninfluenced by the simultaneous inclusion of the FLR corrections and suspended particles. The stability of the medium has been proved for the case of stable stratification when the FLR corrections are not considered in the analysis. The growth rate of unstable RT modes with increasing relaxation frequency of the suspended particles is evaluated analytically. It has been shown that the presence of suspended particles in the medium suppresses the growth rate of the unstable RT modes, thereby implying a stabilizing influence of the particles on the considered configuration. 相似文献
10.
H. J. Peng Q. Gao Z. G. Wu W. X. Zhong 《Celestial Mechanics and Dynamical Astronomy》2011,110(4):319-342
In this paper, from a Hamiltonian point of view, the nonlinear optimal control problems are transformed into nonlinear two-point
boundary value problems, and a symplectic adaptive algorithm based on the dual variational principle is proposed for solving
the nonlinear two-point boundary value problem. The state and the costate variables within a time interval are approximated
by using the Lagrange polynomial and the costate variables at two ends of the time interval are taken as independent variables.
Then, based on the dual variational principle, the nonlinear two-point boundary value problems are replaced by a system of
nonlinear equations which can preserve the symplectic structure of the nonlinear optimal control problem. Furthermore, the
computational efficiency of the proposed symplectic algorithm is improved by using the adaptive multi-level iteration idea.
The performance of the proposed algorithm is tested by the problems of Astrodynamics, such as the optimal orbital rendezvous
problem and the optimal orbit transfer between halo orbits. 相似文献
11.
The effect of Hall currents and collision with neutrals on the instability of a horizontal layer of a self-gravitating partially-ionized plasma of varying density have been studied. It is assumed that the plasma is permeated by a variable horizontal magnetic field stratified vertically. A variational principle is shown to characterize the problem. By making use of the existence of the variational principle, proper solutions have been obtained for a semi-infinite plasma in which density has a one-dimensional (exponential) vertical stratification. The dispersion relation has been derived and solved numerically. It is found that the collisions with neutrals have a stabilizing influence while Hall currents have a destabilizing influence. 相似文献
12.
Lawden’s primer vector theory gives a set of necessary conditions that characterize the optimality of a transfer orbit, defined accordingly to the possibility of adding mid-course corrections. In this paper a novel approach is proposed where, through a polar coordinates transformation, the primer vector components decouple. Furthermore, the case when transfer, departure and arrival orbits are coplanar is analyzed using a Hamiltonian approach. This procedure leads to approximate analytic solutions for the in-plane components of the primer vector. Moreover, the solution for the circular transfer case is proven to be the Hill’s solution. The novel procedure reduces the mathematical and computational complexity of the original case study. It is shown that the primer vector is independent of the semi-major axis of the transfer orbit. The case with a fixed transfer trajectory and variable initial and final thrust impulses is studied. The acquired related optimality maps are presented and analyzed and they express the likelihood of a set of trajectories to be optimal. Furthermore, it is presented which kind of requirements have to be fulfilled by a set of departure and arrival orbits to have the same profile of primer vector. 相似文献
13.
The condition of hydrostatic equilibrium of relativistic stellar models is formulated as an optimal control problem. Application
of Pontryagin's maximum principle leads directly to the Tolman-Oppenheimer-Volkoff equation.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
14.
A solution to the fixed-time minimum-fuel two-impulse rendezvous problem for the general non-coplanar elliptical orbits is
provided. The optimal transfer orbit is obtained using the constrained multiple-revolution Lambert solution. Constraints consist
of lower bound for perigee altitude and upper bound for apogee altitude. The optimal time-free two-impulse transfer problem
between two fixed endpoints implies finding the roots of an eighth order polynomial, which is done using a numerical iterative
technique. The set of feasible solutions is determined by using the constraints conditions to solve for the short-path and
long-path orbits semimajor axis ranges. Then, by comparing the optimal time-free solution with the feasible solutions, the
optimal semimajor axis for the two fixed-endpoints transfer is identified. Based on the proposed solution procedure for the
optimal two fixed-endpoints transfer, a contour of the minimum cost for different initial and final coasting parameters is
obtained. Finally, a numerical optimization algorithm (e.g., evolutionary algorithm) can be used to solve this global minimization
problem. A numerical example is provided to show how to apply the proposed technique. 相似文献
15.
Nonradial oscillations of a partially degenerate standard model, approximating a class of low-mass stars, have been studied in the presence of a weak poloidal magnetic field. The magnetic field in the interior of the configuration is taken to be continuous across the equilibrium surface and is matched with an external dipole field. Using a variational formulation, corrections to the oscillation frequencies of the Kelvin mode have been found for different values of the central degeneracy. It has been noted that the effect of the magnetic field is to increase the frequency of nonradial (l=2) mode of pulsation. 相似文献
16.
David Clarke Gerry Deighan Gillian Fry Susan Goodsir Donald Macleod 《Astrophysics and Space Science》1996,239(2):229-235
Experiments are described which demonstrate that the dead-time constant associated with a photon counting stellar photometer/polarimeter is readily determinable by the application of the Malus law. It is also proposed that corrections for dead-time losses should be applied by an iteration technique to the exact equation rather than using the available approximation formulae. 相似文献
17.
The equilibrium-configurations of the Magnetic-Binary problem are investigated in the case of equatorial motion. The law of this constrained motion is derived and then the procedure for localizing the equilibrium points is developed. The type of equilibrium is also studied by means of the known method of variational equations. 相似文献
18.
Station-keeping for a translunar communication station 总被引：1，自引：0，他引：1
John V. Breakwell Ahmed A. Kamel Martin J. Ratner 《Celestial Mechanics and Dynamical Astronomy》1974,10(3):357-373
A translunar communication station is to be kept close to a nominal unstable periodic ‘Halo’ orbit, visible at all times from Earth. The analytically computed nominal orbit is not perfect, requiring an average control acceleration of about 10?6 g's for tight control. An adjustable quadratic combination of position deviation and control acceleration is minimized to provide an (adjustable) control law with period feedback gains and a periodic bias. The average control acceleration can be reduced to less than 10?8 g's with an error settling time of less than 21/2 months. The resulting limiting motion provides, in turn, an improved nominal, permitting the same low control cost with much tighter control, corresponding to settling times of the order of one day. 相似文献
19.
The motion of a particle about a non-rotating 2nd degree and order-gravity field is investigated. Averaging conditions are applied to the particle motion and a qualitative analysis which reveals the general character of motion in this system is given. It is shown that the orbit plane will either be stationary or precess about the body's axis of minimum or maximum moment of inertia. It is also shown that the secular equations for this system can be integrated in terms of trigonometric, hyperbolic or elliptic functions. The explicit solutions are derived in all cases of interest.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
20.
《Planetary and Space Science》2007,55(14):2192-2202
Nonlinear propagating dust-acoustic solitary waves (DASWs) in a warm magnetized dusty plasma containing different size and mass negatively charged dust particles, isothermal electrons, high- and low-temperature ions are investigated. For this purpose, a reasonable normalization of the hydrodynamic and Poisson equations is used to derive the Zakharov–Kuznetsov (ZK) equation for the first-order perturbed potential. As the wave amplitude increases, the width and the velocity of the solitons deviate from the prediction of the ZK equation, i.e., the breakdown of the ZK approximation. To describe the soliton of larger amplitude, a linear inhomogeneous Zakharov-Kuznetsov-type (ZK-type) equation for the second-order perturbed potential is derived. Stationary solutions of both equations are obtained using the renormalization method. Numerically, the effect of power law distribution on the higher-order corrections is examined. It is found that the soliton amplitude in case of power law distribution is smaller than that of monosized dust grains. The higher-order corrections play a role to reduce the strength of the nonlinearity for power law distribution case. The relevance of the present investigation to Saturn's F-ring and laboratory experiment is discussed. 相似文献