simplifies
465-479
appropriate singular arc
strong variations
variation
orbit rendezvous problem
maximum
neighboring singular arc
optimal trajectories
neighborhood
neighboring
fuel expenditure
higher-order cost
unsymmetrical version
four
initial state displacement
coast
1975-12
order 5/2
period
cost
Fuller's problem
analysis
singular control component
midcourse guidance
Minimum-fuel rocket trajectories involving intermediate-thrust arcs
field of neighboring
terminal short period
final conditions
thrust acceleration magnitude
expenditure
minimization
minimumfuel orbit rendezvous problem
addition
article
short period
junction simplifies
state vector
magnitude
https://scigraph.springernature.com/explorer/license/
singular trajectories
second-variation analysis
trajectories
singular arcs
guidance
https://doi.org/10.1007/bf00932784
identification
rendezvous
dimension four
en
space
infinite number
rocket trajectories
state space
acceleration magnitude
1975-12-01
suitable Jacobi condition
Jacobi condition
conditions
intermediate-thrust arcs
dimensions
junctions
state displacements
six-dimensional state vector
rendezvous problem
vector
acceleration
components
control components
version
problem
Minimum-fuel rocket trajectories
thrust
displacement
specific impulse
impulses
number
switch
false
cases
unbounded thrust
articles
field
solution
arc
optimal intermediate-thrust arc
The optimal trajectories in the neighborhood of an optimal intermediate-thrust arc are investigated for the minimumfuel orbit rendezvous problem with fixed specific impulse. Since such an arc is singular, the thrust acceleration magnitude being the singular control component, a second-variation analysis leads to the identification of a field of neighboring, singular arcs in a state space of dimension four rather than six, provided that a suitable Jacobi condition is met. A given neighboring initial six-dimensional state vector does not generally lie on a neighboring singular arc, and junction onto the appropriate singular arc must be accomplished by a short period of strong variations in the acceleration. This contributes an addition to the fuel expenditure which is of order 5/2 rather than 2 in the initial state displacement. The minimization of this higher-order cost, in the case of bounded acceleration, leads to an unsymmetrical version of Fuller's problem, whose solution requires an infinite number of switches between maximum and zero thrust during the short period. For unbounded thrust, the junction simplifies to either coast-impulse-singular trajectories or impulse-coast-impulse-singular trajectories. The neighboring singular arc meets the final condition in 4 dimensions, rather than 6 dimensions, and rendezvous must be completed by another, terminal short period of strong variations in the acceleration. Implications for midcourse guidance near a singular arc are discussed.
implications
2022-01-01T18:01
Stanford University, Stanford, California
Stanford University, Stanford, California
Journal of Optimization Theory and Applications
0022-3239
Springer Nature
1573-2878
5-6
J. F.
Dixon
Applied Mathematics
J. V.
Breakwell
Jet Propulsion Laboratory, Pasadena, California
Jet Propulsion Laboratory, Pasadena, California
Springer Nature - SN SciGraph project
10.1007/bf00932784
doi
Engineering
17
pub.1000224929
dimensions_id
Numerical and Computational Mathematics
Electrical and Electronic Engineering
Mathematical Sciences